Question

In a one dimensional collision between two identical particles $A$ and $B$ , $B$ is stationary and $A$ has momentum $p$ before impact. During impact $B$ gives an impulse $J$ to $A$ . Then the coefficient of restitution between the two is

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

Answer 1

Answer: (A)

Let $p_1$ and $p_2$ be the momenta of $A$ and $B$ after collision.


Then applying impulse = change in linear momentum for the two particles
For $B:J=p_1\dots (i)$
For $A:J=p-p_2$
Or $p_2=p-J\dots (ii)$
Coefficient of restitution $e=\frac{P_1-P_2}{P}$
$=\frac{p_1-p+J}{p}$
$=\frac{J-p+J}{p}=\frac{2J}{p}-1$