The moment of inertia of a ring about an axis perpendicular to its plane and passing through its center is $4 \,kg \,m^2$. Its moment of inertia about the tangent in the plane is

$A$ sphere of radius $R$ is cut from a larger solid sphere of radius $2R$ as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the $Y$-axis is

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

Consider a thin uniform square sheet made of a rigid material. If its side is $a$,mass is $m$,and the moment of inertia about one of its diagonals is $I$,then:

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $L/3$ from one of its ends and perpendicular to the rod is:

The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through its center and normal to its length is $\alpha$. Now,the rod is cut into two equal parts,and these parts are joined symmetrically to form a cross shape. The moment of inertia of the cross about an axis passing through its center and normal to the plane containing the cross is: