A block of mass `M` with a semi - circular track of radius `R` rests on a smooth floor. A sphere of mass `m` and radius `r` is released from rest from `A`. Find the velocity of sphere and track , when the sphere reaches `B`.

Explanation

When the sphere reaches at `B`
Let `v_(1) = v_(m//g)`
`v_(2) = v_(M//g)`
By the momentum conservation in the horizontal direction
`mv_(1) = Mv_(2)` (i)
Applying the energy conservation between between `A` and `B`
`mg(R - r) = (1)/(2) mv_(1)^(2) + (1)/(2) Mv_(2)^(2)` (ii)
Solving , `v_(1) = sqrt((2 Mg(R - r))/(M + m))`
`v_(2) = (m)/(M) sqrt((2 Mg (R - r))/(M + m))`