Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected at the ends of a massless rod of length $2R$. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod?

According to the parallel axis theorem,$I = I_C + Mx^2$. Which of the following graphs of $I$ versus $x$ is correct?

Consider a uniform horizontal solid cylinder of mass $10 \,kg$ such that its length is $9$ times its radius. Let the radius be $40 \,cm$. Calculate the moment of inertia of the cylinder about a line passing through its edge and perpendicular to its axis.

What is the moment of inertia of a ring of mass $M$ and radius $R$ about a tangent to the circle of the ring in its own plane?

The moment of inertia of a rod of length $l$ about an axis passing through its centre of mass and perpendicular to the rod is $I$. The moment of inertia of a hexagonal shape formed by six such rods,about an axis passing through its centre of mass and perpendicular to its plane,will be (in $I$)

$M$ and $R$ are the mass and radius of a disc. $A$ small disc of radius $R/3$ is removed from the bigger disc as shown in the figure. The moment of inertia of the remaining part of the bigger disc about an axis $\text{AB}$ passing through the centre $O$ and perpendicular to the plane of the disc is $\frac{4}{x} MR^2$. The value of $x$ is . . . . . . .