A body X with a momentum p collides with another identical stationary body Y one dimensionally. During the collision. Y gives an impulse J to body X. Then coefficient or restitution is

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$\frac{2 J}{p} - 1$

$\frac{J}{p} + 1$

$\frac{J}{p} - 1$

$\frac{J}{2 p} - 1$

answer is A.

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Detailed Solution

$υ_{1} = \frac{P}{m}, υ_{2} = 0, ν_{1} = \frac{(p - J)}{m}, ν_{2} = \frac{J}{m}$ Now apply $e = \frac{ν_{2} - ν_{1}}{υ_{1} - υ_{2}}$

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