Question

Two billiard balls of the same size and mass are in contact on a billiard table. A third ball of the same size and mass strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the ball is:

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (C)

$\frac{2}{3}$

u=initial velocity

velocity off approach along AB=ucos60

Since ball moves with velocity v

$2mvcos\theta =muv=\frac{u}{2cos\theta }$ =velocity of separation

Hence coefficient of restitution =$\frac{\frac{u}{2cos\theta }}{ucos\theta }=\frac{1}{2{\cos }^2\theta }=\frac{1}{2{\cos }^{2}60}=\frac{2}{3}$