If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

If the force is proportional to square of velocity, then the dimension of proportionality constant is

How many gram make 1deca gram?

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

s-t graph shown in figure is a parabola. From this graph we find that:

From this velocity-time graph, which of the following is correct?

An object of mass m held against a vertical wall by applying horizontal force F as shown in the figure.The minimum value of the force F is

A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

Dimensional formula for work done is ________________.

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is,

A planet moving along an elliptical orbit is closest to the Sun at distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are linear speeds at these points respectively. Then the ratio \({v_1\over v_2}\) is

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_A, K_B and K_C respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then
 

A small sphere of radius 2cm falls from rest in a viscous liquid. Heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to

Two thermally insulated vessels 1 & 2 are filled with air at temp (T₁, T₂), volume (V₁, V₂ & pressure (P₁, P₂) If the valve going to the 2 vessels is opened, the temperature on the inside of the vessel at equilibrium will be ______________.

Assuming that the frequency \(\gamma\) of a vibrating string may depend upon
(i) applied force (F) 
(ii) length (I)
(ill) mass per unit length (m), prove that \(\gamma\alpha{{1}\over{l}}\sqrt{{{F}\over{m}}}\) using dimensional analysis.

Find the magnitude of vector 3\(\hat { i } -2\hat { j } +\sqrt { 3 } \hat { k } \) ?

Imagine that the gravitational force between Earth and Moon is provided by an invisible string that exists between the Moon and Earth. What is the tension that exists in this invisible string due to Earth's centripetal force? (Mass of the Moon = 7.34\(\times\)10²² kg, Distance between Moon and Earth = 3.84 \(\times\) 10⁸m).

A particle strikes a horizontal frictionless floor with a speed u at an angle \(\theta\)  with the vertical and rebounds with the speed v at an angle φ with an vertical. The coefficient of restitution between the particle and floor is e. What is the magnitude of v?

Calculate moment of inertia with respect to rotational axis xx' in following figures (a) and (b).

What is the gravitational potential energy of the Earth and Sun? The Earth to Sun distance is around 150 million km. The mass of the Earth is 5.9\(\times\)10²⁴ kg and mass of the Sun is 1.9\(\times\)10³⁰ kg.

A comet orbits the sun in highly elliptical orbit. Does a comet has a constant.
(i) Lineal speed
(ii) Angular momentum
(iii) Total Energy throughout its orbit

Consider the following cyclic process consist of isotherm, isochoric and isobar which is given in the figure.

Draw the same cyclic process qualitatively in the V-T diagram where T is taken along x direction and V is taken along y-direction. Analyze the nature of heat exchange in each process.

Define the Avogadro's number?

In a physical units, how many units are there in 1 metre?
1 parallactic second (parsec) = 3.08\(\times\)10¹⁶ m
Given data:
1 AU = 1.496\(\times\)10¹¹m
1 ly = 9.467\(\times\)10¹⁵m
1 mm = 10^-6m
1 parsec = 3.08\(\times\)10¹⁶m

Find the dimensions of a and b in the formula \(\left[ P+{{a\over V^2}} \right][V-b]=RT\) where P is pressure and V is the volume of the gas

When an object is moving with veritable acceleration then the object possesses different accelerations at different instants. The acceleration of the object at a given instant of time or at a given point of motion is called instantaneous acceleration.

Two vectors \(\vec A\) and \(\vec B\) are given in the component form as \(\overrightarrow { A } =5\hat { i } +7\hat { j } -4\hat { k } \) and \(\overrightarrow { B } =6\hat { i } +3\hat { j } +2\hat { k } \). Find \(\vec { A } +\vec { B } ,\vec { B } +\vec { A } ,\vec { A } -\vec { B } ,\vec { B } -\vec { A } \)

A cricket ball of mass 35 g hits a stumps at an angle of 30° with a velocity of 20 m/s. If the ball rebounds at 60° the to the direction of incidence, calculate the impulse received by the cricket ball.

The following graph shows a V-T graph for isobaric processes at two different pressures. Identify which one occurs at higher pressure.

Apply Newton's second law to a mango hanging from a tree. (Mass of the mango is 400 gm).

A metal plate of area 2.5\(\times\)10^-4m² is placed on a 0.25\(\times\)10^-3m thick layer of castor oil. If a force of 2.5 N is needed to move the plate with a velocity 3\(\times\)10^-2m s^-1, calculate the coefficient of viscosity of castor oil.
Given: A = 2.5\(\times\)10-4 m², dx = 0.25\(\times\)10^-3 m, F = 2.5N and dv = 3×10^-2 m s^-1

A vehicle of mass 1250 kg is driven with an acceleration 0.2 along a straight level road against an external resistive force 500 N. Calculate the power delivered by the vehicle's engine if the velocity of the vehicle is 30 ms^-1.