Question

The pulley arrangements of figures $\left(a\right)$ and $\left(b\right)$ are identical. The mass of the rope is negligible. In Fig. (a), the mass $m$ is lifted up by attaching a mass $2m$ to the other end of the rope. In Fig. (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.

• A. True
• B. False

Answer 1

The correct option is B False

For (a)

$T-mg=ma.....\left(1\right)$

$2mg-T=2ma....\left(2\right)$

Adding (1) and (2) we get

$T-mg+2mg-T=ma+ma$

$mg=3ma$

$a_1=\frac{g}{3}$

For (b)

$\because$ 2mg is the force appilied So,

$2mg=2m{a}_2$

$a_2=g$

Hence the acceleration of m is not same for both the cases.