$A$ ring,a solid sphere,and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest?

Two point-like objects of masses $20 \text{ g}$ and $30 \text{ g}$ are fixed at the two ends of a rigid massless rod of length $10 \text{ cm}$. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass,as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is $1.2 \times 10^{-8} \text{ N m rad}^{-1}$. The angular frequency of the oscillations is $n \times 10^{-3} \text{ rad s}^{-1}$. The value of $n$ is

$A$ flywheel is an important part of a steam engine because it

State the equivalent physical quantities in linear motion corresponding to the moment of inertia and torque in rotational motion.

$A$ cube of side $a$ is moving with velocity $v$ on a smooth horizontal surface. It hits a linear raised obstacle $O$ on the horizontal surface (as shown in the figure). The angular speed of the block after hitting $O$ will be

In the following problem,indicate the correct direction of the friction force acting on a cylinder of mass $M$ and radius $R$,which is pulled on a rough surface by a constant horizontal force $F$ applied at its center. The friction force can be represented by which of the following diagrams?