1.

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. Theminimum velocity `v` imparted to block so that it will overcome the highest point of `M` is A. `sqrt(2gh)`B. `sqrt(2(1+m/M)gh)`C. `sqrt((2m)/Mgh)`D. `sqrt(2(1+M/m)gh`

Answer» Correct Answer - B
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)`


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