In a one dimensional collision between two identical particles A … - Vidyadip

MCQ

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 impulse $J$ to $A.$

A
The total momentum of the $‘A$ plus $B’$ system is $p$ before and after the impact, and $(p-J)$ during the impact.
B
During the impact $A$ gives impulse $J$ to $ B$
C
The coefficient of restitution is $\frac{{2J}}{p} - 1$
✓
Both $(B)$ and $(C)$

✓

Answer

Correct option: D.

Both $(B)$ and $(C)$

d
Let $u=$ speed of A before impact. Thus, $p=m u$

Let $v_{1}, v_{2}=$ speeds of $A$ and $B$ after impact.

$u=v_{1}+v_{2}$ and $v_{1}-v_{2}=-e u$

$u=v_{1}+v_{2}$ and $v_{1}-v_{2}=-e u$

$\therefore v_{1}=\frac{1}{2} u(1-e)$ and $v_{2}=\frac{1}{2} u(1+e)$

$J=m v_{2}=m\left[\frac{1}{2} u(1+e)\right]=\frac{1}{2} p(1+e)$

$\Rightarrow e=\frac{2 J}{p}-1$

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