The radius of gyration of a body depends upon

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

Consider a sphere of mass $M$ and radius $R$ centered at the origin. The density of the material of the sphere is $\rho = A r^\alpha$, where $r$ is the radial distance, and $\alpha$ and $A$ are constants. If the moment of inertia of the sphere about the axis passing through the centre is $\frac{6}{7} M R^2$, then the value of $\alpha$ is

Four point masses each of mass $m$ are placed at the corners of a square $ABCD$ of side length $\ell$. What is the moment of inertia about an axis passing through $A$ and parallel to $BD$?

$A$ thin uniform wire of mass $m$ and linear density $\rho$ is bent in the form of a circular ring. The moment of inertia of the ring about a tangent parallel to its diameter is

If the radius of a solid sphere is doubled while keeping its mass constant,what is the ratio of its moment of inertia about any of its diameters?