First slide

Coefficient of restitution

Question

A ball of mass m moving with a speed u undergoes a head - on elastic collision with a ball of mass nm initially at rest. The fraction of the incident energy transferred to the heavier ball is

Easy

A

$\frac{n}{1 + n}$
B

$\frac{n}{{(1 + n)}^{2}}$
C

$\frac{2 n}{{(1 + n)}^{2}}$
D

$\frac{4 n}{{(1 + n)}^{2}}$

Solution

Let the velocities of the two balls, after collision be $v_{1}$ and $v_{2}$ is the direction of u which is taken as positive.
$m u = m v_{1} + n m v_{2}, e = 1$
$v_{2} - v_{1} = u, v_{2} = \frac{2 u}{n + 1},$
Fractional energy transferred $= \frac{K . E . o f b a l l o f m a s s n m}{i n c i d e n t e n e r g y} = \frac{\frac{1}{2} n m \times {(\frac{2 u}{n + 1})}^{2}}{\frac{1}{2} m u} = \frac{4 n}{{(n + 1)}^{2}}$

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