The moment of inertia of a square plate of side $l$ and mass $M$ about an axis passing through one of its corners and perpendicular to the plane of the square plate is given by:

Suppose there is a uniform circular disc of mass $M$ and radius $r$ shown in the figure. Two shaded circular regions,each of radius $r/4$,are cut out from the disc. The centers of these cut-out discs are at a distance of $3r/4$ from the center of the original disc. The moment of inertia of the remaining part about the axis $A$ (passing through the center of the disc and perpendicular to its plane) is given by $\frac{x}{256} Mr^2$. The value of $x$ is . . . . . . .

$A$ 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:

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

The moment of inertia of a sphere about its diameter is $I$. Four such spheres are arranged as shown in the figure. Calculate the moment of inertia of the system about the axis $XX'$. (in $I$)

What is the moment of inertia of a rod of mass $M$ and length $l$ about an axis perpendicular to it passing through one end?