Question

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

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

Answer 1

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

Coefficient of restitution = Relative velocity of separation/ Relative velocity of approach

By momentum conservation along the line of impact.Line of impact is the initial direction of the C1 ball. U be the initial velocity of the first ball and v be the final velocity of the two stationary balls.

$mu=2mvcos30$

=$2mv\frac{\surd 3}{2}$

$u=\surd 3v$

Newton's law of restitution along line of impact.

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

= $\frac{v}{\frac{\sqrt{3}u}{2}}=e$

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