Question

Two identical billiard balls are in contact on a table. A third identical ball strikes them symmetrically and come 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

Answer: (A)

$\frac{2}{3}$

Answer 2

$\sin\theta = \frac{r}{2r} = \frac{1}{2}$ ⇒ θ = 30⁰

From conservation of linear momentum $mu = 2mv\cos 30^{o}$ or $v = \frac{u}{\sqrt{3}}$

Now $e = \frac{\text{Relative velocity of separation}}{\text{Relative velocity of approach}}$ in common

normal direction.

Hence, $e = \frac{v}{u\cos 30^{o}} = \frac{u/\sqrt{3}}{u\sqrt{3}/2} = \frac{2}{3}$