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. $\frac{2 J}{P}-1$
• B. $\frac{2 J}{P}+1$
• 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 $B:J=p_{1} \, \ldots \left(\right.i\left.\right)$
For $A:J=p-p_{2}$
Or $p_{2}=p-J \, \, \ldots \left(\right.ii\left.\right)$
Coefficient of restitution $e=\frac{P_{1} - P_{2}}{P}$
$=\frac{p_{1} - p + J}{p}$
$=\frac{J - p + J}{p}=\frac{2 J}{p}-1$