The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis touching the disc at its diameter and normal to the disc is

Find the moment of inertia of a plate cut in the shape of a right-angled triangle of mass $M$ and sides $AC = BC = a$,about an axis perpendicular to the plane of the plate and passing through the midpoint of the side $AB$.

$I_{CM}$ is the moment of inertia of a circular disc about an axis $(CM)$ passing through its center and perpendicular to the plane of the disc. $I_{AB}$ is its moment of inertia about an axis $AB$ perpendicular to the plane and parallel to the axis $CM$ at a distance $\frac{2}{3}R$ from the center,where $R$ is the radius of the disc. The ratio of $I_{AB}$ and $I_{CM}$ is $x:9$. The value of $x$ 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:

The moment of inertia of a ring of mass $m = 3 \ gm$ and radius $r = 1 \ cm$ about an axis passing through its edge and parallel to its natural axis is:

$A$ 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