A ball of mass m moving at a speed v makes a head on inelastic collision with an identical ball at rest. The kinetic energy of the balls after the collision is `3/4th` of the original. Find the coefficient of restitution.

Answer

A, B

Explanation

For the given conditons, we can use Eq. (xiv) or
`v_1^()'=((1+e)/(2))v` and `v_2^()'=((1-e)/(2))v`
Given that `K_f=3/4K_i`
or `1/2mv_1^()'^2+1/2mv_2^()'^2=3/4(1/2mv^2)`
Substituting the value, we get
`((1+e)/(2))^2+((1-e)/(2))^2=3/4`
or `(1+e)^2+(1-e)^2=3`
or `2+2e^2=3`
or `e^2=1/2`
or `e=1/sqrt2`