Draw position-time graph for a non-uniform motion, when body starts from origin with increasing velocity.

1

(a)

In the above x-t graph, the slope of x-t graph is increasing, it means that the velocity is increasing.

Can the mass of body be taken to be concentrated at its centre of mass for the purpose of calculating its rotational inertia?

1

(a)

No, the moment of inertia greatly depends on the distribution of mass about the axis of rotation.

At what factor between the two particles gravitational force does not depend?

1

(a)

Gravitational force does not depend upon the medium between the two particles.

Two particles of masses m₁ and m₂ attract each other gravitationally and are set in motion under the influence of the gravitational force? Will the centre of mass move?

1

(a)

Since, gravitational force is an internal force, therefore the centre of mass would not move.

Work done in moving a particle round a closed path under the action of gravitation force zero. Why?

1

(a)

Gravitational force is a conservative force which means that work done by it, is independent of path followed.

An artificial satellite revolving around the earth does not need any fuel.On the other hand,the aeroplane requires fuel to fly at  certain height why?

1

(a)

The satellite move in air-free regions while the aeroplane has to overcome air resistance.

When we step barefoot into an office with a marble floor, we feel cold. Why?

1

(a)

This is because marble is a better conductor of heat than concrete. When we walk barefooted on a marble floor, heat flows our body through the feet and we feel cold.

A tightened glass stopper can be taken out easily by pouring hot water around the neck of the bottle. Why?

1

(a)

The neck expands but not the stopper due to poor conductivity of glass. Thus, the stopper can be taken out easily.

Which object will cool faster when kept in open air, the one at 300 \(^{0}\) C or the one of 100 \(^{0}\)C? Why?

1

(a)

The object at 300 \(^{0}\)C will cool faster than the object at 100 \(^{0}\)C. This is in accordance with Newton’s law of cooling. As we know, rate cooling of an object \(\alpha \)  temperature between the object and its surroundings.

If there are f degrees of freedom with n moles of a gas, then find the internal energy possessed at a temperature T.

1

(a)

For 1 mole with f degrees of freedom,
Internal energy, U = 1 x C_v x T = \(\frac { f }{ 2 } RT\)
For n moles, U = nC_vT = \(\frac { nf }{ 2 } RT\)