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:

$M$ and $R$ are the mass and radius of a disc. $A$ small disc of radius $R/3$ is removed from the bigger disc as shown in the figure. The moment of inertia of the remaining part of the bigger disc about an axis $\text{AB}$ passing through the centre $O$ and perpendicular to the plane of the disc is $\frac{4}{x} MR^2$. The value of $x$ is . . . . . . .

$A$ disc and a ring both have the same mass and radius. The ratio of the moment of inertia of the disc about its diameter to that of a ring about a tangent in its plane is

The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about its base parallel to the $x$-axis is

Calculate the moment of inertia of a disc about an axis tangent to its inner circle and lying in the plane of the disc. The mass of the disc is $M$,the inner radius is $R_1$,and the outer radius is $R_2$.

What is the moment of inertia of a ring of mass $M$ and radius $R$ about the axis $PQ$ as shown in the figure?