Question

The equal billiard balls are in contact on a table. A third identical ball strikes them symmetrically and remains at rest after impact . The coefficient of restitution is

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. $\sqrt{\frac{2}{3}}$

Answer 1

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

By momentum conservation along the line of impact.

$mu=2mv\cos 30$

$=2mv\cdot \frac{\sqrt{3}}{2}$

$u=\sqrt{3}v$

Newton's law of restitution along line of impact

$\frac{V-0}{0-u\cos 30}=-e$

$\frac{V}{\sqrt{3}u/2}=e$

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