Two rods of equal mass $m$ and length $l$ lie along the $x$-axis and $y$-axis with their centers at the origin. What is the moment of inertia of both about the line $x=y$?

The moment of inertia of a uniform rectangular plate about an axis passing through its center and parallel to its length $(l)$ is ($b =$ width of the rectangular plate):

$A$ square sheet of edge length $L$ and uniform mass per unit area $\sigma$ is used to form a hollow cylinder. The moment of inertia of this cylinder about its central axis is

Three point masses $m$ are placed at the corners of an equilateral triangle of side length $\ell$. What is the moment of inertia of the system about an axis passing through one side of the triangle?

$A$ system consists of two identical spheres,each of mass $1.5\, {kg}$ and radius $50\, {cm}$,attached to the ends of a light rod. The distance between the centers of the two spheres is $5\, {m}$. What is the moment of inertia of the system about an axis perpendicular to the rod and passing through its midpoint? (in ${kgm}^{2}$)

$A$ uniform solid cylinder with radius $R$ and length $L$ has a moment of inertia $I_1$ about its central axis. $A$ concentric solid cylinder of radius $R' = \frac{R}{2}$ and length $L' = \frac{L}{2}$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved-out portion of the cylinder about the same axis,then $\frac{I_1}{I_2} = ..........$