A particle of mass `m` moving with kinetic energy `K`, makes a head - on elastic collision with a stationary particle of mass `eta m`. The maximum potential energy stored in the system during the collision is

Options

A. `(eta)/(eta + 1) K`
B. `(eta + 1)/(eta) K`
C. `(eta - 1)K`
D. `(eta - 1)K`

Answer

A

Explanation

During the impact , some part of incident kinetic energy is temporarily stored in the form of potential energy. The potential energy will be maximum when particles compress to the maximum, at the maximum compression , both particles move with the same velocity.
`m u = (m + eta m)v rArr v = ((u)/( 1 + eta))`
`K_(i) = (1)/(2) m u^(2)`
`K.E.` at the maximum compression,
`(1)/(2) ( m + eta m) v^(2) = (1)/(2) m u^(2) ((1)/( 1 + eta))`
`(P.E.)_(max) = (1)/(2) m u^(2) - (1)/(2) m u^(2) ((1)/(1 + eta))`
`= ((eta)/( eta + 1))^(2) (1)/(2) m u^(2) = ((eta)/( eta + 1))K`