Consider a uniform square plate of side $a$ and mass $m$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

From a circular disc of radius $\mathrm{R}$ and mass $9\mathrm{M}$, a small disc of radius $\frac{R}{3}$ is removed, Fig. 11.159. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is

A uniform rod $AB$ of length $l$ and mass $\mathrm{m}$ is free to rotate about point $A$. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{m{l}^2}{3}$, the initial angular acceleration of the rod will be

Consider a body, shown in figure, consisting of two identical balls, each of mass $\mathrm{M}$ connected by a light rigid rod. If an impulse $J=MV$ is imparted to the body at one of its ends, what would be its angular velocity ?

Let $\overrightarrow{F}$ be the force acting on a particle having position vector $\overrightarrow{r}$ and $\overrightarrow{\tau }$ be the torque of this force about the origin. Then