Question

Two identical billiard balls are in contact on a table. A third identical ball collides with them simultaneously, symmetrically and comes to rest after impact. The coefficient of restitution is

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{2}{3}$

By momentum conversation $mu=2mV\cos {30}^0$ $=2mV\frac{\sqrt{3}}{2}$

$V=\frac{u}{\sqrt{3}}$

By newton's law restitution along the line of impact $e=\frac{V-0}{4\cos {30}^0-0}=\frac{\frac{4}{\sqrt{3}}}{4\times \frac{\sqrt{3}}{2}}=\frac{2}{3}$

$e=\frac{2}{3}$