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 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. 3g/2
• B. g
• C. 2g/3
• D. g/3

Answer 1

The correct option is C 2g/3

The free body diagram of pulley and mass

Equation of motion of block: mg - T = ma
$\therefore a=\frac{mg-T}{m}$ ...(i)
$\therefore$ Angular acceleration of pulley $\alpha =\frac{\tau }{I}$ ...(ii)
Here, $\tau =T\times R$
and $I=\frac{1}{2}m{R}^2$ (For circular disc)
$\therefore T=\frac{mR\alpha }{2}$ (Using (ii))
Therefore, $a=\frac{mg-\frac{mR\alpha }{2}}{m}$ (Using (i))
$ma=mg-\frac{ma}{2}(\because \alpha =\frac{a}{R})$
$\therefore a=\frac{2g}{3}$