The pulley arrangements of Figs. (a) and (b) are identical. The mass of the rope is negligible. In (a) the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force `F=2mg`. The acceleration of m is the same in both cases

Explanation

Case (i) For mass m
`T-mg=ma`
For mass 2m
`2m-T=2ma`

From (i) and (ii)
`a=g//3`
Case(ii) `T-mg=ma^'`
`2mg-mg=ma^'` `[:. T=2mg]`
`:.` `a^'=g`
Hence, `alta^'`