The moment of inertia of a circular disc of radius $2 \,m$ and mass $1 \,kg$ about an axis passing through the centre of mass but perpendicular to the plane of the disc is $2 \,kg \,m^{2}$. Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is (see the given figure).

The moment of inertia of a sphere about its diameter is $40 \ kg \cdot m^2$. Find the moment of inertia about any tangent.

$ABC$ is a plane lamina in the shape of an equilateral triangle. $D$ and $E$ are the midpoints of $AB$ and $AC$,respectively,and $G$ is the centroid of the lamina. The moment of inertia of the lamina about an axis passing through $G$ and perpendicular to the plane $ABC$ is $I_{0}$. If the part $ADE$ is removed,the moment of inertia of the remaining part about the same axis is $\frac{NI_{0}}{16}$,where $N$ is an integer. The value of $N$ is

The moment of inertia of a ring about one of its diameters is $I$. What will be its moment of inertia about a tangent parallel to the diameter?

Four spheres,each of mass $M$ and radius $a$,are placed at the four corners of a square of side $b$. Calculate the moment of inertia of the system about one of the sides of the square as the axis.

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 $R_2$.