The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through a point midway between the center and the end is:

Seven identical discs are arranged in a planar pattern,so as to touch each other as shown in the figure. Each disc has mass $m$ and radius $R$. What is the moment of inertia of the system of six outer discs about an axis passing through the centre of the central disc and normal to the plane of all discs?

$A$ square lamina of side $b$ has the same mass as a disc of radius $R$. The moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $\frac{b}{R}$ is

Consider a uniform square plate of mass $m$ and side length $a$. What is the moment of inertia of this plate about an axis passing through one of its vertices and perpendicular to its plane?

From a disc of mass $M$ and radius $R$,a circular hole of diameter $R$ is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre is

$A$ thin wire of length $l$ and uniform linear mass density $\rho$ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ is