A sphere of mass m moving with velocity v collides head -on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (where, e is coefficient of restitution and collision is inelastic)

Options

A. `(e-1)/(2)`
B. `e/2`
C. `(e+1)/(2)`
D. e

Answer

C

Explanation

Moment before Collision = moment after collision
`mV+ 0 =m V_(1) +m V_(2)`
`e = (v_(2)-v_(1))/(u_(1) -u_(2))therefore v_(1) =v-v_(2)`
`e =(v _(2)- v_(1))/(v )` substitute `v_(1)`
`e= (v_(2)- v - v_(1))/(v)`