In fig. the block of mass M is at rest on the floor . At what acceleration with which should a boy of mass m climb along the rope of negligible mass so as to lift the block from the floor?

Explanation

Equation of motion for M:
Since M is stationary, `T-Mg=0`
`implies T=Mg` …(i)
Since the boy moves up with an acceleration a,
`T-mg=ma`
`implies T=m(g+a)`…(ii)
Equating (i) and (ii), we obtain
`Mg=m(g+a)`
`implies a=((M)/(m)-1)g`
that means, if `a gt (M/m-1)g`, block M can be lifted from floor.