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

$A$ solid cylinder of length $L = 80 \, \text{cm}$ and mass $M$ has a radius $r = 20 \, \text{cm}$. Calculate the density of the material used if the moment of inertia of the cylinder about an axis $CD$ parallel to the central axis $AB$ (as shown in the figure) is $2.7 \, \text{kg m}^2$.

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:

The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is:

Four identical discs each of mass $M$ and diameter $a$ are arranged in a plane as shown in the figure. If the moment of inertia of the system about $OO'$ is $\frac{x}{4} Ma^2$,then the value of $x$ will be:

According to the theorem of parallel axes $I = I_g + Md^2$,the graph between $I$ and $d$ will be