First slide

Coefficient of restitution

Question

Two billiard balls of same size and mass are in contact on a billiard table. A third ball of the same size and mass strikes symmetrically and then comes to rest right after the impact. The coefficient of restitution between the balls is

Moderate

A

$\frac{1}{2}$
B

$\frac{3}{2}$
C

$\frac{2}{3}$
D

$\frac{9}{4}$

Solution

$\sin θ = \frac{r}{2 r} = \frac{1}{2} θ = 30^{o}$
From conservation of momentum $m u = 2 m v \cos 30^{o}$
$\Rightarrow V = \frac{u}{\sqrt{3}}$
$e = \frac{v}{u \cos 30^{o}} = \frac{u / \sqrt{3}}{\frac{\sqrt{3} u}{2}} = \frac{2}{3}$

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