A wave motion is a means of transferring energy and momentum from one point to another without any actual transportation of matter between these points. In wave motion, disturbance travels through some medium but medium does not travel along with the disturbance. For propagation of wave, medium must possess two essential property viz. inertia and elasticity. Disturbance produced at one point is communicated to the adjoining particle which also start vibrating simple harmonically about their mean positions. Hence the wave motion travels on and on. Wave motion is categorised as longitudinal and transverse on the basis of mode of vibration of particles of medium.
(i) What are elastic waves?
(ii) Explain two types of wave motion.
(iii) Mention the characteristic of medium in which longitudinal and transverse waves propagate.
(iv) What are compression and rarefaction in a longitudinal wave propagation?
(v) Why are longitudinal waves called pressure waves?
(vi) What type of waves are the sound and the light waves?
(vii) An explosion occurs inside a lake. What type of waves are produced inside the water?

Sound travels through a gas in the form of compressions and rarefactions. Newton assumed that the changes in pressure and volume of gas, when sound waves are propagated through it, are isothermal. The amount of heat produced during compression, is lost to the surrounding and similarly the amount of heat lost during rarefaction is gained from the surroundings. So as to keep the isothermal elasticity. Laplace, a french mathematician pointed out that Newton's assumption was wrong. According to Laplace, the changes in pressure and volume of a gas, when sound waves propagated through it, are not isothermal but adiabatic.
(i) Write the Newton's formula for velocity of sound in gases and Laplace correction in it.
(ii) What is the effect of pressure on velocity of sound in gases?
(iii) Find the ratio of velocity of sound in Hydrogen and Oxygen.
(iv) Define temperature coefficient of velocity of sound in air.
(v) What is effect of humidity on the speed of sound in air?
(vi) Explain why propagation of sound in air is an adiabatic process?
(vii) If tension of a wire is increased to four times, how is the wave speed changed?

The principle of super position of waves enables us to determine the net waveform when any number of individual waveforms overlap. The net displacement at a given time is the algebraic sum of the displacements due to each wave at that time. When two sets of progressive wave trains of the same type having the same amplitude and same time period travelling with the same speed along the same straight line in opposite directions superimpose a new set of waves are formed. These are called strationary waves or standing waves. The resultant waves do not propagate in any direction, nor there is any transfer of energy in the medium. In stationary waves, there are nodes and anti nodes point where particles are at rest and have largest amplitude respectively.
(i) How amplitude of vibration vary in stationary wave?
(ii) What is energy of stationary wave?
(iii) What is distance between consecutive node, antinode and between node and antinode?
(iv) What is phase difference between particles vibrating in a segment of stationary wave and between adjoining segments?
(v) Why is a stationary wave so named?
(vi) Where will a person hear maximum sound, at node or antinode?
(vii) Name the type of stationary wave produced by an organ pipe, open at both ends.

When two sound waves of-nearly same frequency and amplitudes travelling in a medium along the same direction, super-impose on each other, then the intensity of the resultant sound at a particular position rises and falls alternately with time. This phenomenon is known as beat. if intensity of sound is maximum at time t = 0, one beat is said to be formed when intensity becomes maximum again, after becoming minimum once in between. The time interval between two successive beats is called beat period. The number of beats produced per second is called beat frequency.
(i) Two sound waves of frequency v₁ and v₂ superimpose to form beats. What is the beat frequency?
(ii) What should be the difference in frequency of two sound waves to form beats? Give reason
(iii) Write two applications of the phenomenon of beats.
(iv) Two sounds of very close fequencies, say 256 Hz and 260 Hz are produced simultaneously. What is the frequency of resultant sound and also write the number of beats heard in one second?
(v) A sitar wire and a tabla, when sounded together, produce 5 beats per second. What can be concluded from this? If the tabla membrane is tightened will the beat rate increase or decrease?
(vi) A tuning fork of unknown frequency gives 4 beats with a tuning fork of frequency 310 Hz. It gives the same number of beats on filing. Find the unknown frequency.

Whenever there is a relative motion between the source of sound, the observer and the medium, the frequency of sound as received by the observer is different from the frequency of sound emitted by the source. For example to a man standing on a railway platform, when a train blowing its whistle, approaches him, the pitch of the whistle appears to rise and it suddenly appears to drop as the engine moves away from him. Similar effect is observed when the source is at rest and observer moves towards or away from the source. This phenomenon is noticeable only when the relative velocity between the source and the observer is an appreciable fraction of the wave velocity.
(i) Name the phenomenon observed in the passage. Define it.
(ii) On what factors does the apparent frequency of sound depends?
(iii) What physical change occurs when a source of sound moves and the listener is stationary?
(iv) What physical change occurs when the source of sound is stationary but the listener moves?
(v) A particle travelling with a speed of 0.9 of the speed of sound and is emitting radiations of frquency of 1 KHz and moving towards the observer. What is the apparent frequency of radiation?
(vi) Write the condition in doppler effect when apparent frequency of sound increases.
(vii) Write two applications of Doppler effect.

In our daily life, we come across various types of motions: such as periodic, non-periodic, oscillatory and non oscillatory. The study of oscillatory motion is of great importance as its concepts are required for the understanding of many physical phenomena, for example
(i) vibrating strings produces pleasant. sounds in musical instruments like the sitar, guitar or the violin
(ii) the oscillations of the atoms in solid about their mean positions to convey the sensation of temperature.
All oscillatory motions are periodic motions but all periodic motion may not be oscillatory. An oscillatory motion is further classified as harmonic and non-harmonic oscillation.
(i) What are oscillatory motions? Give example.
(ii) Give example of periodic motion which are not oscillatory.
(iii) Differentiate between harmonic and non-harmonic oscillations.
(iv) What causes a system to oscillate?
(v) On what factor does the time period of a simple harmonic oscillator depends?
(vi) What are periodic functions? Express one graphically.

Simple harmonic motion is a special type of periodic motion, in which a particle moves to and fro repeatedly about a mean position under a restoring force, which is always directed towards the mean position and whose magnitude at any instant is directly proportional to the displacement of the particle from the mean position at that instant i.e., Fresloring =-Kx, where K is force constant and x - the displacement of the particle executing S.H.M. It can be expressed in terms of one simple harmonic function x = a sin \(\left(\omega t+\phi_{0}\right)\) 0)' where a - is the amplitude of oscillation and \(\left(\omega t+\phi_{0}\right)\) is the phase of vibrating particle at the instant t, \(\phi_{0}\) is initial phase and co is the angular frequency of the vibrating particle in S.H.M.
(i) Give geometrical interpretation of S.H.M.
(ii) Express the velocity and acceleration of S.H.M in terms of displacement and angular frequency \((\omega)\).
(iii) State the condition when S.H.M particle velocity is in phase and opposite in phase with the acceleration of particle.
(iv) What is the average value of total energy of a particle in S.H.M in one complete oscillation?
(v) What is the frequency of P.E, K.E and total energy in S.H.M?
(vi) What will be the time period of second's pendulum if its length is doubled?
(vii) The girl sitting on a swing stands up. What will be the effect on the periodic time of the swing?

Consider two springs of spring constants K_J and K₂ . Let there be three spring combinations as shown in fig (a), (b), and (c). A body of mass rn oscillates about its mean position under influence of restoring force (F) produced when displaced from the equilibrium position of the body.


(i) Determine the net restoring force and spring constant of the combination of spring in fig (a) for a displacement of y in mass from mean position.
(ii) Determine the spring constant of combination of spring in fig (b) and also the restoring force produced when displaced from mean position.
(iii) Determine the spring constant of combination of spring in fig (c) an,d also the restoring force produced when displaced from mean position.
(iv) Determine the frequency of oscillation in each of combination.

A body capable of oscillating S.H.M when displaced from mean position start oscillating. During oscillation amplitude of oscillating body may either vary or remain constant. It is categorised as undamped, damped and free or forced vibraton depending on whether there is some resistive force present in the medium where body is oscillating or not and also if the body under the influence of some external force or not. Amplitude of oscillation is function of resistive force of the medium, external periodic force and phase difference between external force and oscillating body.
(i) What are undamped simple harmonic oscillations?
(ii) Define damped oscillations. Give example.
(iii) What are free oscillations? On what factor does the natural frequency of an oscillating system depends?
(iv) What are forced oscillations?
(v) Give an example of forced oscillation.
(vi) What are resonant oscillations? Give example.
(vii) Is the damping force, constant on a system executing S.H.M?

A 2 kg block hangs without vibrating at the bottom end of a spring with a force constant of 800 N/m. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of 10 ms^-2. When the acceleration suddenly ceases at time t = 0, the car moves upward with constant speed. (g = 10 ms^-2 )
(i) What is the angular frequency of oscillation of the block if their acceleration' ceases?
(ii) Determine the amplitude of the oscillation.
(iii) Determine the initial phase angle observed by a rider in the elevator, taking downward direction to be positive.
(iv) A particle starts oscillating from half the amplitude position. What is its initial phase?
(v) A simple harmonic motion of amplitude A, has a time period T. What will be the acceleration of the oscillator when its displacement is half of the amplitude?

The Kinetic theory was developed by Maxwell and Boltzmann to explain the behaviour of gases based on the idea that gases consist of rapidly moving atoms or molecules. The inter atomic forces binding the atoms are negligible and their size is. negligible. The theory is consistent with various gas laws and Avogadro's hypothesis. It gives molecular interpretation oftemperature pressure. Specific heat capacities. Compared to solids and liquids, it is easier to understand the properties of gases. This is because molecules in gases are far apart.
(i) Write the characteristics of ideal gas. Write the conditions at which real gases acquire ideal gas behaviour.
(ii) State Avogadro's hypothesis? What is Avogadro number?
(iii) Write the perfect gas equation by explaining Boyle's law and Charles's law.
(iv) What is meant by Boltzmann constant? Calculate its value in S.I units.
(v) The graph shows the variation of the product PV w.r.t the pressure P of given masses of three gases, A, Band C. The temperature is kept constant. State with proper arguments which of these gases is ideal.

The molecules of a gas move in all directions with various speeds. The speeds of the molecules of a gas increase with rise in temperature. During its random motion, a fast molecule of ten strikes against the walls of the container of the gas. The collisions are assumed to be prefectly elastic i.e., the molecule bounces back with the same speed with which it strikes the wall. Since the number of molecules is very large, billions of molecules strike against the walls of the container every second. These molecules exert force on the wall. The force exerted per unit area is the pressure exerted by the gas on the walls. According to the kinetic theory, the pressure of a gas of density p at absolute temperature T is given by \(P=\frac{1}{3} \rho\) \(v_{r m s}^{2}, \) where v_rms is the root mean square speed of the gas molecule and is given by \(v_{r m s}=\sqrt{\frac{3 K_{B} T}{M}}\) where M is the mass of a molecule and KB is Boltzmann constant.
(i) State the relation between pressure and kinetic energy of the gas.
(ii) On what factors does the average kinetic energy of translation per molecule of the gas depends?
(iii) State absolute zero temperature in terms of root mean square velocity of gas.
(iv) Define root mean square speed and establish its relation with temperature.
(v) The absolute temperature of a gas is made four times. How many times will its total kinetic energy pressure and r.m.s velocity become?
(vi) Two different gases have exactly the same temperature. Does this mean that their molecules have the same r.ms. speed?
(vii) On reducing the volume of the gas at constant temperature, the pressure of the gas increases. Explain on the basis of kinetic theory.

The number of degrees of freedom of a dynamical system is the total number of co-ordinates or independent quantites required to describe completely the position and configuration of the system. For a dynamical system, the number of degrees of freedom is obtained by subtracting the number of independent relations from the total number of co-ordinates required to specify the position of constituebnt particles of the system.
N = 3A - R, where N - number of degrees of freedom of the system.
A - number of particles in the system
R - number of independent relations among the particles.
Each degree of freedom contributes equally In the distribution of the energy associated with each molecule. In thermal equilibrium the energy associated with each molecule per degree of freedom is \(\frac{1}{2} K_{B} T\) .
(i) Determine the number of degrees of freedom of a non-linear triatomic molecule.
(ii) State law of equipartition of energy.
(iii) If a gas has n degrees of freedom, determine the ratio of principal specific heat of the gas.
(iv) Determine the energy contributed by a vibrational mode in total energy.
(v) Determine the ratio of specific heat for monoatomic gas molecule.

During their random motion, the molecules of a gas often come close to each other. Molecules are perfect elastic spheres and their size is very small compared to the distance between them. Gas molecules undergo elastic collision. Therefore, they cannot move straight unhindered. The paths of molecules keep on getting deflected incessantly. Path of a single gas molecule consists of a series of short zig zag paths of different lengths. These paths of different lengths are called free paths of the molecules and their mean is called mean free path. Mean free path of gas molecules depends on diameter (d) of gas molecule and molecular density (n) as follows \(\lambda=\frac{1}{n \pi d^{2}}\)
(i) Define mean free path of gas molecules.
(ii) On what factors do the mean free path of gas molecules depends?
(iii) What is significance of mean free path?
(iv) How many collisions per second does each molecule of a gas make, when the average speed of a molecule is 500 ms^-1 and mean free path is 2.66 x 10^{- 7} m?
(v) Calculate the mean free path of molecules, if number of molecules per cm³ is 3 x 10¹⁹ and diameter of each molecule is 2A.

A change in pressure and volume of a gas without any change in its temperature is called an isothermal change. In such a change, there is free exchange of heat between the gas and its surrounding. These changes are governed by Boyle's law i.e., PV = Constant. The change in pressure and volume of a gas when temperature also changes is called an adiabatic change. In such a change, no heat is allowed to enter into or escape from the gas. The equation of adiabatic changes \(P V^{\gamma}\) = constant or \(T V^{\gamma-1}\) constant or \(P^{1-\gamma} T^{\gamma}\) = constant, where \(\gamma\) - ratio of two principal specific heats of the gas = \(\frac{C_{P}}{C_{V}}\) .
(i) What are conditions for the changes to be isothermal and for adiabatic?
(ii) A gas is compressed isothermally to half its volume. By what factor does the pressure of the gas increase? 
Given \(\gamma\) = 1.4.
(iii) A gas is compressed adiabatically to half its volume. By what factor does the pressure of gas increases? 
Given \(\gamma\) = 1.4.
(iv) A gas is suddenly compressed to \(\frac{1}{4}\)th of its original 4 volume. Calculate the rise in temperature, when the original temperature is 27°C and  \(\gamma\) = 1.5.
(v) Draw PV variation diagram representing isothermal and adiabatic processes respectively.
(vi) Ice at 0 °C is converted into steam at 100°C. State the isothermal changes in this process

Thermodynamics is the study of transformation of heat into other forms of energy and vice-versa. Thermodynamical system is said to be in equilibrium when macroscopic variables like pressure, volume, temperature, mass, composition, etc. that characterise the system variables which are not necessarily independent. Some important thermodynamic processes are: isothermal, adiabatic, isobaric, and isochoric. A thermodynamic state is represented by equation of state that represents the connection between the state variables of a system.
(i) Which physical quantity determine the thermal equilibrium of a system? State zeroth law of thermodynamics.
(ii) What is quasi static process? What does it represent? 
(iii) What is equation of state? Write equation of state for adiabatic operation.
(iv) Determine the specific heat of gas during isothermal and adiabatic process.
(v) The volume of an ideal gas is Vat a pressure P. On increasing the pressure by \(\Delta \boldsymbol{P}\) , the change in volume of the gas is \(\Delta \boldsymbol{V}_{\mathbf{1}}\) under isothermal conditions and \(\Delta \boldsymbol{V}_{2}\) under adiabatic condition. Is \(\Delta V_{1}>\Delta V_{2}\) or vice versa and why?
(vi) An ideal gas at temperature T_1, undergoes expansion under adiabatic conditions, to attain temperature T_2. Write expression for workdone.

Every system (solid, liquid or gas) possess a certain amount of energy. This energy is called the internal energy and is consists of two parts
(i) Kinetic energy due to the motion (translation, rotational, and vibrational) of the molecules and
(ii) potential energy due to the configuration (separation) of the molecules. The internal energy of a homogeneous system depends on its thermodynamic state i.e., on its thermodynamic coordinates P, V, and T. Each definite state of the system possesses a definite quantity of internal energy. A change in the internal energy can occur only if a transfer of energy between the system and surrounding is permitted. This can take place if some work is performed on or by the system and some heat is absorbed or given out by the system.
(i) How temperature, pressure and volume of gas change in an isothermal process?
(ii) 200 J of work is done on a gas to reduce its volume by compressing it. If this change is done under adiabatic conditions. Find the change in internal energy of the gas and also the amount of heat absorbed by the gas?
(iii) In a given process on an ideal gas dW = 0 and dQ >0, then what change would occur in temperature and internal energy?
(iv) What are two different modes of changing state of a thermodynamic system?
(v) Write the sign convention regarding to change in heat content, internal energy change and work done over a thermodynamic system during a thermodynamic process.
(vi) What will be the change in internal energy during isothermal, adiabatic and cyclic process?

The first law of thermodynamics establishes the essential equivalence between work and heat, as according to this law, internal energy (and hence temperature) of a system can be increased either by supplying heat to it or by doing work on the system or both. However, this law has limitations as it does not indicate the direction in which the change can occur and gives no idea about the extent of change. Limitations of first law of thermodynamics is overcome by second law of thermodynamics expressed as Kelvin Planck statement and Clausius statement based on working of heat engine and refrigerator respectively.
(i) Write the relation between two principal specific heats of an ideal gas based on first law of thermodynamics.
(ii) Which fundamental law of conservation is represented by first law of thermodynamics?
(iii) State Kelvin Planck statement and Claus statement of second law of thermodynamics.
(iv) Define thermal efficiency of a heat engine.
(v) Define coefficient of performance of a refrigerator \(\text { ( } \beta \text { ) }\).State the relation between \(\eta \text { and } {\beta}\) .
(vi) Can a heat engine of 100% efficiency be designed? Explain.

A sample of2 kg of mono atomic helium is taken through the process ABC and another sample of 2 kg of the same gas is taken through the process ADC as shown in diagram. The molecular mass of Helium = 4 and R (gas constant) = 8.3 JK^-1 mol^-1.

(i) If number of moles of helium being 500, then Determine the temperature of State A.
(ii) What is isochoric process? Determine the temperature at state B.
(iii) What is isobaric process? Determine the temperature at state C and D.
(iv) Determine the work done in process ABC.

Heat is a form of energy which produces the sensation of warmth. It is total thermal energy of the body which is sum of kinetic energies of all the individual molecules of the body. It is transferred from one body to the other on account of temperature difference between two bodies. Joule found that when' mechanical work (W) is converted into heat (Q), then the ratio of Wand Q is always constant, represented by J i.e., Joule's mechanical equivalent of heat.
\(J=\frac{W}{Q} \text { or } W=J Q\) 
A measure of temperature is obtained using a thermometer that use Physical Properties which change uniformly with temperature, for example, in common liquid in glass thermometers, mercury, alcohol etc are used whose volume varies linearly with temperature over a wide range.
(i) Define temperature and its significance.
(ii) Define One calorie.
(iii) How does a thermometer work?
(iv) Name the two convenient fixed reference point for measuring temperature.
(v) How celsius temperature and Fahrenheit scale are related to each other?
(vi) What is absolute zero temperature?
(vii) What is Kelvin scale? How it is related with celsius scale?

When solid is heated, the amplitude of vibration of atoms and molecules increases. Therefore effective interatomic separation increases and cause thermal expansion. Thermal expansion of solids are of three types:
(i) Linear expansion
(ii) Area expansion
(iii) Volume expansion. Thermal expansion of liquid are of two kinds. Real expansion and apparent expansion that occurs in form of volume expansion. Thermal expansion of water is anomalous i.e., volume of given amount of water first decreases with increase in temperature from 0 °C to 4 °C and beyond 4 °C volume of water increases with rise of temperature. In thermal expansion of gases is more than solid and liquid but coefficient of volume expansion is dependent on temperature for gases.
(i) On what factors does the coefficient of thermal expansion depend? Write its S.I. unit.
(ii) Write the relation between the three coefficients of expansion \(\alpha, \beta\) and \(\gamma\) for solid.
(iii) A body at higher temperature contains more heat. Comment.
(iv) Why are clock pendulums usually made of invar?
(v) Draw graphical variation of volume and temperature for water.
(vi) How is coefficient of thermal expansion of gases related to temperature?
(vii) State water equivalent.

States of matter viz: solid, liquid and gas are function of temperature and heat content. During the change of state of a substance, the exchange of heat takes place between the substance and surrounding. In this process temperature of substance remains constant. At certain temperature known as melting point. Both the solid and liquid states of the substance coexist in thermal equilibrium. Similarly, at boiling point both the liquid and vapour states of the substance co-exist in the thermal equilibrium. There are certain substance which on heating directly pass from solid to vapour state without passing through the liquid state. This is sublimation process in which solid changes to vapour state of the substance. Process of change of state depends on pressure and temperature.
(i) Define triple point.
(ii) Define latent heat of a substance. 
(iii) What is principle of calorimetry?
(iv) What is effect of pressure on the melting point of a substance?
(v) State phenomenon of relegation.
(vi) What is boiling point? What is effect of pressure on the boiling point?
(vii) What is sublimation?

Three cylindrical rods A, Band C of equal lengths and equal diameters are joined in series as shown in the figure. Their thermal conductivities are 2K, K and 0.5 K respectively.
100°C \(\begin{array}{|l|l|l|} \hline \mathrm{A} & \mathrm{B} & \mathrm{C} \\ \hline \end{array}\) 0°C
In the steady-state, the free ends of rods A and C are at 100 °C and a 0°C respectively. Neglecting loss of heat from the curved surfaces of rods.
(i) Determine the temperature of the junction between rods A and B.
(ii) Determine the temperature of the junction between rods Band C.
(iii) Determine the equivalent thermal conductivity of the combination.
(iv) Define coefficient of thermal conductivity of a solid. Write its S.I unit.
Two rods A and B are of equal length. Each rod has the ends at temperature T₁ and T₂ What is the condition that will ensure equal rates of flow of heat through the rods A and B?

All bodies emit heat energy from their surface by virtue of their temperature. This heat energy is called radiant energy or thermal radiation. The heat that we receive from the sun is transferred to us by a process which, unlike conduction and convection, does not require the help of a medium in intervening space which is almost free of particles. Radiant energy travels in space as electromagnetic waves in the infra-red region of electromagnetic spectrum. They exhibit the phenomenon of interference, diffraction, and polarization as light does.
The emission of radiation from a hot body is expressed in terms of that emitted from a reference body (called the black body) at the same temperature. A black body absorbs and emits radiations of all wavelengths. The total energy E emitted by a unit area of a black body per second is given by E = \(\sigma T^{4}\) 
Where T - is absolute temperature of the body and a is Stefan's constant, if the body is not the perfect black body, then E = \(\varepsilon \sigma T^{4}\) , where \(\varepsilon\) is the emissivity of the body.
(i) Determine the dimensions of Stefan's constant a from Stefan - Boltzman law.
(ii) What is S.I unit of Stefan's constant?
(iii) In which region of the electromagnetic spectrum do thermal radiation lie?
(iv) Which device is used to detect thermal radiation?
(v) When a body A at a higher temperature T₁ is surrounded by another body B at a lower temperature T₂. Write the relation between the rate of loss of heat from body A and temperature.
(vi) On what factor does the rate at which energy is radiated by a body depends?
(vii) On which parameter does the colour of a star depends upon?

Fluid is the name given to a substance which begins to flow when external force is applied on it. Shape and volume of the fluid changes by the application of very small shear stress. The branch of physics which deals the study of fluids at rest is called hydrostatics and that branch of physics which. deals with study of fluid in motion is called hydrodynamics when liquid is at rest in a container, it exerts a force on the surface of object in contact with liquid, which is always normal to the surface of object. The total normal force exerted by liquid at rest on a given surface in contact with it is called thrust of liquid on that surface.
(i) What is the cause of thrust of liquid on surface in contact?
(ii) Define hydrostatic pressure. Write its S.I. unit
(iii) Is hydrostatic pressure a vector quantity or scalar quantity? Give reason.
(iv) Define relative density of a substance
(v) What will be the measure of total preassure at a depth h below the liquid surface?
(vi) What is gauge pressure? On what factors does it depend?
(vii) What is hydrostatic paradox?

It is observed that if gravity effect is neglected the pressure at every point of liquid in equilibrium of rest is same and the increase in pressure at one point of the enclosed liquid in equilibrium of rest is transmitted equally to all other points of the liquid. This is accounted to Pascal's law. Hydraulic lift and hydraulic brakes working is based on the Pascal's law, in which a small force applied on the smaller piston will appear as a very large force on the large piston.
(i) State Pascal's law
(ii) A bottle full of a liquid is fitted with a tight cork. Explain why a slight blow on the cork may be sufficient to break the bottle?
(iii) Two Pistons of hydraulic press have diameter of 30.0 cm and 2.5 cm. Find the force exerted by longer piston when 50.0 kg wt is placed on smaller Piston.
(iv) In the above question, find the distance through which the longer piston would move after 10 strokes if the stroke of the smaller piston is 40 cm.
(v) In a car lift, compressed air exerts a force F₁ on a small piston having a radius of 5.0 cm. This pressure is transmitted to a second piston of radius 10.0 cm, If the mass of the car to be lifted is 1300 kg. Calculate F₁. What is pressure necessary to accomplish the task?

It has been found that a liquid in small quantity at rest, free from external force like gravity, always tends to have a spherical shape. Since for a given volume, a sphere has the least surface area, hence it shows that the free surface of every liquid at rest has a tendency to have a least surface area. The free surface of liquid behaves as if covered by a stretched membrane, having tension in all directions parallel to the surface. This tension in the free surface of liquid at rest is called the surface tension. It arises due to the fact that the free surface of liquid at rest has some additional potential energy.
(i) What is surface tension and its origin?
(ii) Why does oil spread over the surface of water?
(iii) At what temperature the surface tension of a liquid is zero?
(iv) Surface tension of all lubricating oils and paints is kept low. Why?
(v) What is the effect of impurities on the surface tension of liquid?
(vi) What is work done in blowing a soap bubble of radius r and surface tension S?
(vii) Define surface energy of liquid.

Stokes' Law: A body falling through a viscous medium experiences a retarding force resulting in absorption of energy by the medium in the form of heat .:The motion of the body produces a relative motion between the different layers of the fluid. Consequently, it experiences a force which tends to retard its motion. When a small spherical body is dropped in a viscous liquid such as glycerine, it accelerates first, but soon begins to experience a retarding force. When the retarding force becomes equal to the effective weight of the body in the fluid, the body experiences no net force and falls with a constant velocity known as the terminal velocity. George stokes found that a small spherical body of radius r moving with a uniform velocity v in a fluid of coefficient of viscosity \(\eta\) experiences a retarding force F given by F = \(6 \pi \eta r v\) 
(i) Define viscosity.
(ii) Define S.I unit of coefficient of viscosity of a liquid.
(iii) Name the forces which act on the small spherical body falling freely through a viscous medium.
(iv) Write the dimenslonal formula of coefficient of viscosity \(\eta\) .
(v) What would be the terminal velocity of the body if the upthrust on the body is negligible to its weight?
(vi) Write the expression for terminal velocity of spherical body of radius r and density \(\rho\) falling freely through a liquid of density \(\sigma\) and coefficient of viscosity \(\eta\).

Equation of continuity is a fundamental equation of liquid flow and is a special case of the general law of conservation of mass. Consider an incompressible and non viscous liquid flowing slowly and steadily through a pipe of non-uniform cross-section. Let A and B be two different sections of a pipe having cross-sectional area Q ₁ and Q ₂ respectively. Let v₁ and v ₂ be the respecstive velocities of the liquid flow through these cross sections. According to the equation of continuity of flow Q ₁ v₁ = Q₂V₂ or QV = constant i.e., the velocity of liquid flow at any section of the pipe is inversely proportional to area of cross-section of the pipe at that section.
(i) Water flows through a horizontal pipe of nonuniform cross-section at the rate of 31.4 litre per minute. Determien the velocity of flow of water at the section of the pipe where diameter is 2 cm.
(ii) Water flows through a horizontal pipe of diameter 2 cm at a speed of 3 cm s^-1. The pipe has a nozzle of diameter 5 mm at its end. Determine the speed of water emerging from the nozzle.
(iii) What is meant by streamline flow?
(iv) Distinguish between laminar flow and turbulent flow.
(v) Still water runs deep, why?

The atoms in solids are held together by interatomic forces. the average locations of the atoms in a lattice do not change with time and lack mobility. This makes a solid rigid and becomes a cause of elasticity in solids. In some solids such as steel, the atoms are bound together by larger inter-atomic forces than in others. Thus elastic behaviour varies from solid to solid. Even fluids exhibit elasticity. All material bodies get deformed when subjected to a suitable force. The ability of a body to regain its original shape and size is called elasticity. The deforming force per unit area is called stress. The change in dimension divided by the original dimension is called strain. The three kinds of stresses are tensile stress, shearing stress and volumetric stress similarly strains too. According to Hooke's law, within the elastic limit stress is proportional to strain.
(i) Which state of matter has volume elasticity?
(ii) When we stretch a wire, we have to perform work. Why? What happens to the energy given to the wire in this process?
(iii) Define elastic limit.
(iv) Define modulus of elastcity on what factors does it depend?
(v) Why solids are more elastic and gases are least?
(vi) The ratio of radii of two wires of same material is 2 : 1. If these wires are stretched by equal force, find the ratio of stresses Produced in them.

A wire of uniform area of cross-section is suspended vertically from a rigid support through one end with the help of an attached hanger by putting different known weights in the hanger Plot a graph between stress and strain for the stretched wire is as shown.

(i) What does the portion OA of graph represent?
(ii) Which point does the elastic limit represent?
(iii) Which region represents permanent set?
(iv) Which point does represent the yield point?
(v) Which point corresponds to breaking point or breaking stress?
(vi) Draw stress-strain variation graph for elastomers.

One end of a string of length L and cross-sectional area A is fixed to a support and the other end is fixed to a bob of mass m. The bob is revolved in a horizontal circle of radius r with an angular velocity co such that the string makes an angle \(\theta\) with the vertical.

(i) Determine the angular velocity \(\omega\) of the bob.
(ii) Determine the tension T in the string.
(iii) Determine the increase in length of the string when bob is freely suspended from rigid support.
(iv) Determine the stress in the string.
(v) A metallic wire is suspended by attaching some weight to it. If \( \alpha \) is the longitudinal strain and Y is Young's modulus, find the ratio between elastic potential energy and the energy density.

When an elastic body is subjected repeatedly to the action of alternating deforming forces, its behaviour corresponds to that of less elastic bodies due to elastic fatigue. In our daily life, elastic properties are considered while designing a structure of the material. For example, the metallic parts of the machinery are never subjected to a stress beyonds elastic limit otherwise they will get permanently deformed. The thickness of the metallic rope used in the crane in order to lift a given load is decided from the knowledge of elastic limit of the material of the rope and the factor of safety. Similarly the bridges are designed in such a way that they do not bend much or break under the load of heavy traffic, force of strongly blowing wind and its own weight.
(i) What does it mean by elastic after effect?
(ii) Define elastic fatigue
(iii) Why are bridges and girders given I shape?
(iv) A hollow shaft is found to be stronger than a solid shaft made of some equal material against twisting. Explain why?
(v) Define Poisson's ratio
(vi) An elastic wire is cut to half its original length. How would it affect the maximum load that the wire can support?
(vii) Why is a spring made of steei, not of copper?
(viii) Why are the bridges declared unsafe after long use?

A thin rod of negligible mass and cross-sectional area 4 x 10^-6m^-2, suspended vertically from one end, has a length of 0.5 m at 100° C, The rod is cooled to 0° C, Young's modulus is 10¹¹ Nm^-2, Coefficient of linear expansion = 10^{- 5} K^-1 and g = 10 ms^-2.
(i) Determine the decrease in length of the rod on cooling.
(ii) What mass must be attached at the lower end of the rod so that the rod is prevented from contracting on cooling?
(iii) Determine the total energy stored in the rod.
(iv) What is origin of elastic potential energy in a stretched wire? Give its relation with Young's modulus and strain.

Galileo was the first to recognise the fact that irrespective of their masses, bodies fall towards the earth with a constant acceleration. Later on gravity and its laws were given by Newton in his universal law of gravitation and motion of planets around the sun was explained by Kepler in his laws of planetary motion. Newton's universal law of gravitation and third law of motion have a similarity that two bodies exert equal and opposite force on each other.
(i) What does the word 'Gravity' mean?
(ii) Define acceleration due to gravity
(iii) State Newton's law of gravitation.
(iv) What would be the gravitational force on a point mass body situated insde the hollow spherical shell of uniform density?
(v) State Kepler's law of period for planetary motion.
(vi) Give relationship between angular momentum and areal velocity of a planet around sun.
(vii) At what distance force of gravitation between two bodies would be zero?

There are three identical point mass bodies each of mass m located at the vertices of an equilateral triangle with side r. They are exerting gravitational force of attraction on each other, which can be given by newton's law of gravitation. Each mass body produces its gravitational field in the surrounding region. The magnitude of gravitational field at a point due to a point mass body is the measure of gravitational intensity at that point. The gravitational potential at a point in a gravitational field is the amount of work done in bringing a unit mass body from infinity to the given point without acceleration.

(i) What is the magnitude of the gravitational force on one body due to other two bodies in the given arrangement.
(ii) What is the work done in taking one body far away from the other two bodies?
(iii) Determine the gravitational potential at the centroid point O.
(iv) When a body falls towards earth, earth also moves towards the body. Why is earth's motion not noticed?

A rocket is fired vertically upwards with speed v = 5 kms^-1 from the surface of earth. It goes up to a height h before returning to earth. At height h a body is thrown from the rocket with speed v_o in such a way so that the body becomes satellite of earth. Let the mass of the earth, M = 6 x 10²⁴kg, mean radius of the earth, R = 6.4 x 10 ⁶ m, G = 6.67 x 10^{- 11} Nm² kg^-2, g = 9.8 ms^-2.
(i) Determine the value of height h above the surface of earth from which body is thrown out from the, rocket.
(ii) Determine the orbital velocity of the satellite.
(iii) Calculate the time period of revolution of satellite around the earth.
(iv) If this satellite is to be taken at double of the present height from the surface of the earth, then find the new time period of revolution of satellite.
(v) What is the value of gravitational field on the surface of earth?
(vi) Is the potential energy of a system of bodies positive or negative? Give reason.
(vii) What is the maximum value of gravitational potential energy and where?

Geostationary satellite is a particular type of satellite used in communication. A number of communication satellites are launched which remain in fixed position at a specified height above the equator. They are called synchronous satellites. These appear fixed at a position above a certain place on the earth, it must corotate with the earth so that its orbital period around the earth is exactly equal to the rotational period of the earth about its axis of rotation.
(i) What is the height of geostationary satellite above the surface of the earth?
(ii) What is the time period and direction of revolution of a geostationary satellite respectively?
(iii) What is the orbital-speed of geostationary satellite?
(iv) Which electromagnetic wave is used in satellite communication?
(v) Can a Pendulum vibrate in an artificial satellite?
(vi) From where does a satellite revolving around planet get the required centripetal Force?

A body moving in an orbit around the earth is called earth satellite. The First artificial satellite was put into earth's orbit in 1956. Artificial satellites are put into orbit at an altitude of a few hundred kilometers. The satellite is carried in a rocket which is launched from the earth with a velocity greater than the escape velocity. The escape velocity is the velocity with which a body must be projected in order that is may escape the gravitational pull of the earth. When the rocket has achieved the desired height, the satellite is released horizontally by imparting to it a very high speed so that it remains moving in a nearly circular orbit around the earth. This velocity is called the orbital velocity which is about 8 kms^-1 for a satellite at a few hundred kilometeres above the earth.
(i) What are the factors on which escape velocity of a rocket fired from the earth depends upon?
(ii) What provides the necessary centripetal force to keep a satellite in a circular orbit around the earth?
(iii) An artificial satellite is orbiting the earth at an altitude of 500 km. A bomb is released from the satellite. How will the bomb move after its release?
(iv) How escape velocity is related to orbital velocity of satellite?
(v) A satellite is orbiting around the earth with a speed v. To make the satellite escape, what is the minimum percentage increase in its speed?
(vi) A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R. By what percentage the period of second satellite is larger than that of first satellite?
(vii) Does the speed of a satellite remain constant in a particular orbit?

The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The \(\vec{r}\) of c.m of the system of two particles of masses m₁ and m₂ with position vector \(\vec{r}_{1} \text { and } \vec{r}_{2}\) is given by 
\(\vec{r}=\frac{m_{1} \vec{r}_{1}+m_{2} \vec{r}_{2}}{m_{1}+m_{2}}\) 
for an isolated system, where no external force is acting \(\overrightarrow{v_{c m}}\) = constant
Under no circumstance, the velocity of centre of mass of an isolated system can undergo a change.
(i) What should be the position of the centre of mass of a system of two particles of unequal masses?
(ii) An electron and a proton move towards each other with velocities v₁ and v₂ respectively. What is the velocity of their centre of mass?
(iii) Two bodies of masses 1kg and 2 kg are located at (1, 2) and (-1, 3) respesctively, determine the coordinates of the centre of mass.
(iv) A bomb dropped from an aeroplane in level flight explodes in the middle. How would be the motion of centre of mass of the fragments?
(v) Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 ms^-1 to the heavier block in the direction of the lighter one. Determine the velocity gained by the centre of mass.
(vi) Can centre of mass of a body lie where there is absolutely no mass? Give example.
(vii) Can centre of mass of a body coincide with the geometrical centre of the body?

Moment of inertia of a body about a given axis is the rotational inertia of the body about that axis. It is represented by 1= MK², where M is mass of body and K is radius of gy ration of the body about that axis. it is a scalar quantity, which is measured in kg m².
When a body rotates about a given axis and the axis of rotation also moves, then total K.E of body = K.E of translation + kinetic energy of rotation.
\(K=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}\)
(i) Is the M.I of a body about a given axis is vector or scalar quantity?
(ii) On what factors does M.I of a body depend?
(iii) Determine the moment of inertia of circular disc and circular ring of same mass and radius about an axis perpendicular to plane.
(iv) A 40 kg flywheel in the form of a uniform circular disc of diameter 1 m is making 120 rpm. What is the M.I about a transverse axis through its centre?
(v) Determine kinetic of rotation of the flywheel in the above case.
(vi) Calculate radius of gyration of a cylindrical rod of mass m and length L about an axis of rotation perpendicular to its length and passing through its centre,
(vii) Determine the ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring.

A hollow sphere of mass M and Radius R is initially at rest on a horizontal rough surface. It moves under the action of constant horizontal force F as shown in Fig.

(i) Determine the direction of frictional force between the sphere and the surface. 
(ii) Determine the linear acceleration of the sphere.
(iii) What is the frictional force between the sphere and the surface?
(iv) State the relationship between angular momentum and torque of rotating body about an axis.
(v) Solid cylinder of mass m and radius r rolling down an inclined plane of \(\theta\)  inclination e without slipping. Determine the acceleration of the cylinder down the inclined plane.

Angular momentum of a rotating body is measure of quantity of motion in rotational motion about an axis which is measured by product of moment of inertia and angular velocity i.e., L = \(I \omega\) . It is moment of linear momentum about axis of rotation. Being a vector quantity its direction is along the axis of rotation. In the absencse of an external torque, angular momentum vector remains constant.
(i) If angular momentum is conserved in a system whose moment of inertia is decreased, will its rotational kinetic energy be also conserved? Explain.
(ii) Why spin angular velocity of a star is greatly enhanced when it collapses under gravitational pull and becomes a neutron star?
(iii) A Person sits near the edge of a circular platform revolving with a uniform angular speed. What will be the change in the motion of the platform?
(iv) What would happen if the person starts moving from the edge toward the centre of the platform?
(v) Why are there two propellers in a helicopter?
(vi) A thin uniform circular disc of mass M and Radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity \(\omega \text { . }\) Another disc of same dimensions but of mass \(\frac{\boldsymbol{M}}{\mathbf{4}}\) is placed gentally 4 on the first disc coaxially show that angular velocity of the system is \(\frac{4}{5} \omega.\) 

Mechanical energy exists in two forms: Kinetic energy and Potential energy. Kinetic energy is the energy possesed by a body by virtue of motion. Potential energy is the energy possessed by the body by virtue of its position or configuration. These two forms of energy are interconvertible. If no other form of energy is involved in a process, the sum of kinetic energy and potential energy always remains constant.
(i) State law of conservation of mechanical energy.
(ii) State two particles having mass m₁ and m₂ , both have equal linear momenta. What is the ratio of their kinetic energies?
(iii) Two particles of masses m₁ and m₂ have equal kinetic energies. What is the ratio of their linear momenta?
(iv) A particle of mass m has half the kinetic energy of another particle of mass m/2. If the speed of the heavier particle is increased by 2 ms^-1, its new kinetic energy equals the original kinetic energy of the lighter particle. What is the ratio of the original speeds of the lighter and heavier Particle?
(v) A uniform rod of mass m and length I is made to stand vertically on one end. What is the potential energy of the rod in this position?
(vi) Give an example where a force does work on a body but fails to change its K-E.
(vii) Does K-E depend upon the direction of motion involved? Can it be negative? Does its value depend on frame of refrence?

Work is said to be done by a force acting on a body, provided the body is displaced actually in any direction except in a direction perpendicular to the direction of the force-mathematically, \(W=\bar{F} \cdot \bar{s}=F s \cos \theta\) whereas energy is the capacity of a body to do the work and Power is the rate at which the body do the work.
\(P=\frac{\mathrm{W}}{t}=\frac{\overline{\mathrm{F}} \cdot \bar{s}}{t}=\overline{\mathrm{F}} \cdot \bar{v}\)
Both, work and energy are measured in Joule while power is measured in watt.
(i) A box is pushed through 4.0 m across a floor offering 100 N resistance. Determine the work done by the applied force.
(ii) In the above question, determine the work done by the resistive force and by the gravity.
(iii) A truck draws a tractor of mass 1000 kg at a steady rate of 20 ms^-1 on a level road. The tension in the coupling is 2000 N. What is the power spent on the tractor?
(iv) Determine the work done on the tractor in one minute?

The work done by a constant force acting on a body is given by \(W=\bar{F} \cdot \bar{r}, \text { where } \bar{F}\) is the force vector and \(\bar{r}\) is displacement vector. the displacement vector \(\bar{r}=\bar{r}_{2}-\bar{r}_{1}\) where r ₁ is the initial position vector and \(\bar{r}_{2}\) is the final position vector. If the force is variable, the work done in moving a body from a Position \(\bar{r}\) to a position \(\bar{r}_{2}\) is given by \(W=\int_{v}^{r_{2}} \bar{F} \cdot d \bar{r}, \text { where } d \bar{r} \) is an infinitesimally small displacement.
(i) A particle is moved from a position \(\bar{r}_{1}=(3 \hat{i}+\)\(2 \hat{j}-4 \hat{k})\) metre to position \(\bar{r}_{2}=(5 \hat{i}+6 \hat{j}+9\)\(\hat{\boldsymbol{k}})\) metre under the action of a force \(\overline{\boldsymbol{F}}=\mathbf{(} \hat{\boldsymbol{i}}+\) \(\mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})\) newton. Determine the net work done.
(ii) A body of mass m is projected from a tower of height h at angle \(\theta\) above the horizontal. Determine the workdone by the gravitational force during the time it takes to hit the ground.
(iii) A body of mass m is projected from the ground with a velocity u at an angle \(\theta\) above the horizontal. Determine the work done by the gravitational force in time \(t=\frac{u \sin \theta}{g}\)
(iv) In the above question if \(\theta\) = 45°, then determine the gravitational force in time t = \( \frac{2 u \sin \theta}{g} \)
(v) A force F acting on an object varies with distance x as shown in Fig. Force is in Nand x is m. Determine the work done by the force in moving the object from x = 0 to x = 6 m.

(vi) The Potential energy of a 1kg particle free to move along the x-axis is given by \( V(x)=\left(\frac{x^{4}}{4}-\frac{x^{2}}{2}\right) \mathrm{J} \) .The total mechanical energy of the particle is 2J. Determine the maximum speed of the particle in m/s.

In a conservative force field, we can find the component of force from the potential energy at a point in the field. A positive force means repulsion and a negative force means attraction. From the given potential energy function U (r) we can find the equilibrium position where force is zero. Suppose the potential energy at a distance r from centre of the field is given as
\( \mathrm{U}(r)=\frac{A}{r^{2}}-\frac{B}{r} \)Where A and B are positive constants.
(i) What should be the nature of the field as per conclusion drawn from the form of given potential energy?
(ii) Determine the work done to move the particle from equilibrium to infinity.
(iii) If K.E of a body becomes 4 times of its initial value, then what would be new linear momentum?
(iv) Determine the percentage change in K.E of a body if momentum of a body increases by 0.01 %
(v) What does it meant by unstable equilibrium of a particle? Write condition for unstable equilibrium.
(vi) What are conservative forces?

A ball P moving with a velocity u strikes an identical stationary ball Q such that after the collision, the direction of motion of balls P and Q makes an angle 30° with the original direction of motion of ball P as shown.

(i) Determine the speed V₁ of ball P after collision.
(ii) Determine the ratio of the total kinetic energy of the balls after collision to that before collision.
(iii) Determine the ratio of velocity V₁ and v ₂ after the collision in terms of coefficient of restitution e.
(iv) A ball hits a floor and rebounds after an inelastic collision. What change would occur in total energy, kinetic energy and momentum of ball?

Physical quantities are broadly classified into vectors and scalars. Physical quantities which have a sense of direction are known as vectors, these are categorised as polar and axial. Vectors cannot be added by simple laws of algebra but by adopting vector algebra. Resultant of two or more vectors could be zero depending upon their magnitude and direction. When resultant of three vectors are zero or null then Lami's theorem is applicable. Vector substraction is similar to addition where vector addition of one vector and negative vector of other is done. In our daily life vector addition and vector substraction is very important as far as application of mechanical force is concerned.
(i) Define vector physical quantity. Give example.
(ii) Distinguish between Polar and Axial vectors. Give example
(iii) What are unit vector and null vector?
(iv) State Lami's theorem of equilibrium of three vectors.
(v) State triangle law of vector addition.

An aeroplane is flying with velocity \(\vec{v}_{p}\) (= 100 ms^-1) towards east, with respect to ground through motionless air and \(\vec{v}_{w}\) is the wind velocity with respect to ground. The total velocity of aeroplane is \(\vec{v}=\overrightarrow{v_{p}}+\overrightarrow{v_{w}}\). The magnitude of the velocity is often called speed. The heading of the plane is the direction in which the nose of the plane points. Infact, it is the direction in which the engine propels the plane. Resultant velocity and direction is the vector sum of different components of velocity, while relative velocity is the velocity of one with respect to another obtained by vector substraction.
(i) What is resultant velocity of plane if the wind velocity is towards south with respect to ground at 25 ms^-1?
(ii) Define relative velocity? How it is determined?
(iii) If the wind blows with velocity 25 ms^-1 northwards, then by which angle the plane velocity is deflected from east?
(iv) Vectors cannot be added algebraically. Why?
(v) Mention the condition when the magnitude of vectors \(\overline{\mathbf{A}}-\overline{\mathbf{B}}\)and \(\overline{\mathbf{A}}+\overline{\mathbf{B}}\) is same.

Projectile is the name given to a body thrown with some initial velocity with the horizontal direction and then allowed to move in two dimensions under the action of gravity alone, without being propelled by any engine or fuel. A projectile moves under the combined effect of two velocities: one a uniform velocity in the horizontal direction and other a uniformly changing velocity. It is observed that path of projectile which is known as trajectory is parabolic in shape.
(i) Does the time of flight, horizontal range and maximum height depend on the mass of the projectile?
(ii) State the relation between the maximum height attained by the projectile and the maximum range.
(iii) What is the angle between velocity and acceleration at the highest point of projectile path?
(iv) A body is projected with velocity u at angle e with the horizontal, what would be the angle and speed of projectile when it strike at the ground at same horizontal plane from which it is projected?
(v) What are the angles of projection for same initial velocity of projection at which horizontal range of the projectile is same?
(vi) Write the equation of the path of projectile, projected at angle e with initial velocity u, from a horizontal plane.

If a body moves in circle with a constant speed, then the magnitude of the velocity is constant but the direction of the velocity vector is changing all the time. Thusvelocity is changing with time. Therefore the motion of the body is accelerated. The acceleration is directed towards the centre of the circle and is called centripetal acceleration a_c. If m is the mass of the body then the centripetal force is F_c = ma_c·
(i) What is effect on the linear momentum, angular momentum and kinetic energy of body, moving uniformly in circular path?
(ii) What is the magnitude and direction of a_c of body moving in circular path of radius r with speed v?
(iii) A stone of mass m is tied to a string is whirled in circular path of radius r in horizontal plane at a constant speed v. What is the angle between velocity and acceleration? Also determine the tension in the string.
(iv) State the relation between linear velocity (v) and angular velocity (ω) of body moving in circular path of radius r,
(v) What would be the direction of motion of stone if at certain time its string get broken?
(vi) In a non-uniform circular motion with tangential acceleration a_t and radial acceleration a_r. What would be the resultant acceleration?

It must be clearly understood that distance is not the same as displacement. Distance is a scalar quantity and is given by the total length of the path travelled by the body in a certain interval of time. Displacement is a vector quantity and is given by the shortest distance (in a specified direction) between the initial and the final positions of the body. The direction of the displacement vector is from the initial position to the final position of the motion. Speed IS a scalar quantity. The average speed and average velocity are different in many respect. The direction of the velocity vector is the same as that of the displacement vector. Acceleration is defined as the rate of change of velocity and it is a vector quantity.
(i) Mention a condition when displacement and distance are both equal.
(ii) Define average speed and average velocity.
(iii) Draw position-time graph of uniform accelerated motion.
(iv) What does the area under velocity-time graph and time axis signifies?
(v) What does the slope of position-time graph and velocity-time graph represent at any instant?
(vi) Mention a condition when body is at rest but still it has acceleration.
(vii) A body is moving in circular parth with uniform speed. What is the acceleration and average velocity during one complete revolution?

A sports car passing a police checkpost at 60 km h^-1 immediately started slowing down uniformly until its speed was 40 km h^-1. It continued to move at the same speed until it was passed by a Police car 1 km from the check post. This police car had started from rest at the check post at the same instant as the sport car had passed the check post. The police car had moved with a constant acceleration until it had passed sports car. Assuming that the time taken by the sports car in slowing down from 60 km h-' to 40 km h-' was equal to the time that it travelled at constant speed before passed by the Police car.
(i) Determine the average velocity of sports car.
(ii) Determine the speed of the police car at the instant when it passed the sports car.
(iii) Determine the acceleration of the police car.
(iv) Draw the velocity-time graph for police car and sport car.
(v) How much time taken by police car to pass the sports car?

Kinematics is the branch of mechanics which deals with the study of motion of material objects without taking into account the factors affecting the motion. Rest and motion are relative concept and nothing is absolute. The Position of the object at a given instant of time is described in terms of position coordinates. The coordinate system along with a clock constitutes a frame of reference. Frame of reference can be of two types viz: inertial frame of reference and non-inertial frame of reference. When position of body change in a frame of reference, it is said to be in motion which is categorised as uniform and non-uniform. Motion of a body is studied in terms of position-time graph and velocity-time graph.
(i) "Rest and motion are relative not absolute." Comment.
(ii) What are different types of frames of reference? Explain.
(iii) Draw position-time graph for uniform and Non-uniform motion.
(iv) Draw velocity-time graph for uniform and non-uniform motion.
(v) Relative veolcity of two bodies is zero. What is nature of Position-time graph for it?

The dimensional method is a very convenient way of finding the dependence of physical quantity on other physical quantities of a given system. This method has its own limitations. In a complicated situation, it is often not easy to guess the factors on which a Physical quantity will depend. Secondly, this method gives no information about the dimensionless proportionality constant. Thirdly this method is used only if a Physical quantity depends on the product of other physical quantities. Fourthly this method will not work if a physical quantity depends on another quantity being a trignometric or exponential function. Finally this method does not give complete information in cases where a Physical quantity depends on more than three quantities in problems in mechanics.
(i) What are Physical quantity? Write their types.
(ii) What are dimensional formula of a physical quantity?
(iii) Which principle does the method of dimensional analysis use?
(iv) What is principle of homogeneity?
(v) Write two limitations of dimensional analysis.
(vi) Write one use of dimensional analysis.

In the study of Physics, we often have to measure the physical quantities. The numerical value of a measured quantity can only be approximate as it depends upon the least count of the measuring instrument used. The number of significant figures in any measurement indicates the degree of precision of that measurement. The importance of significant figures lies in calculation. A mathematical calculation cannot increase the precision of a physical measurement. Therefore, the number of significant figures in the sum or product of a group of numbers cannot be greater than the number that has the least number of significant figures because a chain cannot be stronger than its weakest link. The difference in the true value and the measured value of a quantity is the measure of error in measurement.
(i) What are significant figures?
(ii) Define least count
(iii) Is there any relation between precision and accuracy?
(iv) State the relationship between significant figures and precision.
(v) Determine the maximum error in the addition of two physical quantities.
(vi) How Systematic errors can be minimised?

To measure distance or length between two points, various methods are adopted which are categorised as direct and indirect methods. Direct methods are used to measure shorter but accessible distances while indirect methods are used for inaccessible distance. Large distances, such as the distance of a planet or star from earth can be measured by the Parallax method. Parallax is the change in position of an object with respect to fixed background when object is seen from two different positions. Parallex method is used for measuring distances of stars which are less than 100 light years away.
(i) Name the instruments that are used to measure distance of the order 10^{- 5} m.
(ii) Define the terms 'basis' and parallactic angle used in Parallax method for measuring distance.
(iii) What is the measure of basis in measuring distance of a nearby star by Parallax method?
(iv) Why Parallax method is used for measuring distances of nearby stars only?
(v) What is meant by angular diameter of moon?

Physics has revealed that all the forces occuring in different contexts arise from a small number of fundamental forces in nature. Though the origin of derived forces is complex, yet they can be understood in terms of the fundamental forces which govern the macroscopic as well as microscopic world. These fundamental forces are gravitational force, weak nuclear forces, electromagnetic forces, strong nuclear forces. Among these gravitational and electromagnetic forces have some common characteristics like being central, conservative, long range and obeying inverse square law while weak nuclear forces and strong nuclear forces are of nuclear origin, microscopic and very short range attractive forces. All these forces govern the diverse phenomena of physical world.
(i) What is the relative strengths of four types of basic forces in nature?
(ii) In which phenomenon does weak nuclear forces involve? Explain.
(iii) What are graviton and photon?
(iv) What does the inverse square law represent? Show graphically.
(v) What is range of weak nuclear force and strong nuclear force?

Physics is a basic discipline in the category of natural sciences. It refers to the study of the physical world and it is devoted to the study of nature and natural phenomenon. In the study of physics, there are two principal thrusts: unification and Reductionism. Unification means attempt to explain the diverse physical phenomenon in terms of a few concepts and laws, while reductionism attempt to derive the properties of a bigger, more complex system from the properties of its constituent simple parts.
(i) Mention the origin of the word 'Physics' and write its meaning.
(ii) Name some phenomena which are unified by Newton's law of gravitation.
(iii) Name the equation that unified basic laws of electromagnetism.
(iv) What reductionism has done in thermodynamics to explain some macroscopic quantities?
(v) What are main five branches of Physics?
(vi) What is Physics?

The two main domains of interest in Physics are macroscopic and microscopic. The macroscopic domain includes the study of Phenomena involving objects offinite size, this makes up classical Physics, developed upto the year 1900. The microscopic domain includes the study of Phenomenon involving molecules, atoms, nuclei, electron and other. elementary particles. This makes up modern physics developed after the year 1900. Overall Physics has played a key role in the development of many other branches of science.
(i) Mention the different branches of classical Physics.
(ii) What are limitations of classical Physics?
(iii) Which theory explains properly the microscopic domain.
(iv) What does the branch of Physics, Thermodynamics deals with?
(v) Explain how Physics is in relation to mathematics?

The range of strong nuclear force is about

The density of a cube is measured by measuring its mass and the length of its sides. If the maximum errors in the measurement of mass and length are 3% and 2% respectively, then the maximum error in the measurement of density is _____.

In case of a moving body

A particle moves on a given line with a constant speed \(\upsilon \). At a certain time it is at a point P on its straight line path. O is fixed point. The value of \(\overrightarrow { OP } \times \overrightarrow { \upsilon } \) is (where y is perpendicular distance from O to given line)

An insect is crawling up on the concave surface of a fixed hemispherical bowl of radius R. If the coefficient of friction is \({1\over3}\) then the height up to which the insect can crawl is nearly,_______.

Who proposed the wave theory?

The dimensions of entropy are _____.

The displacement x of a particle varies with time according to the relation x=\(\frac { a }{ b } \)(1-e^-bt). Then

A particle moves on a given line with a constant speed \(\upsilon \). At a certain time it is at a point P on its straight line path. O is fixed point. The value of \(\overrightarrow { OP } \times \overrightarrow { \upsilon } \) is (where y is perpendicular distance from O to given line)

A particle of mass 5 kg is pulled along a smooth horizontal surface by a horizontal string. The acceleration of the particle is 10 ms^-2. The tension in the string is_______.

The range of strong nuclear force is about

A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mill and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is _____.

Distance-time graph of a body at rest is

A plane is indined at an angle of 30° with horizontal. The magnitude of component of a vector \(\overset\rightarrow{A}\)=-10\(\hat{k} \) perpendicular to this plane is (here z-direction is vertically upwards

If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may _______.

The range of strong nuclear force is about

The velocity of a body moving in viscous medium is given by v =\(\frac { A }{ B } \left[ 1-{ e }^{ \frac { -t }{ b } } \right] \)where t is time, A and B are constants .Then the dimensions ot A are _____.

In case of a moving body

If \(\overrightarrow { { a }_{ 1 } } \) and \(\overrightarrow { { a }_{ 2 } } \) are two non collinear unit vectors and if \(\left| \overrightarrow { { a }_{ 1 } } +\overrightarrow { { a }_{ 2 } } \right| \) =\(\sqrt{3}\), then the value of \(\left( \overrightarrow { { a }_{ 1 } } -\overrightarrow { { a }_{ 2 } } \right) .\left( 2\overrightarrow { { a }_{ 1 } } +\overrightarrow { { a }_{ 2 } } \right) \) is

A particle of mass 5 kg is pulled along a smooth horizontal surface by a horizontal string. The acceleration of the particle is 10 ms^-2. The tension in the string is_______.

Who proposed the wave theory?

The SI units of the universal gravitational constant G are _____.

The displacement of an object at any instant is given by x = 30 + 20 t², where x is in metres and t in seconds. The acceleration of the object will be

If the resultant of three forces \(\overrightarrow { F } _{ 1 }=p\hat { i } +3\hat { j } -\hat { k } ,\overrightarrow { F } _{ 2 }\)and \(\overrightarrow { F } _{ 3 }=6\hat { i } -\hat { k } \) acting on a particle has a magnitude equal to 5 units, then the value of p is

A rectangular body is held at rest by pressing it against a vertical wall. Which of the following is generally true?

Who proposed the wave theory of light?

A cylindrical solid of mass M has raidus R and length L. Its moment of inertia about a generator is:

A black body is at 727°C. It emits energy at a rate which is proportional to _______.

Which of the following statements is true?

The time period ofmass suspended from a spring is T. Ifthe spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in figure. The speed of each pulse is 2 cms^-1. After 2 second, the total energy of the pulses will be

A transverse wave propagating along X-axis is represented by y(x, t) = 8.0 sin(0.5 πx-4πt-π/4) where x is in metre and t is in seconds. The speed of the wave is

Which of the following statements is true?

A source X of unknown frequency produces 8 beats per second with a source of 250 Hz and 12 beats per second with a source of 270 Hz. The frequency of the source X is

A simple pendulum of frequency n is taken upto a certain height above the ground and then dropped along with its support so that it falls freely under gravity. The frequency of oscillations of the falling pendulum will

The length of a simple pendulum is increased by 44%. What is the percentage increase in its time period?

A particle executing simple harmonic motion along y-axis has its motion described by the equation y = A sin (ωt) + B. The amplitude of the simple harmonic motion is

Masses in and 3m are attached to the two ends of a spring of constant k. If the system vibrates freely, the period of oscillation will be

The following are the quantities associated with a body performing SHM.
1. The velocity of the body.
2. The accelerating of the body.
3. The accelerating force acting on the body.
Which of these quantities are exactly in phase with each other?

According to kinetic theory of gases the r.m.s. velocity of the gas molecules is directly proportional to

The speed of sound in a gas is v. The rms speed of molecules of this gas is C. If \(\Upsilon =\frac { { C }_{ P } }{ C_{ V } } \) then the ratio of v and C is

A sealed container with negligible thermal coefficient of expansion contains helium (a monoatomic gas). When it is heated from 300 to 600 K, the average kinetic energy of the helium atom is

During an adiabatic process, the pressure of a gas is proportional to the cube of its absolute temperature. The value of C_p/ C _v for that gas is

Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmosphere pressure respectively.If both samples are at the same temperature the mean velocity of hydrogen molecule is

The internal energy of an ideal gas depends on: _______.

In an adiabatic change, the pressure P and temperature T of a diatomic gas are related by the relation P ∝ T^C where C equals _______.

An ideal heat engine exhosting heat at 27°C is to have 25%efficiency. It must take heat at: _______.

For a gas, r = 1.4 then atomicity, C_P, and C_V of the gas are _______.

The given quantity of an ideal gas is at pressure P and absolute Temperature T. The isothermal bulk Modulus of the gas is _______.

Black body radiation is white. Comment.

Give the relation between celsis, fahrenheit and reaumur scale temperature.

Van temperature on celsius scale and kelvin scale related?

Two bodies at different temperatures T₁ and T₂, if brought in thermal contact do not necessarily settle at the mean temperature \(\frac { ({ T }_{ 1 }+{ T }_{ 2 }) }{ 2 } \) . Why?

Usually a good conductor of heat is a good conductor of electricity also. Give reason.

The Bernauli's Theorem is based on the conservation of:

The mass of water rises in capillary tube of radius R is M. The mass of water that rises in tube of radius 2R is

Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies before and after the change is:

For a ball falling in a liquid with constant velocity, ratio of resistance force due to the liquid to that due to gravity is

A cylindrical vessel is filled with water upto height H. A hole is bored in the wall at a depth h from the free surface of water. For maximum range, h is equal to

Dimensional formula of stress is same as that of

Young's modulus of a material has the same unit as

Elastic limit is equal to

Which of the following is not a unit of Young's modulus?

A wire suspended vertically from one end, is stretched by attaching a weight 200 N to the lower end. The weight stretches the wire by 1 mm. The energy gained by the wire is

A satellite is orbiting the earth. If its distance from the earth is increased, its

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth,is

If three uniform spheres, each having mass M and radius r, are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

If a particle is fired vertically upwards from the surface of earth and reaches a height of 6400 km, the initial velocity of the particle is (assume R = 6400 km and g = 10 ms^-2)

A couple produces a:

A cylindrical solid of mass M has raidus R and length L. Its moment of inertia about a generator is:

A man of mass M is standing at the centre of a rotating turn table rotating with an angular velocity w. The man holds two 'dumb bells' of mass M/4 each in each of his two hands. If he stretches his arms to a horizontal position, the turn table acquires a new angular velocity w' where

A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

A loaded spring gun of mass M fires a 'shot' of mass m with a velocity \(\vartheta \) at an angle of elevation \(\theta\). The gun is initially at rest on a horizontal frictionless surface. After firing, the centre of mass of the gun-shot system

Equal masses (m each) are attached at the two ends of a string passing over two pulleys. Another mass is attached at the centre of the string. In order that there is no sag in the string, this mass should be

The work done by all the forces (external and internal) on a system equals the change in

A heavy stone is thrown from a cliff of height h with a speed v. The stone will hit the ground with maximum speed if it is thrown

Two bodies of masses m and 4 m are moving with equal kinetic energy. The ratio of their linear momenta is

Two bodies of masses m and 4 m are moving with equal linear momentum. The ratio of their kinetic energies is

If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may _______.

The dimension of Impulse is _______.

A force of 200 N is required to push a car of mass 500 kg slowly at constant speed on a level road. If a force of 500 N is applied, the acceleration of the car (in m S^-2) will be_______.

A block of mass m is placed on a smooth inclined plane of inclination \(\theta\) with the horizontal. The force exerted by the plane on the block has a magnitude _______.

An insect is crawling up on the concave surface of a fixed hemispherical bowl of radius R. If the coefficient of friction is \({1\over3}\) then the height up to which the insect can crawl is nearly,_______.

If \(\overrightarrow { { a }_{ 1 } } \) and \(\overrightarrow { { a }_{ 2 } } \) are two non collinear unit vectors and if \(\left| \overrightarrow { { a }_{ 1 } } +\overrightarrow { { a }_{ 2 } } \right| \) =\(\sqrt{3}\), then the value of \(\left( \overrightarrow { { a }_{ 1 } } -\overrightarrow { { a }_{ 2 } } \right) .\left( 2\overrightarrow { { a }_{ 1 } } +\overrightarrow { { a }_{ 2 } } \right) \) is

The sum of magnitudes of two forces acting at a point is 18 units and the magnitude of their resultant is 12 units. The resultant is at 90° with the force of the smaller magnitude. The magnitude of the individual forces is

If the resultant of three forces \(\overrightarrow { F } _{ 1 }=p\hat { i } +3\hat { j } -\hat { k } ,\overrightarrow { F } _{ 2 }\)and \(\overrightarrow { F } _{ 3 }=6\hat { i } -\hat { k } \) acting on a particle has a magnitude equal to 5 units, then the value of p is

A particle moves on a given line with a constant speed \(\upsilon \). At a certain time it is at a point P on its straight line path. O is fixed point. The value of \(\overrightarrow { OP } \times \overrightarrow { \upsilon } \) is (where y is perpendicular distance from O to given line)

From the top of a tower of height 40 m, a ball is projected upwards with a speed of 20 m/ s at an angle of elevation of 30°. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (Take g = 10 m/s²)

The displacement x of a particle varies with time according to the relation x=\(\frac { a }{ b } \)(1-e^-bt). Then

The displacement of an object at any instant is given by x = 30 + 20 t², where x is in metres and t in seconds. The acceleration of the object will be

The area under the velocity time graph between any two instants t = t₁ and t = t₂ gives the distance covered in a time \(\delta \) t = t₂ - t₁.

Which of the following is not a vector quantity?

The SI units of magnetic field is _____.

The dimensions of energy per unit volume are the same as those of _____.

A physical quantity is represented by X = M^a L^b T^-c . If percentage error in the measurement of M, Land Tare \(\alpha \)%, \(\beta \)% and \(\gamma \)% respectively, then total percentage error is _____.

'Parsec' is the unit of _____.

A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mill and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is _____.

Who gave Universal Law of Gravitation?

Who discovered scattering of light?

Which scientific principle is steam engine based on:

Who gave theory of relativity?

Who proposed the wave theory of light?

Which scientific principle is steam engine based on:

Who proposed the wave theory of light?

Who proposed the wave theory?

Who did not discover radioactivity?

Who discovers famous theory of relativity?

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 Å). Why is this ratio so large ?

Find an expression for viscous force F acting on a tiny steel ball of radius r moving in a viscous liquid of viscosity \(\eta \) with a constant speed v by the method of dimensional analysis.

Briefly explain how you will estimate the molecular diameter of oleic acid.

The speed-time graph of a particle moving along a fixed direction is shown in Fig. Obtain the distance traversed by the particle between
(a) t = 0 s to 10 s.
(b) t = 2 s to 6 s.

What is the average speed of the particle over the intervals in (a) and (b)?

Derive the three basic kinematic equations by calculus method.

Write down the number of significant figure in the following.
12.000

In successive measurements, the reading of the period of oscillation of a simple pendulum were found to be 2.63 s,2.56 s,2.42 s,2.71 s and 2.80 s in an experiment.Calculate express the result in proper form.

Check whether the given equation is dimensionally correct  \(\frac { 1 }{ 2 } mv^{ 2 }=mgh\)

The two thigh bones (femurs), each of cross-sectional area10 cm² support the upper part of a human body of mass 40 kg. Estimate the average pressure sustained by the femurs.

Write in about 1000 words, a fiction piece based on your speculation on the science and technology of the twenty second century.

Write in about 100 words a fiction piece based on your speculation on the science and technology of the twenty-second century.

Compute the following with regards to significant figures.
(i) \(4.6\times 0.128\).
(ii) \(\frac { 0.9995\times 1.53 }{ 1.592 } \).
(iii) 876 + 0.4382.

A train 500m long crosses a bridge of 1000 m in 10s. Find the average speed of the train when it just crosses the bridge.

Name that branch of science which deals with the study of stars.

A jeweller put a diamond weighing 5.42 g in a box weighing 1.2 Kg. Find the total weight of the box and the diamond to correct number of significant figures.

The farthest objects in our universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the earth.These objects(known as quasars) have many puzzling features which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?

What are uses of a velocity  - time graph ?

Two tuning forks A and B give 5 beats. A resounds with a closed column of air 15 cm long and B with an open column of ar 30.5 cm long. Caluculate their frequencies. Negelct and correction.

A SONAR system fixed in a submarine operates at a frequency 40.0 KHz. An enemy submarine of 360 km/h. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 \({ ms }^{ -1 }\)

For the harmonic travelling wave  \(y=2\cos { 2\pi } \left( 10t-0.0080x+3.5 \right) \) , where, x and y are in cm and t is in second. What is the phase difference between the oscillatory motion at two points separated by a distance of \(\frac { \lambda }{2 } \).

For the harmonic travelling wave \(y=2\cos { 2\pi } \left( 10t-0.0080x+3.5 \right) \), where, x and y are in cm and t is in second. What is the phase difference between the oscillatory motion at two points separated by a distance of What is the phase difference between the oscillation of a particle located at x=100 cm, at t=Ts and t = 5s?

Explain why (or how) bats can ascertain distance, directions, nature and sizes of the obstacles without any eyes?

A particle is subjected to two simple harmonic otions in the same direction having equal magnitude and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motion. Fnd the phase difference between two individual motions.

A particle moving with SHM ina stright line has a speed of 6 m/s when 4 m/s from the centre of oscillation and a speed of 8 m/s when 3 m from the oscillation and the shortest time taken by the partile in moving from the extreme position to a point mid way between the extreme position and the centre.

A spring of force constant \({ 1200\ Nm }^{ -1 }\)is mounted on a horiontal table as a mass of 3 kg is attached to the free end of the spring, pulled sideways to adistance of 2.0 cm and released. Determine
(i) The frequency of oscillations.
(ii) The maximum acceleration of the mass, and
(iii) the maximum speed of the mass?

The motion of a particle executing simple harmonic motion is described by the displacement function, x(t) = A cos (ωt + φ ).
If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is π s^–1. If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.

A box of 1.00 m³ is filled with nitrogen at 1.5 atm at 300 K. The box has a hole of an area 0.010 mm² . How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm.

Given below are densities of some solids and liquids.Give rough estimate of the size of their atoms.

[Hint : Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use the known value of Avogadro’s number. You should, however, not take the actual numbers you obtain for various atomic sizes too literally. Because of the crudeness of the tight packing approximation, the results only indicate that atomic sizes are in the range of a few Å].

A Carnot cycle is performed by 1 mole of air (r = 1.4) initially at 327^o C. Each stage represents a compression or expansion in the ratio 1:6 (a) Calculate the lowest temperature
(b) Calculate network done during each side
(c) Calculate efficiency of the engine
Take R = 8.31 J/ mol^-K

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system in thermally insulated. The stopcock is suddenly opened. Answer the following
(a) What is the change in internal energy of the gas?
(b) What is the change in temperature of the gas?
(c) Do the intermediate states of the system (before settling to the final equilibrium state) lie on its p - V - T surface?

A circular disc made by iron is rotating about its axis of rotation with a uniform angular speed \(\omega \)
Determine the change in the linear speed of particle at the rim in percentage. The disc of rim is slowly heated from 20^o C to 50^o C keeping the angular speed uniform. Give that coefficient of linear expansion for the material of iron is  \(1.2\times 10^{ -5\quad }\)\(^{0}\)C^-1

A copper cube of mass 200 g slides down on a rough inclined plane having inclination 37^o at a constant speed. If any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperature of the block as it slides down through 60 cm. Given, specific heat of copper is 420 J Kg^-1K^-1 .

A brass wire 1.8 m long at 27^o C is held taut with little tension between two rigid support. If the wire is cooled to a temperature of -39^o C, what is the tension developed in the wire if its diameter is 2mm?

Answer the following.
(a) The triple-point of water is a standard fixed point in modern thermometry. Why ? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale) ?
(b) There were two fixed points in the original Celsius scale as mentioned above which were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one of the fixed points is the triple-point of water, which on the Kelvin absolute scale is assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale?
(c) The absolute temperature (Kelvin scale) T is related to the temperature t_c on the Celsius scale by t_c = T – 273.15 Why do we have 273.15 in this relation, and not 273.16?
(d) What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?

What is the temperature of the triple point of water on an absolute scale whose unit interval size is equal to that of the fahrenheit scale?

The flow of blood in a larger artery of an anesthetised dog is diverted through a venturimeter. The wider part of the meter has a cross-sectional area equal to that of the artery, a1 = 8mm2. The narrow part has an area a2 = 4mm2. The pressure drop in the artery is 24 Pa. What is the speed of the blood in the artery?

A fully loaded Boeing aircraft has a mass of 3.3\(\times \)10⁵ kg. Its total wing area is 500 m². It is in level flight with a speed of 960 km/h
Estimate the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface.[The density of air is \(\rho \)= 1.2 kgm^-3

Near the surface of the river, the velocity of water is 160 kmh ^-1 .Find the shearing stress between horizontal layers of waters, if the river is 6 m deep and the coefficient of viscosity of water is 10^-2 poise.

If 27 drops of rain were to be combine to form one new large spherical drop, then what should be the velocity of this large spherical drop? Consider the terminal velocity of 27 drops of equal size falling through the air is 0.20 ms^-1

The flow rate of water is 0.58 L/mm from a tap of diameter of 1.30 cm. After some times, the flow rate is increased to 4 L/min. Determine the nature of the flow for both the flow rates. The coefficient of visocity of water is 10^-3 Pa-s and the density of water is 10³ kg/m³.

Perfect Black Body
Calculate the temperature (in K) at which perfect black body radiates energy at the rate of 5.67 W/cm² .Given, \(\sigma\) = 5.67 x 10^{- 8} Wm^-2 K^-4

A Hot Body Radiating Energy
A hot body having the surface temperature 1327⁰C. Determine the wavelength at which it radiates maximum energy. Given wien's constant = 2.9 x 10^-3 mK.

What do you understand by thermal resistance?
closed cubical box is made of perfectly insulating material and the only way for heat to enter or leave the box is through two solid cylindrical metal plugs, each of cross-sectional area 12 cm² and length 8 em fixed in the opposite walls of the box. The outer surface of one plug is kept at a temperature of 100°C while the outer surface of other plug is maintained at a temperature of 4°C. The thermal conductivity of the material of the plug is 2.0 W/m-°C. A source of energy generating 13 W is enclosed inside the box. Find the equilibrium temperature of the inner surface of the box assuming that it is the same at all points on the inner surface

Find the ratio of \(\frac { \triangle Q }{ \triangle U } \quad and\quad \frac { \triangle Q }{ \triangle W } \) in an isobaric process. The ratio of molar specific heats, \(\frac { C_{ p } }{ { C }_{ v } } =\gamma \) .

1g of water at 100⁰C is converted into steam of the same temperature.If the volume of steam is 1551 cm³, find out the change in internal energy of the water.Latent heat of steam= \(2256\times { 10 }^{ 3 }J/kg\) . Consider atm pressure.

Consider a Carnot cycle operating between T₁ = 500K and T₂ = 300K producing 1KJ of mechanical work per cycle. Find the heat transferred to/by the engine by/to the reservoir.

A refrigerator has to transfer an average of 263J of heat per second from temperature -10⁰C to 25⁰C.Calculate the average power consumed, assuming no energy losses in the process.

What is the average distance between atoms (interatomic distance) in water? Use the data given in Examples : (i) The density of water is 1000 kgm^-3. The density of water vapour at 100⁰C and 1 atm pressure is 0.6 kgm ^-3 .The volume of a molecule multiplied by the total number gives ,what is called, molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure.
(ii) Estimate the volume of a water molecule using the data in Example : The density of water is 1000 kgm^-3. The density of water vapour at 100⁰C and 1 atm pressure is 0.6 kgm ^-3 .The volume of a molecule multiplied by the total number gives ,what is called, molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure.

Two non-reactive gases are kept in a container. The ratio of their partial pressures is given 5:3. Find the ratio of number of molecules.

A gas at 27⁰C in a cylinder has a volume of 4L and pressure 100 N/m². If the gas is first compressed at constant temperature so that the pressure is 150 N/m². Estimate the change in volume.  

A container is filled with a gas at a pressure of 76 cm of mercury at a certain temperature. The mass of a gas is increased by 50% by introducing more gas in the container at same temperature. Calculate the final pressure of the gas.

If the mass of each molecule of a gas is halved and speed is doubled. Find the ratio of initial and final pressure.

Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both:
(a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.
(b) Waves produced in a cylinder containing a liquid by moving its piston back and forth.
(c) Waves produced by a motorboat sailing in water.
(d) Ultrasonic waves in air produced by a vibrating quartz crystal.

A Cubical Body Gets Deformed
If the angle of shear is 30\(^0\) for a cubical body and the change in length is 250 cm, then what must be the volume of this cubical body ?

An Elongated Wire
If a wire of length 4 m and crosssectional area of 2m² is stretched by a force of 3 KN, then determine the change in length due to this force. Given Young's modulus of material of wire 110 x 10⁹ N/m².

Elongation of Copper Wire
A copper wire is streched by 10 N force. If radius of wire decreases by 2%. How will Young's modulus of wire be affected?

Volumetric Analysis 
What will be the decrease in vloume of 100 cm³ of water under pressure of 100 atm if the compressibility of water is 4 x 10^-5 per unit atmospheric pressure?

Shear Modulus is Less than Young's Modulus
The shear modulus of a material is always considerably smaller than the Young's modulus for it. What does it signify?

The potential energy of a particle of mass 1 kg in motion along the x-axis is given by U = 4 (1 - cos 2x) J Here x is in metres . Find the period of small oscillations.

A body of mass m falls from a height h on to the pan of a spring balance. The masses of the pan and spring are negligible. The spring constant of the spring is k. Having stuck to the pan the body starts performing harmonic oscillations in the vertical direction. Find the amplitude and energy of oscillation.

Two linear simple harmonic motions of equal amplitudes and frequencies ω and 2ω are impressed on a particle along the axes of X and Y respective/yo If the initial phase difference between them is π/2 find the resultant path followed by the particle.

A particle is vibrating in SHM when the displacements of the particle from its equilibrium position are x₁ and x₂ it has velocities v₁ and v₂ respectively. Show that its time period is given by \(T=2\pi\sqrt{x_1^2-x_2^2\over v_2^2-v_1^2}\)

What will be the value of g at the bottom of sea 7 km deep?Diameter of the earth is 12800 km and g on the surface of the earth is 9.8 ms^-2 .

As you will learn in the text, a geostationary satellite orbits the earth at a height of nearby 36000 km from the surface of the earth.What is the potential due to the earth's gravity at the site of this satellite?(take the potential energy at infinity to be zero).Mass of the earth = \(6.0\times { 10 }^{ 24 }\)kg, radius = 6400 km.

An earth's satellite has a period of 90 min.Assuming the orbit to be circular, calculate its height.Take radius of the earth equal to 6380 km and g at the surface of the earth equal 9.8m/s² .

Shweta was reading a book on the biography of Issac Newton. She read that Newton was sitting under an apple tree when a falling apple led him to develop a whole new science of gravity. After reading the book, shweta realised that every phenomenon in universe has some scientific fact associated with it, it depends on us whether we look for a scientific fact or associate a superstition with it.
How can you find the mass of the earth using law of gravitation?

Arjun was a student of class IX. He was sitting in a garden along with his grandmother, who was a retired physics teacher. Suddenly he saw an orange falling from the tree. Immediately he asked his grandmother that both of the orange and earth experience equal and opposite forces of gravitation, then why it is the orange that falls towards the earth and not the earth towards the orange. His grandmother explained him the reason in a simple way.
(i) What are the values being displayed by Arjun?
(ii) What in your opinion may be the reason for this observation?

Two bodies of masses 1 kg and 2 kg are located at (1, 2) and (-1, 3), respectively. Calculate the coordinates of the centre of mass.

Centre of gravity of a body on the earth coincides with its centre of mass for a small object and for a large object, it may not. What is the qualiative meaning of small and large in this regards? For which following two of them coincides, a building, a pond, a lake, a mountain.

The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds.
(i) What is its angular acceleration, assuming the acceleration to be uniform?
(ii) How many revolutions does the engine make during this time?

To maintain a rotor at a uniform angular speed of 200 rad s^-1, an engine needs to transmit a torque of 180 N m. What is the power required by the engine ? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100% efficient.

Since his childhood Sanjay had always seen his mother grinding flour in the grindstone. He had observed that his mother had to do a lot of hand work in order to get flour from wheat. He felt very helpless at that time. As he grew older he thought of an idea to connect an electric motor to the wheel of grindstone . Now, it become very easy to get flour with help of grindstone and now his mother is very happy and felt proud of his intelligence.
A grinding stone of diameter 4 m revolving at 120 rpm accelerates to 660 rpm in 9s. Calculate the angular acceleration and linear acceleration.

The nucleus Fe²⁷ emits a \(\gamma \)-ray of energy 14.4 keV. If the mass of the nucleus is 56.935 amu, calculate the recoil energy of the nucleus.

One day Pawan went to super market to purchase some groceries. There he saw an old lady struggling with her shopping. He immediately showed her the lift and explained to her how she can carry her goods from one floor to the other. Even then the old lady showed hesitation to use the lift. On seeing this, Pawan took the lady into the lift and showed her how to operate the lift. The old lady was very happy and easily finished her shopping.
(i) An elevator which can carry a maximum load of 1800 of 2m/s. The frictional force opposing he motion is 4000 N.Determine the maximum power delivered by the motor to the elevator in horse power.

Rocket Propulsion
A toy rocket of mass 0.1 kg has a small fuel of mass 0.02 kg which it burns out in 3 s. Starting from rest on horizontal smooth track it gets a speed of 20 ms^-1 after the fuel is burnt out. What is the approximate thrust of the rocket ? What is the energy content per unit mass of the fuel ? (Ignore the small mass variation of the rocket of the rocket during fuel burning).

When a pebble Hits the Ground
Consider a drop of small pebble of mass 1.00 g falling from a cliff of height 1.00 km. It hits the ground with a speed of 50.0 ms^-1. What is the work done by the unknown resistive force ?

A railway carriage of mass 9000kg moving with a speed of 36km/h collides with stationary carriage of the same mass. After the collision, the carriage get coupled of the same mass. After the collision, the carriage get coupled and move together. What is their common speed after collision? what type of collision is this?

A cyclist speeding at 18 km/h on a level road takes a sharp circular turn of radius 3 m without reducing the speed. The co-efficient of static friction between the tyres and the road is 0.1. Will the cyclist slip while taking the turn?

A circular racetrack of radius 300 m is banked at an angle of 15°. If the coefficient of friction between the wheels of a race-car and the road is 0.2, what is the (a) optimum speed of the racecar to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping ?

The radius of curvature of  a railway track at a place, where the train is moving at  a speed of 72kmh^-1 is 625m. The distance between the rails is 1.5m. Find the angle and the elevation of the out rails so that there may be no side pressure on the rails. Take, g = 9.8 \({ m }/{ { { s }^{ 2 } } }\)
\(\left[ { tan }^{ -1 }(0.00653)=3.7{ 4 }^{ o },sin3.7{ 4 }^{ o }=0.06522 \right] \)

A girl riding a bicycle along a straight road with a speed of 5 m/ s throws a stone of mass 0.5 kg which has a speed of 15 m /s with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown ? What is the change in speed, if so ?

Vipul was driving on the road with his old grandmother. She was sitting on the front seat with him. When vipul was about to reach his destination, he stopped the engine and did not apply the brakes. Even then the car was running on the road for sometimes.
His grandmother surprised and asked her grandson the reason the car running without the engine on. Vipul was the student of science studying in class XIth. He explained his grandmother that it is only the momentum due to which the car is going on.
(i) What values Vipul exhibit here ?
(ii) What is momentum and on which factor it depends ?

The reading of pressure meter attached with a closed pipe is \(3.5\times { 10 }^{ 5 }Nm^{ -2 }\)  .On opening the valve of the pipe, the reading of the pressure meter is reduced to \(3.0\times { 10 }^{ 5 }Nm^{ -2 }\) .Calculate the speed of the water flowing in pipe.

A liquid is kept in cylindrical vessel which is rotated along its axis. The liquid rises at the sides. If the radius of vessel is 0.05 m and the speed of rotation is 2 rev/s, find the difference in height of the liquid at the centre of the vessel and its sides.

Explain why
(a) To keep a piece of paper horizontal, you should blow over, not under, it
(b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
(c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
(d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel (e) A spinning cricket ball in air does not follow a parabolic trajectory

Explain why?
A fluid flowing out of small hole in vessel results in a backward thrust on the vessel.  According to Bernoulli's theorem, for horizontal flow of fluids,  \(\left( p+\frac { 1 }{ 2 } \rho { v }^{ 2 }=constant \right) \) Therefore, when velocity of fluid increases, its pressure decreases and vice-versa.

Mercury has an angle of contact equal to 140⁰ with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of th experiment is 0.456 N/m .Density of mercury? =13.6\(\times\)10³ kg/m³

What is the length of a wire that breaks under its own weight when suspended vertically? Breaking stress = 5 x 10⁷ Nm^-2 and density of the material of the wire = 3 x 10³ kg/m³

Two wires of equal cross-section but one made of steel and the other copper are joined end to end. When the combination is kept under tension, the elongation in the two wires is found to be equal. Given Young's moduli of steel and copper are 2.0 x 10¹¹ Nm^-2 and 1.1 x 10¹¹Nm^-2 Find the ratio between the lengths of steel and copper wires

The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm² . Calculate the elongation of the wire when the mass is at the lowest point of its path.

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column. Young's modulus, \(\Upsilon \) = 2.0 x 10¹¹ Pa.

A spaceship is launched into a circular orbit close to the surface of the earth. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull.

Consider two solid uniform spherical object of the same density \(\rho \) . One has a radius R and the other a radius 2R. They are in outer space where the gravitational field from other objects are negligible. If they are at rest with their surfaces touching, then what is the contact force between the objects due to their gravitational attraction?

Choose the correct alternatives.
Acceleration due to gravity increases/decreases with increasing depth(assume the earth to be a sphere of uniform density).

The planet Neptune travels around the sun with a period of 165 yr. Show that the radius of its orbit is approximately thirty times that of the earth's orbit, both being considered as circular.

A particle is fired vertically upwards with a speed of 15 km/s. Find the speed of particle when it goes out of the earth's gravitational pull.

In given pulley mass system, mass m₁ = 500 g, m₂ = 460 g and the pulley has a radius of 5 cm. When released from rest, heavier mass falls through 7.50 cm in 5 s. There is no slippage between pulley and string.
(i) What is magnitude of acceleration of mass?
(ii) What is magnitude of pulley's angular acceleration?

Find the centre of mass for a solid cone of base radius r and height h.

A man stands on a rotating platform with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform in 30 rpm. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90 cm to 20 cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg-m².
Is kinetic energy conserved in the process? If not, from where does the change come about?

A motorboat is racing towards north at 25 km/h and the water current in that region is 10 km/h in the direction of 60° east of south. Find the resultant velocity of the boat.

A soccer player kicks a ball at an angle of \({ 30 }^{ \circ }\)with an initial speed of 20m/s. Assuming that the ball travels in a vertical plane. Calculate the maximum height reached\(g=10m/s^{ 2 }\)

A cricket ball us thrown at a speed of 28\({ ms }^{ -1 }\)in a direction \({ 30 }^{ \circ }\)above the horizontal. 
(i) the maximum height
(ii) the time taken by the ball to return to the same level and
(iii) the distance from the thrower to the point where the baU returns to the same level.

A body of mass 10 kg revolves in a circle of diameter 0.4m making 1000 revolutions per minute. Calculate its linear velocity and centripetal acceleration.

From a school, a group of boys went for a picnic in a village. They went through fields and enjoyed the beauty of nature. While walking, they saw a well which they had never seen in the city. They were very excited and started drawing water from well. They planned to have a competition in which they decide that the who would draw more water would become winner . A villager who was listening to them, went to them and told them about the importance of water. He also explained that they use the water of this for irrigating their fields and also for drinking.
If the two boys raising the bucket, pull it an angle \(\theta \) to each other and each exerts a force of 20N, their effective pull is 30N. What is the angle between their arms?

A train 100 m long is moving with a speed of 60 km/h. In what time shall it cross a bridge of 1 km long?

During a hard sneeze, your eyes might shut for 0.5 s. If you are driving a car at 90 km/h during such a sneeze, how far does the car move during that time?

If the average speed of the particle is [ \({ 2t }^{ 2 }\hat { i } +3t\hat { j } \) ], then find out the instantaneous speed of the particle.

Prove Galileo's Law of Odd Numbers

The sun's angular diameter is measured to be 1920. The distance r of the sun from the earth is \(1.496\times { 10 }^{ 11 }\) m. What is the diameter of the sun?

Write down the number of significant figure in the following.
0.060

A drop of olive oil of radius 0.25 mm spreads into a circular film of radius 10 cm on the water surface. Estimate the molecular size of olive oil.

The refractive index of water is found to have the values 1.29,1.33,1.34,1.35,1.32,1.36,1.30 and 1.33.Calculate mean absolute error

The refractive index of water is found to have the values 1.29,1.33,1.34,1.35,1.32,1.36,1.30 and 1.33.Calculate fractional error

A guitar string is 90 cm long and has a fundamental frequency of 124 H. Where should it be pressed to produce a fundamental frequency of 180 Hz?

A standing wave is formed by two harmonic waves, \({ Y }_{ 1 }=Asin(kx-\varpi t)\)and \({ Y }_{ 2 }=Asin(kx-\varpi t)\)travelling on a string in opposite directioons. Mass density of the string is \(\rho \) and area of cross-section is s. Find the total mechanical energy between two adjacent nodes on the string.

A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. What is the speed of sound in each case? The speed of sound in still air can be taken as 340ms^-1.

One end of a long string of linear mass density 8.0 x 10^-3 kg m^-1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90kg. The pulley end absorbs all the incoming energy so that reflected waves at the end have negligible amplitude. At t=0, the left and (fork end) of the string  x = 0 has zero transverse displacement (y=0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string.

When the mass is displaced a little to one side, one spring gets compressed and another is elongated.Due to which the combination of sp[rings. Here, effective spring factor k will be given by \(k={ k }_{ 1 }+{ k }_{ 2 }=600+600=1200{ Nm }^{ -1 }\)

The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis sjows that T is greater than \(2\pi \sqrt { \frac { l }{ g } } \) .Think of a qualitative argument to appreciate this result.

Let us take the position of mass when the spring is unstretched as x = 0 and the direction from left to right as the positive direction of the x-axis. Given x as a function of time t for the oscillating mass, if at the moment we start the stopwatch (t = 0), the mass is at the maximum stretched position.
In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?

A body weighing 10 g has a velocity of 6 cms^-1 after one second of its starting from mean position. If the time period is 6 s, then find the kinetic energy, potential energy and the total energy.

Write the difference between ideal gas and real gas.

If one mole of a monoatomic gas is mixed with three moles of a diatomic gas.What is the molar specific heat of mixture at constant value?[Take, R = 8.31 J mol^-1K^-1]

A gaseous mixture contain 16 g of helium and 16g of oxygen, then calculate the ratio of C_p/C_V of the mixture.

What will be the mean free path of nitrogen gas at STP of given diameter of nitrogen molecule = 2\(\overset { 0 }{ A } \) ?

A monoatomic ideal gas\((\gamma =\frac { 5 }{ 3 } )\)initialy at 17⁰C is suddenly compressed to one-eight of its original volume. Find the final temperature after compression.

Explain why
(a) Two bodies at different temperatures T₁ and T₂ if brought in thermal contact do not necessarily settle to the mean temperature (T₁ + T₂ )/2.
(b) The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.
(c) Air pressure in a car tyre increases during driving. (d) The climate of a harbour town is more temperate than that of a town in a desert at the same latitude.

In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case ? (Take 1 cal = 4.19 J)

At what temperature, if any, do the following pairs of scales gives the same reading?
Fahrenheit and Kelvin.

A box having total surface area 0.05 m² and of 6 mm thick side walls is filled with melting ice and kept in room. Calculate the thermal conductivity of the box material if 0.5 kg of ice melts in 1 h. The room temperature is 40^o C and latent heat of fusion of ice = \(3.33\times { 10 }^{ 5 }J{ kg }^{ -1 }\)

Explain the following
(i) Hot tea cools rapidly when poured into the saucer from the cup.
(ii) Temperature of a hot liquid falls rapidly in the beginning but slowly afterward.
(iii) A hot liquid cools faster if outer surface of the container is blackened.

A fat man is used to consuming about 3000 kcal worth of food every day. His food contains 50g of butter plus a plate of sweets every day, besides items which provide him with other nutrients (proteins, vitamins, minerals, etc) in addition to fats and carbohydrates. The calorific value of 10g of butter is 60kcal and that of a plate of sweets is of average 700kcal per day? Assume the man cannot resist eating the full plate of sweets once it is offered to him.

A metallic ball has a radius of 9.0 cm at 0⁰C. Calculate the change in its volume when it is heated to 90⁰ C. Given the coefficient of linear expansion of metal of ball is 1.2 x 10^-5 K.

27 identical drops of water are falling down vertically in air each with a terminal velocity 0.15\(ms^{ -1 }\)>if they combine to form a single bigger drop, what will be its terminal velocity?

Two soap bubbles have radii in the ratio2:3.Compare the excess of pressure inside these bubbles.

(a) What is the largest average velocity of blood flow in an artery of radius 2 \(\times\) 10^{- 3}m, if the flow must remain laminar?
(b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 x 10^–3 Pa -s)

What is the corresponding flow rate? (Take viscosity of blood to be 2.084\(\times\) 10^{- 3}Pa-s)

Show that ifn equal rain droplets falling through air with equal steady velocity ono cms^-1 coalesce, the resultant drop attains a new terminal velocity ono n^2/3cms^{- 1}.

Two parallel steel wires A and B are fixed to rigid support at the upper ends and subjected to the same load at the lower ands. The lengths of wires are in the ratio 4:5 and their radii are in the ratio 4:3. The increase in the length of the wire A is 1mm. Calculate the increase in the length of the wire B.

Determine the volume contraction of a solid copper cube, 10cm on an edge, when subjected to a hydraulic pressure of 7 x 10⁶ Pa. Bulk modulus for copper = 140 x 10⁹ Pa.

Read the following two statements below carefully and state, with reasons, if it is true or false.
(a) The Young’s modulus of rubber is greater than that of steel;
(b) The stretching of a coil is determined by its shear modulus.

A steel wire of length 4 m is stretched through 2 mm. The cross-section area of the wire is 2.0 mm². If Young's modulus of steel is 2.0 x 10¹¹ N/m², find
(i) the energy density of the wire and
(ii) the elastic potential energy stored in the wire.

Explain why steel is more elastic than rubber.

An artificial satellite is going round the earth, close to the surface. What is the time taken by it to complete one round?

The distances of two planets from the sun are 10¹³ m and 10¹² m, respectively. Calculate the ratio of time period and the speeds of the two planets

If the earth is 1/4 of its present distance from the sun, then what is the duration of he year?

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R(radius of earth) are 10\({ m }/{ { s }^{ 2 } }\)and 6400km, respectively.What is the required energy for this work done?

What will be the potential energy of a body of mass 67kg at a distance of \(6.6{ \times 10 }^{ 10 }m\)from the centre of the earth? Find gravitational potential at this distance.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weight 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.
(Hint: The moment of inertia of the door about the vertical axis at one end is ML²/3.)

A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination \({ 30 }^{ \circ }\). The coefficient of static friction, \({ \mu }_{ s }=0.25\).
(a) How much is the force of friction acting on the cylinder?
(b) What is the work done against friction during rolling?
(c) If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?

A particle on a rotating disc have initial and final angular position are -2rad, +6rad. In which case, particle undergoes a negative displacement.

A particle on a rotating disc have initial and final angular position are -4rad, -8rad. In which case, particle undergoes a negative displacement.

The blades of windmill sweep out a circle of area A.
(i) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?
(ii) What is the kinetic energy of the air?
(iii) Assume that the windmill converts 25% of the wind's energy v=36km/h and density of the air is 1.2 kg m. What is the el;ectrical power produced?

Under the correct alternative.
Whan a conservation force does positive work on a body, the potential energy of the body increase decrease/remains unaltered.

Work done by a body against friction always results in a loss of its kinetic/potential energy

The rate of change of total momentum of a many particle systems is proportional to the external force/sum of the internal forces on the system.

A hammer weighing 1 kg moving with the speed of 20 m / s strikes the head of a nail driving it 20 cm into a wall. Neglecting the mass of the nail, calculate
(i) the acceleration during the impact
(ii) the time interval during the impact
(iii) the impulse.

Give the magnitude and direction of the net force acting on a cork of mass 10 g floating on water.

Give the magnitude and direction of the net force acting on a kite skillfully  held stationary in the sky.

A stone of mass 0.4 kg is thrown vertically upward wit a speed of 9.8 m/s/ Find the potential and kinetic energies after half second?

A running man has half the kinetic energy that a boy of his mass has. the man speeds up by 1.0 m/s and then same energy as the boy. what were the original speeds of the man and the boy?

State if each of the following staement is true or false. Give reasons for your answer.
(i) Total energy of a system is always conserved, no matter what internal and external forces on the body are present?
(ii) Work done in the motion of a body over a closed loop is zero for every force in nature.
(iii) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Answer carefully with reasons
(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls i.e. when they are in contact?
(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls ?
(c) What are the answers to (a) and (b) for an inelastic collision ?
(d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful
Adding a scalar to a vector of dimensions

State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful
Adding any two vectors

State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful.
adding a component of a vector to the same vector.

If A and B are two vectors such that \(\left| A\times B \right| =\sqrt { 3 } A.B\) Then,
Also, find the value of  \(\left| A\times B \right| \)

A ball rolls of the top of a stairway with horizontal velocity of 1.8 m/s. The steps are 0.24 m high and 0.2 m wide. Which step will the ball hit first? Take g=9.8 m/s²

Two parallel rail tracks run North-South.Train A moves North with a speed of 54 kmh^-1. and train B moves South with a speed of 90 kmh^-1. What is the relative velocity of ground with respect to B?

(i) Draw position-time graph for
(a) Accelerated motion  
(b) Retarded motion
(ii) A juggler throws balls into air. He throws one whenever the previous one is at its highest point.How high do the balls rise if he throws n balls in each second? Take acceleration due to gravity as g.

A juggler throws balls into air. He throws one whenever the previous one is at its highest point.How high do the balls rise if he throws n balls in each second? Take acceleration due to gravity as g.

A motor boat covers the distance between two spots on the river in t₁= 8 h and t₂ = 12 h, downstream and upstream, respectively.What is the time required for the boat to cover this distance in still water?

A train passes a station A at 40 kmh -I and maintains its speed for 7 km an? is then uniformly retarded, stopping at B which is 8.5 km from A. A second train starts from A at the instant the first train passes and being accelerated some part of the journey and uniformly retarded for the rest, stops at B at the same times as the first train. Calculate the maximum speed-of the second train, use only the graphical method.

Write down the number of significant figure in the following.
3.08 x 10¹¹

The refractive index of water is found to have the values 1.29,1.33,1.34,1.35,1.32,1.36,1.30 and 1.33.Calculate mean value of refractive index

Derive the dimensions formula of physical quantities. Velocity gradient

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 Å). Why is this ratio so large ?

Two resistors of resistance \({ R }_{ 1 }=\left( 100\pm 3 \right) \Omega \) and \({ R }_{ 2 }=\left( 200\pm 4 \right) \Omega \) are connected (i) in series, (ii) in parallel. Find the equivalent resistance of the series combination. Use for the relation R = R₁ + R₂.

The shells of crabs found around a particular coastal location in Japan seem mostly to resemble the legendary face of a Samurai. Given below are two explanations of this observed fact. Which of these strikes you as a scientific explanation?
(a) A tragic sea accident several centuries ago drowned a young Samurai. As a tribute to his bravery, nature through its inscrutable ways immortalized his face by imprinting it on the crab shells in that area.
(b) After the sea tragedy, fishermen in that area, in a gesture of honour to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a Samurai. Consequently, the particular shape of the crab shell survived longer and therefore in course of time the shape was genetically propagated. This is an example of evolution by artificial selection.
[Note: This interesting illustration taken from Carl Sagan's 'The Cosmos' highlights the fact that often strange and inexplicable facts which on the first sight appear 'supernatural' actually turn out to have simple scientific explanations. Try to think out other examples of this kind].

Give the salient features of Einstein's theory.

Name four fundamental forces in nature.

Does imagination play any role in physics?

Physics has a very limited scope and only in practice of a few blessed ones. Do you agree?

A helicopter of mass 1000 kg reises with a vertical acceleration of 15m /s². The crew and the passengers weigh 300 kg. Give the magnitude and direction of the force on the helicopter due to the surrounding air, take g = 10 m/s².

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?

An aircraft executes a horizontal loop at a speed of 720km/h with its wings banked at 15^o . What is the radius of the loop?

Ten one-rupee coins are put on top of each other on a table. Each coin has mass m. Give the magnitude and direction of  the reaction of the 6th coin on the 7th coin.(counted from the bottom)

A light, inextensible string connects two blocks of mass M₁, and M₂. A force Facts upon M_I. Find acceleration of the system and tension in siring.

The velocity of a particle, when it is at the greatest height is \(\sqrt { 2/5 } \) times its velocity when it is at half of its greatest height. Determine its angle of projection.

Find the angle made by vector, \(A=2\hat { i } +2\hat { j } \)  with x-axis

Two billiard balls are rolling on a flat table. One has the velocity components \({ v }_{ x }=1{ ms }^{ -1 },\ { v }_{ y }=\sqrt { 3 } { ms }^{ -1 }\) and the other has components v'_x =2 ms^-1 and v'_y =2 ms^-1 If both the balls start moving from the same point, what is the angle between their paths?

To what height does the ball rise and after how long does the ball return to the player's hands?(Take g = 9.8ms^-2 and neglect air resistance)

Read each statement below carefully and state with reasons and examples, if it is true or false ; A particle in one-dimensional motion
(a) with zero speed at an instant may have non-zero acceleration at that instant
(b) with zero speed may have non-zero velocity,
(c) with constant speed must have zero acceleration,
(d) with positive value of acceleration must be speeding up.

A particle starts moving from position of rest under a constant acceleration. It is travels a distance x in t second, what distance will it travel in next t second?

A police van moving on a highway with a speed of 30 km h^–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h–1. If the muzzle speed of the bullet is 150 m s^–1, with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

A person travels along a straight road for the first half with avelocity v1 and the second half with velocity v₁ and the second half with velocity v₂. What is the mean velocity of the person?

The sides of a rectangle are \((10.5\pm 0.2)\) cm and \((5.2\pm 0.1)\) cm. Calculate its perimeter with error limits.

A capacitor of capacitance \(C=(2.0\pm 0.1)\mu F\) is charged to a voltage \(V=(20\pm 0.5)V\). Calculate the charge Q with error limits.

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

It is often said that the world is witnessing now a second industrial revolution which will transform the society as radically as did the first. List some key contemporary areas of science and technology which are responsible for this revolution.

Though the law gives women equal status in India, many people hold unscientific views on a woman's innate nature, capacity and intelligence and in practice give them a secondary status and role.
Demolish this view using scientific arguments and by quoting examples of great women in science and other spheres and persuade yourself and others that given equal opportunity, women are on par with men.

The shells of crabs found around a particular coastal location in Japan seem mostly to resemble the legendary face of a Samurai. Given below are two explanations of this observed fact. Which of these strikes you as a scientific explanation?
(a) A tragic sea accident several centuries ago drowned a young Samurai. As a tribute to his bravery, nature through its inscrutable ways immortalized his face by imprinting it on the crab shells in that area.
(b) After the sea tragedy, fishermen in that area, in a gesture of honour to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a Samurai. Consequently, the particular shape of the crab shell survived longer and therefore in course of time the shape was genetically propagated. This is an example of evolution by artificial selection.
[Note: This interesting illustration taken from Carl Sagan's 'The Cosmos' highlights the fact that often strange and inexplicable facts which on the first sight appear 'supernatural' actually turn out to have simple scientific explanations. Try to think out other examples of this kind].

Textbooks on science may give you a wrong impression that studying science is dry and all too serious and that scientists are absent-minded introverts who never laugh or grin. This image of science and scientists is patently false. Scientists, like any other group of humans, have their share of humorists, and many have led their lives with a great sense of fun and adventure, even as they seriously pursued their scientific work. Two great physicists of this genre are Gamow and Feynman. You will enjoy reading their books listed in the Bibliography.

Give the salient features of Einstein's theory.

What frequency of the sound you hear coming directly from the siren?

A steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed of a transverse wave on this wire when a tension of 2.06\(\times \)10⁴N is applied?

A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of 1237.5 Hz? (sound velocity in air = 330ms^-1)

Equation of a plane progressive wave is given by y = 0.6 sin\(2\pi \left( t-\frac { x }{ 2 } \right) \) On reflection from a denser medium, its amplitude becomes 2/3 of the amplitude of  incident wave. What will be equation of reflected wave?

At what temperature (in ⁰C) Will be speed of sound air be 3 times its value at 0⁰ C?

A body of mass 12 kg is suspended by coil spring of natural length 50 cm and force constant 2.0 x 10³Nm^-1. What is the streched length of the spring?If the bosy is pulled down further streching the spring to a length of 5.9 cm and then released,then what is the frequencyof oscillation of the suspended mass?

A spring compressed by 0.1 m develops a restoring force 10 N. A body of mass 4 kg placed on it . Deduce
(i) the force constant of the spring
(ii) the depression of the spring under the weight of the body (take g=10 N/kg)
(iii) the period of oscillation, the body is distributed and
(iv) the frequency of oscillation 

A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillation is found to be 1.5 s. The radius of the disc is 15 cm.Determine the torsional spring constant of the wire.
This is a question based on torsion pendulum for which \(T=2\pi \sqrt { \frac { \quad }{ \alpha } } \) where I = moment of inertia of the disc about axis of rotation,\(\alpha \) = torsion constant which is restoring couple per unit twist.

Define the restoring force and it characterstic in case of an oscillating body.

A particle excutes SHM of period 8 s. After what time of its passing through the mean position will be energy be half kinetic and half potential?

The value of root mean square speed for O₂ is 400 m/s. Find the temperature of the O_2.

If value of most probable speed for an ideal gas is 500 m/s. Find the value of root mean square speed for this gas.

Find the temperature at which rms speed of a gas is half of its value of 0⁰C, pressure remaining constant.

We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state? (Hydrogen molecules can be consider as spheres of radius 1 \(\overset { o }{ A }\)).

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules ? Is the root mean square speed of molecules the same in the three cases? If not, in which case is v_rms the largest ?

A person of mass 60 kg wants to lose 5 kg by going up and down a 10 m high stairs. Assume he burns twice as much fat while going up than coming down. If 1kg of fat is burnt on expending 7000 kcal calories, how many times must he go up and down to reduce his weight by 5 kg?

What amount of heat must be supplied to 2.0 × 10^–2 kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure ? (Molecular mass of N₂ = 28, R = 8.3 J mol^-1 K^-1)

The efficiency of a heat engine is more in hilly area than in plain.Explain it.

Is the coefficient of performance of a refrigerator, a constant quantity?

Why is it theoretically not possible to have a device which create no thermal pollution?

By how much the temperature of a copper rod to be raised so as to increase its length by 1% ? Given that coefficient of linear expansion of copper = 1.7 x 10^-5 K^-1 . 

The density of mercury is \(13.6\times { 10 }^{ 3 }Kg\quad { m }^{ -3 }\)  at 0^o C and its coefficient of volume expansion is \(1.82\times { 10 }^{ -4 }{ K }^{ -1 }\)  . Find the density at 50^o C.

What value of temperature in the Celsius and Fahrenheit scales give the same reading?

There is a slight temperature different between the water fall at the top and the bottom. Why?

Given below are observations on molar specific heats at room temperature of some common gases.

The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine ?

For a fluid in a steady flow, the increase in flow speed at a constriction follows (conservation of mass / Bernoulli’s principle)

For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater / smaller)

If the required pressure in the tyre of a car is 199 kPa, then what is the absolute pressure?

A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm² . What maximum pressure would the smaller piston have to bear ?

A vertical off-shore structure is built to withstand a maximum stress of 10⁹ Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.

A solid sphere of radius R made of a material of bulk modulus B is surrounded by a liqiud in a cylindrical container. A massless piston of area  A floats on the surface of the liqiud. When a mass M is placed on the piston on the piston to compress the liqiud, find fractiional change in the radius of the sphere?

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%? (The Bulk modulus of rubber is 9.8 x 10⁸ N/m²; and the density of seawater is 10³ kg/m ³ .)

The stress-strain graphs for materials A and B are shown in Fig. (a) and Fig. (b).

The graphs are drawn to the same scale.
(a) Which of the materials has the greater Young’s modulus?
(b) Which of the two is the stronger material?

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force j, its length increases by l. Another wire of the same material of length 2L and radius 2r, is pulled by a force 2f Find the increase in length of this wire.

A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain?

A plant moving along an elliptical orbit is closet to the Sun at a distance r₁ and farthest away at a distance of r₂ . If V₁ and V₂ are the linear velocities at these points respectively, then find the ratio v_1/v₂

If the earth be at one half of its present distance from the sun, them how many days will be there in  a year?

Calculate the force of attraction between two bodies, each of mass 100 kg 1 m apart on the surface of the earth.

The acceleration due to gravity on a planet is 1.96\({ ms }^{ -2 }\). If it is safe to jump from a height of 2m on the earth, then what will be the corresponding safe height on the planet?

Does the concentration of the earth's mass near its centre change the variation of g with height compared with a homogeneous sphere, how?

A person is standing on a rotating table with metal spheres in his hands. If he withdraw his hands to his chest, what will be the effect on his angular velocity?

Two boys of the same weight it at the opposite ends of a diameter of a rotating circular table. What happens to the speed of rotation if they move nearer to the axis of rotation?

If ice on poles melts, then what is the change in duration of day?

A solid cylinder of mass 20 kg rotates about its axis with angular speed of 100 rad/s. The radius of cylinder is 0.25m. What is KE of rotation of cylinder?

If earth contract to half its radius. What would be the length of the day?

Calculate the velocity of the bob of a simple pendulum at its mean position if it is able to rise to a vertical height of 10 cm. [g = 9.8 m/s²]

Can a body have without momentum? If yes, then explain how they are related with each other?

A spring balance reads forces in Newtons. The scale is 20 cm long and read from 0 to 60 N. Find potential energy of spring when the scale reads 20 N.

A steel spring of spring constant 150 N/m is compressed from its natural position through a mud wall 1m thick, the speed of bullet drops to 100m/s. Calculate the average resistance of the wall. Neglect friction of air.

A trolley of mass 300 kg carrying a sand bag of 25 Kg is moving uniformly with a speed of 27km/h on a frictionless track. After a while , sand starts leaking out of a whole on the floor of the trolley at the rate of 0.052 kg^-1.What is the speed of the trolley after the entire sand bag is empty?

Why are porcelain objects wrapped in paper or straw before packing for transportation ?

A passenger of mass 72.2 kg is riding in an elevator while standing on a platform scale. What does the scale read when the elevator cab is 
(i) descending with constant velocity
(ii) ascending with constant acceleration, 3.5 m/s²?

A force of 128 If acts on a mass of 490 g for 10 s. What velocity will it give to the mass ?

A body of mass 2 kg is being dragged with a uniform velocity of 2 ms ^-1 on a rough horizontal plane. The coefficient of friction between the body and the surface is 0.2. Calculate the amount of heat generated per second. Take  g =9.8 ms^-2 and J = 1.2Jcal^-1

Explain why passengers are thrown forward from their seats when a speeding bus stops suddenly,

We can order events in time and there is no sense of time, distinguishing past, present and future. Is time a vector?

The angle between vector A and B is 60⁰  .What is the ratio of A.B and \(\left| A\times B \right| \) ?

A person sitting in a running train throws a ball vertically upwards. What is the nature of the path described by the ball to a person?
(i) Sitting inside the train
(ii) Standing on the ground outside the train

A railway carriage moves over a straight track with acceleration a. A passenger in the carriage drops a stone. What is the acceleration of the stone w.r.t. the carriage and the earth?

For what condiion, an object could be considered as a point object? Describe in brief

The displacement o a particle is given by at². What is the dependency of accleration on time?

Thye position x of a body is given by x = A sin(wt). Find the time at which the displacements is maximum.

What are uses of a velocity  - time graph ?

The position of an object is given by x  = 2t² + st. Find out that its motion is uniform and nonuniform.

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance ?

Express an acceleration of 10 m/s² in km/h².

Which of the following length measurement is most accurate and why? 40.00 cm

What is common between bar and torr?

Calculate the surface area of a solid cylinder of diameter 4 cm and height 20 cm in mm²

Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said, "The most incomprehensible thing about the world is that it is comprehensible"?

Politics is the art of possible. Similarly, Science is the art of the soluble. Explain this beautiful aphorism on the nature and practice of science.

Though India now has a large base in science and technology which is fast expanding, it is still a long way for realizing its potential for becoming a world leader in Science. Name some important factors, which in your view have hindered the advancement of science in India.

The industrial revolution in England and Western Europe more than two centuries ago was triggered by some key scientific and technological advances. What were these advances?

Name the two most important contributions of Albert Einstein.

What is the nature of water waves produced by a motorboat sailing in water ?

In a hot summer day, pitch of an organ pipe will be higher or lower?

Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3loops and 4loops, the frequencies are in the ratio 1:2:3:4.

When two waves of almost equal frequencies n₁ and n₂ reach at a point, simultaneously. What is the time interval between successive maxima?