What do you mean by propagation of errors? Explain the propagation of errors in addition and multiplication.

A body starting from rest has an acceleration of 25 ms^-2. Find the distance travelled by it in 20^th second.

Two vectors \(\vec A\) and \(\vec B\) of magnitude 5 units and 7 units respectively make an angle 60° with each other as shown below. Find the magnitude of the resultant vector and its direction with respect to 7 unit the vector \(\vec A\).

A three storey building of height 100m is located on Earth and a similar building is also located on Moon. If two people jump from the top of these buildings on Earth and Moon simultaneously, when will they reach the ground and at what speed? (g = 10m s^-2)

Describe Galileo's experiments concerning motion of objects on inclined planes?

A body of mass 500 g initially at rest is moved by a horizontal force of 1 N. Calculate the workdone by the force in 20s and show that is equal to the change in kinetic energy of the body.

Find the moment of inertia of a hydrogen molecule about an axis passing through its center of mass and perpendicular to the interatomic axis. Given: mass of hydrogen atom 1.7\(\times\)10^-27 kg and inter atomic distance is equal to 4\(\times\)10^-10m.

A massless right tangled triangle is suspended with its right angle corner. A mass of 100 kg is suspended from another corner B which subtends an angle \(53^{0}\). Find the mass m that should be suspended from other corner C so that BC (hypotenuse) remains horizontal. 

Consider four masses m₁, m₂, m₃, and m₄ arranged on the circumference of a circle as shown in figure below.

Calculate
(a) The gravitational potential energy of the system of 4 masses shown in figure.
(b) The gravitational potential at the point O due to all the 4 masses

Moon is the natural satellite of Earth and it takes 27 days to go once around its orbit. Calculate the distance of the Moon from the surface of the Earth assuming the orbit of the Moon as circular.

An deal gas is expanded such that ρT² = a constant find the coefficient of volume expansion of the gas.

A student comes to school by a bicycle whose tire is filled with air at a pressure 240 kPa at 27°C. She travels 8 km to reach the school and the temperature of the bicycle tire increases to 39°C. What is the change in pressure in the tire when the student reaches school?

Estimate the mass of air in your class room at NTP. Here NTP implies normal temperature (room temperature) and 1 atmospheric pressure.

A student had a breakfast of 200 food calories. He thinks of burning this energy by drawing water from the well and watering the trees in his school. Depth of the well is about 25 m. The pot can hold 25L of water and each tree requires one pot of water. How many trees can he water? (Neglect the mass of the pot and the energy spent by walking. Take g = 10 ms^-2)

Explain Joule’s Experiment of the mechanical equivalent of heat.

Derive the expression for Carnot engine efficiency.

What is meant by coefficient of linear expansion superficial & cubical expansion?

Calculate the equivalent spring constant for the following systems and also compute if all the spring constants are equal:

Consider two sources A and B as shown in the figure below. Let the two sources emit simple harmonic waves of same frequency but of different amplitudes, and both are in phase (same phase). Let O be any point equidistant from A and B as shown in the figure. Calculate the intensity at points O, Y and X. (X and Y are not equidistant from A & B)

Audible frequencies have a range of 20 Hz to 20 x 10³ Hz. Express 't' is range in terms of 
(i) period T
(ii) wavelength air at
(iii) angular frequency w (Given velocity of sound in O°C = 331 m/s)