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.

(D) False: In an elastic collision,the total momentum and total energy of the system are conserved,not the momentum and energy of each individual body.
$(b)$ False: The total energy of a system is conserved only if no external work is done on the system. External forces can change the total energy of a system.
$(c)$ False: The work done over a closed loop is zero only for conservative forces (e.g.,gravitational force). For non-conservative forces (e.g.,friction),the work done is not zero.
$(d)$ True: In an inelastic collision,some kinetic energy is always converted into other forms of energy such as heat,sound,or deformation,resulting in a decrease in the final kinetic energy compared to the initial kinetic energy.