$A$ solid cylinder has mass $M$,length $L$,and radius $R$. What is the moment of inertia of this cylinder about one of its generators?

The moment of inertia of a thin uniform rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

Three identical spheres,each of mass $M$ and radius $R$,are placed as shown in the figure. Consider an axis $XX'$ which passes through the diameter of the top sphere and is tangent to the two bottom spheres. The moment of inertia of the system consisting of these three spheres about the $XX'$ axis is:

$A$ square lamina of side $b$ has the same mass as a disc of radius $R$. The moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $\frac{b}{R}$ is

$A$ solid sphere of mass $M$ and a disc of mass $M/2$ have the same radius $R$. The ratio of the moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent 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: