Two circular rings $A$ and $B$ of radii $nR$ and $R$ are made from the same wire. The moment of inertia of $A$ about an axis passing through the centre and perpendicular to the plane of $A$ is $64$ times that of the ring $B$. The value of $n$ is:

The moment of inertia depends on:

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

$A$ thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma (r) = kr^2$,where $r$ is the distance from its centre. Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Moment of inertia of a circular disc of mass $M$ and radius $R$ about $X, Y$ axes (passing through its plane) and $Z$-axis which is perpendicular to its plane were found to be $I_{x}, I_{y}$ and $I_{z}$ respectively. The respective radii of gyration about all the three axes will be the same.
Reason $R$: $A$ rigid body making rotational motion has fixed mass and shape.
In the light of the above statements,choose the most appropriate answer from the options given below:

The ratio of the radii of two solid spheres of same mass is $2:3$. The ratio of the moments of inertia of the spheres about their diameters is