Q. 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) $g$
B) $\frac{2}{3}g$
C) $\frac{g}{3}$
D) $\frac{3}{2}g$
Explanation
(b) [image:7_image138.emf]
For the motion of the block
$mg - T = ma$ …(i)
For the rotation of the pulley
$\tau = TR = I\alpha$
$\Longrightarrow$ $T = \frac{1}{2}mR\alpha$ …(ii)
As string does not slip on the pulley
$a = R\alpha$ …(iii)
On solving Eqs. (i), (ii) and (iii)
$a = \frac{2g}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.