$A$ solid sphere $A$ is rotating about an axis $PQ$. If the radius of the sphere is $5 \, cm$ and the distance of its center from the axis $PQ$ is $10 \, cm$,then its radius of gyration about $PQ$ will be $\sqrt{x} \, cm$. The value of $x$ 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 $K_d : K_c$ is

The moment of inertia depends on:

Two discs having moment of inertia $I_1$ and $I_2$ are made from the same material and have the same mass. Their thicknesses and radii are $t_1, t_2$ and $R_1, R_2$ respectively. The relation between the moment of inertia of each disc about an axis passing through its centre and perpendicular to its plane and its thickness is:

The ratio of the radius of gyration of a circular disc to that of a circular ring,each of the same mass and radius,about their respective central axes is:

$A$ 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