A circular disc is rolling down an inclined plane without slipping. If the angle of inclination is $30°$, the acceleration of the disc down the inclined plane is

Downward force $F=Mg\sin \theta$. The effective mass of the rolling disc is $M_{\text{eff }}=M+\frac{I_{\mathrm{CM}}}{R^2}$, where $I_{\mathrm{CM}}$ is the moment of inertia about its centre of mass, which is
$$\begin{gathered} I_{\mathrm{CM}}=\frac{1}{2}M{R}^2 \\ \therefore M_{\text{eff }}=M+\frac{1}{2}\frac{M{R}^2}{R^2}=\frac{3M}{2} \\ \therefore \text{ Acceleration }a=\frac{F}{M_{\text{eff }}}=\frac{Mg\sin {\theta }^{{ }^{ }}}{3M/2} \\ =\frac{2}{3}g \sin 30°=\frac{g}{3} \\ \mathrm{alternate} \mathrm{method} \mathrm{accelaration} \mathrm{of} \mathrm{a} \mathrm{rolling} \mathrm{body} \mathrm{along} \mathrm{an} \mathrm{inclined} \mathrm{plane} \\ {\mathrm{a}}_{\mathrm{cm}}={\frac{\mathrm{gsin\theta }}{1+{\displaystyle \frac{{\mathrm{k}}^2}{{\mathrm{R}}^2}}}}_{ }=\frac{2\mathrm{gsin\theta }}{3} \mathrm{for} \mathrm{disc} \end{gathered}$$