Question

A body X with a momentum p collides with another identical stationary body Y one dimensionally. During the collision, Y gives an impulse J to body X. Then coefficient of restitution is

• A. $\frac{2J}{p}-1$
• B. $\frac{J}{p}+1$
• C. $\frac{J}{p}-1$
• D. $\frac{J}{2p}-1$

Answer 1

The correct option is A $\frac{2J}{p}-1$

$u_1=\frac{p}{m},u_2=0,v_1=\frac{(p-J)}{m},v_2=\frac{J}{m}$
Now apply $e=\frac{v_2-v_1}{u_1-u_2}$
$e=\frac{\frac{J}{m}-\frac{(p-J)}{m}}{\frac{p}{m}-0}$
$e=\frac{2J}{p}-1$