Four spheres,each of mass $M$ and diameter $2a$,are placed at the corners of a square of side $b$ as shown in the figure. Calculate the moment of inertia about the axis $AA'$.

Three rods are arranged in the form of an equilateral triangle. Calculate the moment of inertia about an axis passing through the centroid and perpendicular to the plane of the triangle. (Each rod has mass $M$ and length $L$)

Suppose there is a uniform circular disc of mass $M$ and radius $r$ shown in the figure. Two shaded circular regions, each of radius $r/4$, are cut out from the disc. The centers of these cut-out discs are at a distance of $3r/4$ from the center of the original disc. The moment of inertia of the remaining part about the axis $A$ (passing through the center of the disc and perpendicular to its plane) is given by $\frac{x}{256} Mr^2$. The value of $x$ is . . . . . . .

Two spheres each of mass $M$ and radius $R/2$ are connected by a massless rod of length $2R$ as shown in the figure. The moment of inertia of the system about an axis passing through the center of one of the spheres and perpendicular to the rod is:

$A$ thin wire of length $l$ having linear mass density $\rho$ is bent into a circular loop with $C$ as its centre, as shown in the figure. The moment of inertia of the loop about the line $AB$ is

Consider a thin uniform square sheet made of a rigid material. If its side is $a$,mass is $m$,and the moment of inertia about one of its diagonals is $I$,then: