One quarter sector is cut from a uniform circular disc of radius $R$. This sector has mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_{c}$. Radius of gyration of the same disc about a diameter of the disc is $K_d$. The ratio $K_c: K_d$ is

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $PQ$ is about ..... $kg-m^2$.

If the radius of a solid sphere is doubled while keeping its mass constant,what is the ratio of its moment of inertia about any of its diameters?

The moment of inertia of a uniform rod of mass $M$ and length $L$ about an axis passing through its center and perpendicular to it is $\frac{1}{12} ML^2$. The rod is bent at the center such that the two halves make an angle of $60^\circ$ with each other. Find the moment of inertia of the bent rod about the same axis passing through the center of the rod (the point of bending) and perpendicular to the plane containing the two halves.

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is: