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A body X with a momentum p with anothe...

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

Text Solution

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From the law of conservation of linear momentum,
`m_(1)u_(1) +m_(2)u_(2) = m_(1)v_(1)+m_(2)v_(2)`
`m u +m(0) = mv_(1) + mv_(2)`
`rArr P -P_(1) = P_(2)` where `P_(2) = J`, (given)
`:. e = (v_(2) -v_(1))/(u_(1) -u_(2)) = (mv_(2) - mv_(1))/("mu" -0) = (P_(2)-P_(1))/(P)`
=`(P_(2)-(P-P_(2)))/(P) = (2P_(2)-P)/(P) =(2J -P)/(P) =(2J)/(P) -1`.
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