The ratio of radii of gyration of a circular ring and a circular disc of the same mass and radius,about an axis passing through their centres and perpendicular to their planes is

$A$ thin metal rod of mass $M$ and length $L$ is cut into $4$ equal parts by cutting it perpendicular to its length. If the moment of inertia of the rod about an axis passing through its centre and perpendicular to its axis is $I$,then what is the moment of inertia of each part about a similar axis?

The figure shows two solid discs with radius $R$ and $r$ respectively. If the mass per unit area is the same for both,what is the ratio of the moment of inertia $(MI)$ of the bigger disc about axis $AB$ (which is perpendicular to the plane of the disc and passing through its centre) to the $MI$ of the smaller disc about one of its diameters lying on its plane? Given $M$ is the mass of the larger disc.

For a cube of side $a$ and mass $M$,the moment of inertia is minimum about which axis?

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 $A$ and $B$ of same material and thickness have radii $R$ and $3R$ respectively. Their moments of inertia about their axis will be in the ratio