Q. 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 coefficient of restitution between the two is
A) $\frac{2J}{P} - 1$
B) $\frac{2J}{P} + 1$
C) $\frac{J}{P} + 1$
D) $\frac{J}{P} - 1$
Explanation
(a) Let $p_{1}$ and $p_{2}$ be the momenta of $A$ and $B$ after collision.
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Then applying impulse = change in linear momentum for the two particles
For $B\ :J = p_{1}\ \ \ \ \ \ \ \ \ \ \ldots(i)$
For $A\ :J = p - p_{2}$
Or $p_{2} = p - J\ \ \ \ \ \ \ \ \ldots(ii)$
Coefficient of restitution $e = \frac{P_{1} - P_{2}}{P}$
$= \frac{p_{1} - p + J}{p}$
$= \frac{J - p + J}{p} = \frac{2J}{p} = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.