Question

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

• A. True
• B. False

Answer 1

The correct option is B False

As given in the figure,

For (a) $\to$ $T-ma=ma\Rightarrow T=ma+mg⟶\left(i\right)$

$2mg-T=2ma$,

from (i) For (b) $\therefore$ force $=2$ mg

$2mg-(ma+mg)=2m{a}_1$ $2mg=2m\times a_2$

$2mg-ma-mg=2m{a}_1$ $a_2=g$

$mg-{ma}_1=2{ma}_1$ $\therefore$ $a_1=\frac{a_2}{3}$

$g=3a_1$

$a_1=\frac{g}{3}$ $\therefore a_1\ne a_2$

$false$