The moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameters is $\frac{MR^2}{4}$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be $\frac{x}{2} MR^2$. The value of $x$ 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

What is the moment of inertia of a disc about one of its diameters?

Two spheres each of mass $M$ and radius $R$ are connected with a massless rod of length $4R$. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

Four holes of radius $R$ are cut from a thin square plate of side $4R$ and mass $M$. The moment of inertia of the remaining portion about the $z-$ axis is

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.