The moment of inertia of a thin rod about an axis passing through its midpoint and perpendicular to the rod is $2400 \,g \,cm^2$. The length of the $400 \,g$ rod is nearly: (in $\,cm$)

$A$ circular disc of radius $R$ and thickness $R/8$ has a moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of the sphere about an axis passing through its diameter is:

Three particles of mass $m$ each are placed at the vertices of an equilateral triangle $ABC$ of side length $\ell$. What is the moment of inertia of the system about the axis $AX$ passing through vertex $A$ and perpendicular to side $AB$ in the plane of the triangle?

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

Four point masses,each of value $m$,are placed at the corners of a square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is

Two rings have their moments of inertia in the ratio $2:1$ and their diameters are in the ratio $2:1$. The ratio of their masses is