Question

A body P strikes another body Q of mass that is $p$ times that of body P and moving with a velocity that is $\frac{1}{q}$ of the velocity of body P. If body P comes to rest, the coefficient of restitution is

• A. $\frac{p+q}{p-q}$
• B. $\frac{p-q}{q(p-1)}$
• C. $\frac{p-q}{p(q-1)}$
• D. $\frac{p+q}{p(q-1)}$

Answer 1

The correct option is D

$\frac{p+q}{p(q-1)}$

Let the mass and velocity of body P be $m$ and $v$ respectively. So, the mass of body Q is $mp$ and its velocity is $\frac{v}{q}$.
From the principle of conservation of momentum, we have (since body P comes to rest after collision)
$mv+mp\times \frac{v}{q}=mp\times v^{\prime }$
where $v^{\prime }$ is the velocity of body Q after the collision.
Solving we get, $v^{\prime }=v\left(\frac{p+q}{pq}\right)$
Now, the coefficient of restitution is given by
$e=\frac{v^{\prime }}{v-\frac{v}{q}}=\frac{p+q}{p(q-1)}$
Hence, the correct choice is (d).