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

Identical rings are arranged in a hexagonal plane pattern such that each ring touches its neighbouring rings. Each ring has mass $M$ and radius $R$. The moment of inertia of the system of seven rings about an axis passing through the centre of the central ring and normal to the plane of all rings is: (in $MR^2$)

What is the moment of inertia of a square sheet of side $l$ and mass per unit area $\mu$ about an axis passing through the centre and perpendicular to its plane?

$A$ uniform disc of radius $R$ lies in the $x-y$ plane with its centre at the origin. Its moment of inertia about the $z$-axis is equal to its moment of inertia about the line $y = x + c$. The value of $c$ is

The rectangular block shown in the figure is rotated about the $x-x$,$y-y$,and $z-z$ axes passing through its center of mass $O$. Its moment of inertia is:

The moment of inertia of a rod (length $l$,mass $m$) about an axis perpendicular to the length of the rod and passing through a point equidistant from its midpoint and one end is: