A mass $\mathrm{m}$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The…
A mass $\mathrm{m}$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $\mathrm{m}$ and radius $\mathrm{R}$. 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
$\mathrm{g}$
$\frac{2}{3} \mathrm{~g}$
$\frac{\mathrm{g}}{3}$
$\frac{3}{2} g$
Solution
$
\begin{aligned}
& M g-T=M a \quad \quad \ldots \ldots (1)\\
& T \times R=I \alpha=\frac{1}{2} M^2 \alpha \\
& T=\frac{1}{2} M a \quad(a=\alpha R) \quad \quad \ldots \ldots (2)
\end{aligned}
$
From (1) and (2) $a=\frac{2 g}{3}$
