Question $12.$ Two solid disks $($inner: radius $5$ cm $,$ mass $4$ kg and outer: radius $15$ cm $,$ mass $6$ kg $)$ are glued together to form a composite pulley on which the $7$ kg and $12$ kg masses are hung and allowed to accelerate.

a$)$ Calculate the moment of inertia of the pulley, the acceleration of the hanging masses, the tensions $T_1$ and $T_2,$ and the angular acceleration of the pulley.

b$)$ Repeat the calculations when the outer disk is used as the pulley.