A body of mass `M` with a small block `m` placed on it rests on a smooth horizontal surface. The block is set in motion in the horizontal direction with a velocity `v`. To what height relative to the initial level will the block rise after breaking off from the body `M`. Friction can be assumed to be absent.

Answer

`F gt mu(m +M) g "and t" sqrt((2ML)/(F- mu(m+ M)g))`

Explanation

Let both move with same acceleration
`F - f = Ma " " …… (i) `
`f= ma " " …… (ii)`
From Eqs. (i) and (ii)
`F = (m + M) f`

when f is maximum ,
`F = mu(m + M) g`
For slipping to start
`F gt mu( m + M)g `
Now , `" " a_(1) = (F - mu mg)/(M)`
and `" " a_(2) = mu g`
`therefore " " a_(r) = a_(1) - a_(2) = (F mu (m + M)g)/(M)`
`therefore " " L = (1)/(2) a_(r) t^(2)`
`therefore " " t = sqrt((2L)/(a_(r))) = sqrt((2ML)/(F - mu( m + M) g))`