The moment of inertia of a thin circular disc of mass $M$ and radius $R$ about any diameter is

A slender uniform rod of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\mathrm{\theta }$ with the vertical is.

Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres form an equilateral triangle of side length $d$. Find the ratio $I_0/I_{\mathrm{A}}$, where$I_0$ is the moment of inertia of the system about an axis passing through the centroid and $I_{\mathrm{A}}$ is the moment of inertia of the system about an axis passing through the centre of any sphere and perpendicular to the plane of the triangle.

A thin wire of length $l$ and mass $m$ is bent in the form of a semicircle. Its moment of inertia about an axis joining its free ends will be

A thin metal wire of length $L$ and uniform linear mass density $\rho$ is bent into a circular coil with $O$ as centre. The moment of inertia of a coil about the axis $XX\text{'}$ is

The moment of inertia of a uniform ring of mass $M$ and radius $r$ about a tangent lying in its own plane is