Two rings of the same material have radii $R$ and $nR$ respectively. The ratio of their moments of inertia about an axis passing through their centers and perpendicular to their planes is $1 : 8$. The value of $n$ is:

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

Two spheres of equal masses,one of which is a thin spherical shell and the other a solid sphere,have the same moment of inertia about their respective diameters. The ratio of their radii is

Two circular loops $A$ and $B$ of radii $R$ and $NR$ respectively are made from a uniform wire. The moment of inertia of $B$ about its axis is $3$ times that of $A$ about its axis. The value of $N$ is:

From a uniform wire, two circular loops are made: $(i)$ $P$ of radius $r$ and (ii) $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis, the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$). (in $\sqrt{2}$)

If the mass and radius of a hollow sphere are $M$ and $R$ respectively,then its moment of inertia with respect to its diameter is: