The ball `A` of mass `m` is released when the string is horizontal. It strikes a block `B` of mass `3 m` kept on a rough surface of friction coefficient `mu = 0.1`. If a head on elastic collision takes place , find the maximum distance travelled by the block on a rough surface.

Explanation

when the ball reaches at the bottom , its velocity
`u = sqrt( 2g L) = sqrt( 2 xx 10 xx 0.8) = 4 m//s`
Now the head - on elastic collision between the ball and the block
`m xx 4 + 3m xx 0 = mv_(1) + 3 mv_(2)` (i)
`v_(1) + 4 = v_(2) + 0` (ii)
Solving , `v_(2) = 2 m//s`
Now , the block moves on a rough surface
Due to the friction the block will stop after travelling a distance `d`.
Retardation of block is
`a = ( 3 mu m g)/( 3m) = mu g = 0.1 xx 10 = 1 m//s^(2)`
`0 = (2)^(2) - 2ad rArr 0 = 4 - 2 xx 1 xxd rArr d = 2m`