A ball `A` of mass `3 m` is placed at a distance `d` from the wall on a smooth horizontal surface Another ball `B` of mass `m` moving with velocity `u` collides with ball `A`. The coefficient of restitution between the balls and the wall and between the balls is `e`
(a) the velocity of ball `B` after collision is `(u(3e-1))/(4)`.
(b) the velocity of ball `B` after collision is `(u(2e-1))/(4)`.
( c) after collision, ball `A` will have away by distance `(d(2e-1))/((2e-1))` during the time ball `B` returns back to wall.
(d) after collision, ball `A` will move away by distance `(d(e-1))/((3e-1))` during the time ball `B` returns back to wall.

Options

A. a,d
B. a, c
C. b,d
D. c,d

Answer

`(1)`

Explanation

`v_(A) = ((1+e)m_(1)u_(1))/(m_(1) + m_(2)), v_(B) = - ((m_(1) - em_(2))u_(1))/(m_(1) + m_(2))`
`t_(B) = d/(v_(B)), d_(A) = v_(A)^(t)_(B)`