Question

In a one dimensional collision between two identical particle 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

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

Answer 1

The correct option is A $\frac{2J}{p}-1$

We know that impulse is change in momentum therefore,

Initial velocity is $P=mV=>v=P/m$

After collision velocity of mass $B$

$J=m{V}_2{V}_2=\frac{J}{m}$

Velocity of mass $A$ is

$m{V}_1=J-P{V}_1=\frac{J-P}{m}$

Coefficient of restriction is

$e=\frac{V_b}{V_a}=\frac{V_1+V_2}{V}=\frac{\frac{J}{m}-\frac{P}{m}+\frac{J}{m}}{\frac{P}{m}}=\frac{2J-P}{P}=\frac{2J}{P}-1$

Hence, correct option is $\left(A\right)$