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.

What is the moment of inertia of a thin rod of length $L$ and mass $M$ about an axis perpendicular to the rod and passing through a point at a distance of $L/3$ from one of its ends?

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?

For the given uniform square lamina $ABCD$,whose centre is $O$,

$I_{CM}$ is the moment of inertia of a circular disc about an axis $(CM)$ passing through its center and perpendicular to the plane of the disc. $I_{AB}$ is its moment of inertia about an axis $AB$ perpendicular to the plane and parallel to the axis $CM$ at a distance $\frac{2}{3}R$ from the center,where $R$ is the radius of the disc. The ratio of $I_{AB}$ and $I_{CM}$ is $x:9$. The value of $x$ is $........$

The moment of inertia of a sphere about its diameter is $I$. Four such spheres are arranged as shown in the figure. Calculate the moment of inertia of the system about the axis $XX'$. (in $I$)