Question

A block of mass $m$ is hung from a disc shaped pulley of mass $M$ and radius $R$ as shown in the figure. If $M=4m$, then the acceleration of the block just after the system is released from rest is -

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

Answer 1

The correct option is B $\frac{g}{3}$

FBD of the system is shown in the figure.


For block :

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

For pulley :

$TR=\frac{M{R}^2}{2}\times \alpha$

$\Rightarrow TR=\frac{M{R}^2}{2}\times \frac{a}{R}$

$\Rightarrow T=\frac{Ma}{2}=\frac{4ma}{2}=2ma...\left(2\right)$

From equations $\left(1\right)$ and $\left(2\right)$,

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

Hence, option $\left(B\right)$ is the correct answer.