Rotational Motion · Physics · IAT (IISER)

An inextensible cord of negligible mass passes over the rim of a solid disc of mass $M$ and radius $R$. The disc is free to rotate about an axis passing through the centre perpendicular to the plane of the screen, as shown in the figure. Two blocks of masses $M$ and $\widetilde{M} / 2$ are attached to the two free ends of the cord. Assume that there is no slipping of the cord on the disc. The acceleration due to gravity is $g$. What is the value of the angular acceleration of the disc?

Consider a solid rod of mass $m$ and uniform density resting against a vertical wall and horizontal floor as shown in the figure. The coefficients of friction of the rod with the wall and with the floor are given to be $\mu_1$ and $\mu_2$ respectively. Gravity is acting downwards with acceleration due to gravity $g$. What should be the value of the inclination angle $\alpha$ so that the rod stays in equilibrium?