Rotational Dynamics (15-09-2020)

A uniform annular disc of outer radius $R$ and inner radius $r$ is coaxially mounted on a fixed cylinder. Radius of the cylinder is slightly smaller than inner radius of the disc to allow the disc to rotate as a pulley and the fixed cylinder as an axle. Coefficient of friction between the disc and the cylinder is $\mu$ .
A light inextensible rope supporting two loads of masses $m$ and $M>m$ passes along the upper half periphery of the disc.

Find the acceleration a of the load $M$

Details and Assumptions
1) $g=10$
2) $M=4$
3) $m=2$
4) $\mu=0.8$
5) $r=1$
6) $R=2$ .