A ball of mass `m` moving at speed `v` makes a head on 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.

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(1)/(sqrt(2))`
D. `(1)/(sqrt(3))`

Answer

C

Explanation

Since `(K.E.)_(f) lt (K.E.)` ,i.e. loss of `K.E.` , i.e. collision is inelastic.
`K_(f) = (3)/(4) K_(i)` ,i.e. loss of K.E. `Delta K = (1)/(4) K_(i)`
`(1)/(2) ( m xx m)/(m + m) (u - 0)^(2) (1 - e^(2)) = (1)/(4) xx (1)/(2) mu^(2)`
`1 - e^(2) rArr e = (1)/(sqrt(2))`