Mechanics
7.  A cylinder of mass M and radius 2R has a groove of radius R. A block Of 
mass m is hung from the circumference of the cylinder and the cylinder 
itself is hung from a rigid support by a thread wound on the groove as 
shown in the figure. 
If the acceleration of centre of mass of the cylinder is 'a₁' acceleration of 
the block is a₂ downward and angular acceleration of the cylinder is $\alpha$
then relation between a_l, a₂ and $\alpha$ will be ​

$$\begin{gathered} \left(\mathrm{A}\right) {\mathrm{a}}_1-\mathrm{\alpha R}={\mathrm{a}}_2 \\ \left(\mathrm{B}\right) {\mathrm{a}}_1-2\mathrm{\alpha R}={\mathrm{a}}_2 \\ \left(\mathrm{C}\right) {\mathrm{a}}_1+{\mathrm{a}}_2=\frac{\mathrm{\alpha R}}{2} \\ \left(\mathrm{D}\right) {\mathrm{a}}_1-{\mathrm{a}}_2=3\mathrm{\alpha R} \end{gathered}$$