Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls? Here r is the distance between centres of the balls.

The potential energy of a system containing two masses is inversely proportional to the distance between the two masses. Also, if R is the radius of each billiard ball and r is the separation between them, then the potential energy becomes zero when the two balls touch each other, i.e., r = 2R. Only (v) satisfies these conditions. Hence, (i), (ii), (iii), (iv) and (vi) cannot possibly describe a collision of two billiard balls.