Rotational Motion Questions

A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ${\omega }^{\prime }$:

An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_1/F_2$ is:

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the centre is:

Consider a uniform square plate of side ‘$a$ ’ and mass ‘$m$ ’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is: