Question

A pulley is attached to the ceiling of a lift moving upwards. Two particles are attached to the two ends of a massless string passing over the smooth pulley. The masses of the particles are in the ratio 2:1. If the acceleration of the particles is $\frac{g}{2}$ w.r.t. lift, then the acceleration of the lift will be.

• A. $g$
• B. $\frac{g}{2}$
• C. $\frac{g}{3}$
• D. $\frac{g}{4}$

Answer 1

The correct option is B $\frac{g}{2}$

Let, the acceleration of the lift is $a$.

The acceleration of the bigger and smaller masses with respect to the lift

The bigger mass will be accelerated downward and the smaller mass will go upward.

According to the figure,

Now, the acceleration of the bigger mass = $(a-\frac{g}{2})$

The acceleration of the smaller mass = $(a+\frac{g}{2})$

Now,

$T-2mg=2m(a-\frac{g}{2})....\left(I\right)$

$T-mg=m(a+\frac{g}{2}).....\left(II\right)$

Now, from equation (I) and (II)

$-mg=2m(a-\frac{g}{2})-m(a+\frac{g}{2})$

$-mg=2ma-mg-ma-m\frac{g}{2}$

$-mg=ma-mg-\frac{mg}{2}$

$\frac{-2mg+2mg+mg}{2}=ma$

$\frac{mg}{2}=ma$

$a=\frac{g}{2}$

Hence, the acceleration of the lift will be $a=\frac{g}{2}$.