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 $\frac{2J}{p}-1$

Impulse $J=\Delta P$

For X : $-J=p_x-p$ $⟹p_x=p-J$

For Y : $J=p_y$

Coefficient of restitution equation , $\frac{p_y-p_x}{0-p}=-e$

$⟹p_y-p_x=ep$

$J-(p-J)=ep$ $⟹e=\frac{2J}{p}-1$