The radius of gyration of a body depends upon:

Two rings have their moments of inertia in the ratio $4 : 1$ and their diameters are in the ratio $4 : 1$. The ratio of their masses is

Two uniform thin identical rods $AB$ and $CD$ each of mass $M$ and length $L$ are joined so as to form a cross as shown. The moment of inertia of the cross about a bisector line $EF$ is (Line $EF$ is in the plane of the cross and bisects the angle between the rods).

The moment of inertia of a cylinder of mass $M$,length $L$,and radius $R$ about an axis passing through its centre and perpendicular to the axis of the cylinder is $I = M \left(\frac{R^2}{4} + \frac{L^2}{12}\right)$. If such a cylinder is to be made for a given mass of material,the ratio $L/R$ for it to have the minimum possible $I$ is

One quarter sector is cut from a uniform circular disc of radius $R$. This sector has mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

$A$ thin metal rod of mass $M$ and length $L$ is cut into four 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 length is $I$,then the moment of inertia of each part about an axis passing through its own centre and perpendicular to its length is: