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?
$(d)$ If 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) No: In an elastic collision,the total initial kinetic energy is equal to the total final kinetic energy. However,this kinetic energy is not conserved at the instant the balls are in contact. During the collision,part of the kinetic energy is converted into elastic potential energy.
$(b)$ Yes: In an elastic collision,the total linear momentum of the system is always conserved throughout the collision process.
$(c)$ No; Yes: In an inelastic collision,the total kinetic energy is not conserved (there is a loss of kinetic energy),but the total linear momentum of the system remains conserved.
$(d)$ Elastic: If the potential energy depends only on the separation distance between the centers,the forces involved are conservative. Since conservative forces do not dissipate energy,the collision is elastic.