The moment of inertia of a body about a given axis is $2.4\ kg-m^2$.  To produce a rotational kinetic energy of $750\ J$, an angular acceleration of $5\ rad/s^2$ must be applied about that axis for.......... $\sec$

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

$A$ ring of mass $m$ and radius $R$ has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0$. The kinetic energy of the system is: (Slipping is absent)

A solid sphere of mass $1\,kg$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}\,J$. The speed of the centre of mass of the sphere is $.........cm s ^{-1}$.

A metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $f$ rotations per second. It is suddenly stopped at $50\%$ of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is

An automobile engine develops $100\ kW$ when rotating at a speed of $1800\ rev/min$.  What torque does it deliver .......... $N-m$