$A$ body is in pure rotation. The linear speed $v$ of a particle,the distance $r$ of the particle from the axis,and the angular velocity $\omega$ of the body are related as $\omega = \frac{v}{r}$. Thus,

$A$ thin rod is hinged at point $O$ and is in an unstable equilibrium position. It falls under the influence of gravity due to a slight disturbance. It makes angles of $60^{\circ}$,$90^{\circ}$,and $180^{\circ}$ with the vertical in positions $(2)$,$(3)$,and $(4)$ respectively. If $\omega_2$,$\omega_3$,and $\omega_4$ are the angular velocities in these positions,then:

$A$ ball of mass $m$ is released from inside a smooth wedge of mass $m$ as shown in the figure. What is the speed of the wedge when the ball reaches point $B$?

What is a rigid body? Explain the difference between a rigid body and a solid body.

The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r) = kr^2 / 2$,where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. If $v$ is the speed of the particle and $L$ is the magnitude of its angular momentum about $O$,which of the following statements is (are) true?
$(A)$ $v = \sqrt{\frac{k}{2m}} R$
$(B)$ $v = \sqrt{\frac{k}{m}} R$
$(C)$ $L = \sqrt{mk} R^2$
$(D)$ $L = \sqrt{\frac{mk}{2}} R^2$

The moment of inertia of a solid flywheel about its axis is $0.1\,kg\cdot m^2$. $A$ tangential force of $2\,kg\cdot wt$ is applied around the circumference of the flywheel with the help of a string and mass arrangement as shown in the figure. If the radius of the wheel is $0.1\,m$,find the angular acceleration of the solid flywheel (in $rad/s^2$). (Take $g = 9.8\,m/s^2$)