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

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$\frac{2 J}{ρ} - 1$

$\frac{J}{ρ} + 1$

$\frac{2 J}{ρ} + 1$

$\frac{J}{ρ} - 1$

answer is A.

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Detailed Solution

Let $ρ_{2} & ρ_{1}$ be moments of A & B after collision

Impulse=change in linear momentum for two particles

For B; $J = ρ_{1}$ and for A; $J = ρ - ρ_{2}$ i.e $ρ_{2} = ρ - J$

Coefficient of restitution; $e = \frac{ρ_{1} - ρ_{2}}{ρ} = \frac{2 J}{ρ} - 1$

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