If the radius of gyration of a thin circular ring about an axis passing through its centre and perpendicular to its plane is $10 \sqrt{2} \,cm$, then its radius of gyration about its diameter is

Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius,about an axis passing through their axes of symmetry?

The radius of gyration of a disc of mass $50 \, g$ and radius $2.5 \, cm$ about an axis passing through its center of gravity and perpendicular to its plane is ....... $cm$.

Four masses are attached to a light circular frame of radius $a$ as shown in the figure. The radius of gyration of this system about an axis passing through the center $O$ of the circular frame and perpendicular to its plane is:

$A$ 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 $................$.

The ratio of the moments of inertia of two uniform rings of radii $R$ and $nR$ about an axis passing through their centers and perpendicular to their planes is $1 : 8$. What is the value of $n$?