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

Calculate the moment of inertia of an annular disc about an axis tangent to the outer 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 $R_2$.

Three spheres,each of mass $m$ and radius $r$,are placed as shown in the figure. Consider an axis $YY^1$,which is tangent to two spheres (labeled $2$ and $3$) and passes through the diameter of the third sphere (labeled $1$). The moment of inertia of the system consisting of these three spheres about the $YY^1$ axis is:

$ABC$ 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

$A$ solid sphere of mass $5 \ kg$ and radius $10 \ cm$ is kept in contact with another solid sphere of mass $10 \ kg$ and radius $20 \ cm$. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is . . . . . . $kg \cdot m^{2}$.

Four identical thin rods,each of mass $M$ and length $l$,form a square frame. The moment of inertia of this frame about an axis passing through the centre of the square and perpendicular to its plane is