Four particles,each of mass $1 \ kg$,are placed at the four corners of a square of side $2 \ m$. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertices is . . . . . . $kg \ m^2$.

Explain the radius of gyration.

$A$ quarter part is cut from a uniform circular disc of radius $R$. The mass of this cut part is $M$. It rotates about an axis passing through the center of the original disc and perpendicular to the plane of the disc. What will be its moment of inertia about the axis of rotation?

Two discs of the same thickness but different radii are made of two different materials such that their masses are equal. The densities of the materials are in the ratio $1:3$. The ratio of the moments of inertia of the discs about the axes passing through their centers and perpendicular to their planes is:

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to 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 the $y$-axis is: