If the moment of inertia of a thin circular ring about an axis passing through its edge and perpendicular to its plane is $I$, then the moment of inertia of the ring about its diameter is

$A$ uniform square plate of side $a$ and mass $m$ is given. The moment of inertia of this plate about an axis perpendicular to the plate and passing through one of its corners is .......

$A$ solid sphere has mass $M$ and radius $R$. Its moment of inertia about a parallel axis passing through a point at a distance $\frac{R}{2}$ from its centre is

From a disc of mass $M$ and radius $R$,a circular hole of diameter $R$ is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre is

The moment of inertia of a thin square plate $ABCD$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is given by which of the following expressions? Here,$I_1, I_2, I_3,$ and $I_4$ are the moments of inertia about axes $1, 2, 3,$ and $4$ respectively,which lie in the plane of the plate as shown in the figure.

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 $\frac{L}{4}$ from one of its ends and perpendicular to the rod is: