A particle of mass `m` and momentum `p` moves on a smooth horizontal table and collides directly and elastically with a similar particle (of mass m) having momentum `-2p`. The loss `(-)` or gain `(+)` in the kinetic energy of the first particle in the collision is

Options

A. (a) `+(p^2)/(2m)`
B. (b) `-(p^2)/(4m)`
C. (c) `+(3p^2)/(2m)`
D. (d) zero

Answer

C

Explanation

Let `|p|=mv=p`

In elastic head on collision with equal masses, velocities are interchanged.
Gain in kinetic energy of first
`=1/2m[(2v)^2-v^2]`
`=3/2mv^2=(3/2m)(p/m)^2=(3p^2)/(2m)`