The moment of inertia of a semicircular plate of radius $R$ and mass $M$ about an axis $AA'$ in its plane passing through its centre is given by:

The moment of inertia of a sphere of mass $M$ and radius $R$ is $I.$ If $M$ is kept constant and a graph is plotted between $I$ and $R,$ then its form would be:

Two rods of equal length $(l)$ and equal mass $M$ are kept along the $x$ and $y$ axes respectively,such that their center of mass lies at the origin. The moment of inertia about the line $y = x$ is ...........

Let $l$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to:

Three bodies have equal masses $m$. Body $A$ is a solid cylinder of radius $R$,body $B$ is a square lamina of side $R$,and body $C$ is a solid sphere of radius $R$. Which body has the smallest moment of inertia about an axis passing through their centre of mass and perpendicular to the plane (in case of lamina)?

$A$ wire of length $\ell$ and mass $M$ is bent into a semicircle of radius $r$ as shown in the figure. Calculate the moment of inertia about the axis $XX'$.