Question

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

Answer 1

we know, The potential energy of a system containing two masses is inversely proportional to the distance between the two masses. e.g., $V(r)\propto\frac{1}{r}$

if R is the radius of ball and r is the separation between centre of the balls.
then, at r = 2R, e.g.,when two balls touch each other , potential energy becomes zero.
here both conditions is satisfied by option (v)

hence, (i), (ii), (iii), (v) and (vi) cannot possibly describe the elastic collision of two billiard balls.

Answer 2

Explanation:

The potential energy of a system of two masses varies inversely as the distance (r) between 1

them i.e., V (r) α 1/r. When the two billiard balls touch each other, P.E. becomes zero i.e., at r = R + R = 2 R; V (r) = 0. Out of the given graphs, curve (v) only satisfies these two conditions. Therefore, all other curves cannot possibly describe the elastic collision of two billiard balls.