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\\
(1) g\\
(2) $\frac{2}{3}\mathrm{~g}$\\
(3) $\frac{g}{3}$\\
(4) $\frac{3}{2}g$