The radius of gyration of a circular disc of radius $R$ and mass $m$ rotating about its diameter as an axis is:

We have two spheres,one of which is a hollow shell and the other solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by

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 $K_d : K_c$ is

Four particles of mass $m$ each are placed at the four corners of a square of side length $\ell$. The radius of gyration of the system about an axis passing through its center and perpendicular to the plane of the square is .........

If the radius of a solid sphere is $35\,cm,$ calculate the radius of gyration when the axis is along a tangent.

$A$ thin rod of total length $4l$ and total mass $4M$ is bent into the shape shown in the figure. Each segment has length $l$ and mass $M$. What is the moment of inertia of the rod about the axis passing through point $O$ and perpendicular to the plane of the paper?