The ratio of the radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of a thin hollow sphere of the same mass and radius about its axis is:

Consider two uniform discs of the same thickness and different radii $R_{1} = R$ and $R_{2} = \alpha R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$,respectively,about their axes is $I_{1} : I_{2} = 1 : 16$,then the value of $\alpha$ is:

What is the moment of inertia of a solid sphere of radius $R$ and density $\rho$ about its diameter?

The moment of inertia of a sphere of mass $M$ and radius $R$ is $I.$ If $M$ is kept constant and a graph is plotted between $I$ and $R,$ then its form would be:

Match the following columns ($R=$ radius,$k=$ radius of gyration):

Column $I$	Column $II$
$(A)$ 'k' for a solid sphere rotating about its tangent	$(P)$ $\sqrt{2}R$
$(B)$ 'k' for a ring rotating about its tangent perpendicular to its plane	$(Q)$ $\frac{R}{2}$
$(C)$ 'k' for a uniform solid right circular cone rotating about its central axis	$(R)$ $\frac{\sqrt{7}}{\sqrt{5}}R$
$(D)$ 'k' for a uniform disc rotating about its diameter	$(S)$ $\frac{\sqrt{3}}{\sqrt{10}}R$

Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio $1 : 3$. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio: