The potential energy of a system of two masses varies inversely as the distance $(r)$ between them, i.e., $V(r) \propto \frac{1}{r}$. When the two billiard balls touch eath other. P.E. become zero i.e. at $r = R + R = 2R$; $V(r) = 0$. 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.