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

According to the question,

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