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 the body x. Then, the 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

Answer: (B)

$\frac{j}{p}+1$

Answer 2

Coefficient of restitution $e=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{1}}-{{u}_{2}}}$ Here both the bodies are identical i.e., have the same mass, So, $e=\frac{m{{v}_{2}}-m{{v}_{1}}}{m{{v}_{1}}-{{\mu }_{2}}}$ $=\frac{{{P}_{2}}-{{P}_{1}}}{{{p}_{1}}-{{p}_{2}}}$ ${{p}_{1}}=p$ (Intial momentum of first body ${{p}_{2}}=$ Initial momentum of second body) = 0 ( $\because$ Final momentum ${{p}_{2}}=p+J$ ) ( $\therefore$ Impulse = change in momentum) ${{p}_{1}}=0$ ( $\because$ When two bodies of equal masses collide elastically then thy exchange then velocities) $\therefore$ $e=\frac{p+J}{p}$ $=1+\frac{J}{p}$