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?

Options

A. `((M)/(m)-1)g`
B. `((M)/(m)-1)g`
C. `(M)/(m)g`
D. `gt(M)/(m)g`

Answer

B

Explanation

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