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In fig. the block of mass M is at rest o...

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?

A

`((M)/(m)-1)g`

B

`gt((M)/(m)-1)g`

C

`(M)/(m)g`

D

`gt(M)/(m)g`

Text Solution

Verified by Experts

Equation of motion for `M` :
Since `M` is stationery,
`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 Eqs. (`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.
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