State if each of the following statements is true or false. Give reasons for your answer.

A. In an elastic collision of two bodies, the momentum and energy of each body is conserved.

B. Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

C. Work done in the motion of a body over a closed loop is zero for every force in nature.

D. In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Answer the following:

A. The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?

B. Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why?

C. An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth?

D. In Fig. 6.13(i) the man walks 2 m carrying a mass of 15 kg on his hands. In Fig. 6.13(ii), he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of 15 kg hangs at its other end. In which case is the work done greater?

Underline the correct alternative:

A. When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered.

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

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

D. In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.

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. 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).

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to

(i) t^1/2 (ii) t (iii) t^3/2 (iv) t²