Question

A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the pulley is

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

Answer 1

The correct option is C $\frac{2}{3}g$


Condition for pure rolling,
$a=R\alpha$ .....(1)

For pulley,
$TR=\frac{M{R}^2}{2}\alpha$ ....(2)

For weight $m,$
$mg-T=ma$ ...(3)
using eq.(1)
$TR=\frac{m{R}^2}{2}\times \frac{a}{R}T=\frac{ma}{2}$
on putting this value on eq. (3)
$mg-\frac{ma}{2}=maSo,a=\frac{2g}{3}$