To maintain a rotor at a uniform angular speed of $100\, rad\, s^{-1}$, an engine needs to transmit torque of $100\, Nm$. The power of the engine is

Two identical circular loops are moving with same kinetic energy one rolls $\&$ other slides. The ratio of their speed is 

A ring of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega $. Two identical bodies each of mass $m$ are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be

Moment of inertia of a body about a given axis is $1.5\, kg\, m^2$ Initially the body is at rest. In order to produce a rotational kinetic energy of $1200\, J$, the angular acceleration of $20\, rad/s^2$ must be applied about the axis of rotation for a duration of ......... $\sec$.

A meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor assuming that the end at the floor does not slip is ......... $m / s$ $\left(g=9.8 \,m / s ^2\right)$

A body is rolling down an inclined plane. If kinetic energy of rotation is $40\%$ of  translational kinetic energy, then the body is a