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. `gt ((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`
`rArr T=Mg" " ...(1)`

Since the boy moves up with an acceleration .a.,
`T-mg=ma`
`rArr T=m(g+a)" " ...(2)`
Equating (1) and (2), we obtain
`Mg=m(g+a)`
`rArr a=((M)/(m)-1)g`
That means, if `a gt ((M)/(m)-1)g`, the block M can be lifted.