For the system shown in the figure, a small block of mass `m` and smooth irregular shaped block of mass `M`, both free to move are placed on a smooth horizontal plane. The minimum velocity `v` imparted to block so that it will overcome the highest point of `M` is

Options

A. `sqrt(2gh)`
B. `sqrt(2(1+m/M)gh)`
C. `sqrt((2m)/Mgh)`
D. `sqrt(2(1+M/m)gh`

Answer

B

Explanation

For the given situation, block should be able to reach just at highest point of `M`, and their relative velocity is to become zero. Let their common velocity of `v_(C)`.
`COLMrarr (M+m)v_(C)=mvimplies v_(C)=(mv)/(M+m)`
`COME: 1/2 (M+m)v_(C)^(2)+mgh=1/2mv^(2)`
Solve to get `v=sqrt(2(1+m/M)gh)`