A moving particle of mass m makes a head on elastic collision with a particle of mass 2 m which is initially at rest. What fraction of energy of the colliding particle is lost after collision ?

Options

A. `8//9`
B. `7//8`
C. `4//5`
D. `2//3`

Answer

a

Explanation

Here by conservation of momentum
`mu+0=mv_1+2 mv_2` or `u-v_1=2 v_2`
Also by conservation energy
`1/2"mu"^2=1/2mv_1^2+1/2(2m)v_2^2`
or `u^2=v_1^2=2v_2^2` or `(u-v_1)(u+v_1)=2 v_2^2`
From these eqns.`u+v_1=v_2`.Now eliminating `V-2`, we get `v_1=1//3u`
Fraction lost
=`(1/2"mu"^2-1/2mv_1^2)/(1/2mu^2)`
=`(u^2-(-1//3u)^2)/(u^2)=(1-1/9)=8//9`