$A$ thin square plate $ABCD$ has a uniform thickness. What is the moment of inertia about an axis passing through its center and perpendicular to its plane?

State and prove the theorem of perpendicular axes and the theorem of parallel axes.

$A$ circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same mass $M$ and radius $R$ attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis $OO'$,passing through the centre of $D_1$ as shown in the figure,will be:

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:

$A$ thin wire of length $L$ and uniform linear mass density $\lambda$ is bent into a circular coil. The moment of inertia of this coil about a tangential axis in the plane of the coil is:

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