Question

Ball $1$ collides head on with another identical ball $2$, initially at rest. Velocity of ball $2$ after collision becomes two times that of ball $1$ after collision. The coefficient of restitution between the two balls is :

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

Answer 1

The correct option is A $e=\frac{1}{3}$

Before collision,

After collision,




Now, $e=\frac{\text{rel. velocity of separation}}{\text{rel. velocity of approach}}$

$\Rightarrow e=\frac{2V-V}{U}=\frac{V}{U}-\left(1\right)$

According to conservation of momentum principle,

$m\left(U\right)+m\times 0=mV+m\left(2V\right)$
$\Rightarrow 3V=U\Rightarrow \frac{V}{U}=\frac{1}{3}-\left(2\right)$
From (1) & (2), we get, $e=\frac{1}{3}$

Hence, $\left(A\right)$ is the correct answer.