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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.
Solution
$(a)$ False : In an elastic collision, the total energy and momentum of both the bodies, and not of each individual body, is conserved.
$(b)$ False : Although internal forces are balanced, they cause no work to be done on a body. It is the external forces that have the ability to do work. Hence, external forces are able to change the energy of a system.
$(c)$ False : The work done in the motion of a body over a closed loop is zero for a conservation force only.
$(d)$ True : In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system. This is because in such collisions, there is always a loss of energy in the form of heat, sound, etc.
