Figure shows an irregular wedge of mass `m` placed on a smooth horizontal surface. Part `BC` is rough.
What minimum velocity should be imparted to a small block of same mass `m` so that it may each point `B` :

Options

A. `2sqrt(gH)`
B. `sqrt(2gH)`
C. `2sqrt(g(H-h))`
D. `sqrt(gh)`

Answer

A

Explanation

Let `'u'` be the required minimum velocity . By momentum conservation `:`
`m u =(m+m)vrArr v=u//2`

Energy equation `:`
`(1)/(2) m u ^(2)=(1)/(2) ( 2m)v^(2)+mgH`
Substituting `v=u//2:`
`u=2sqrt(gH)`