Question

Two identical balls are placed at rest, in contact on a smooth horizontal surface. A third similar ball strikes the two balls symmetrically and comes to rest after the impact. Coefficient of restitution for the collision is (angle between the velocities of moving balls after impact is ${60}^{\circ }$

Answer 1

Applying momentum conservation law,
$p_i=p_f$
$mu=mv\cos {30}^{\circ }+mv\cos {30}^{\circ }$
$=2mv\cos {30}^{\circ }$
$\therefore u=2v\times \frac{\sqrt{3}}{2}=\sqrt{3}v$
$\therefore$ Coefficient of restitution
$=e=\left(\frac{v-0}{u\cos {30}^{\circ }-0}\right)$
$=\frac{v}{u}\times \frac{2}{\sqrt{3}}=\frac{v\times 2}{\sqrt{3}\times \sqrt{3}v}=\frac{2}{3}=0.67$