A body of moment of inertia of $3\ kg-m^2$ rotating with an angular velocity of $2\ rad/sec$ has the same kinetic energy as a mass of $12\ kg$ moving with a velocity of .......... $m/s$

A disc of mass $M$ and radius $R$ rolls in a horizontal surface and then rolls up an inclined plane as shown in the fig. If the velocity of the disc is $v$, the height to which the disc will rise will be..

A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega $. Its centre of mass rises to a maximum height of

If a solid sphere of mass $1\, kg$ and radius $0.1\, m$ rolls without slipping at a uniform velocity of $1\, m/s$ along a straight line on a horizontal floor, the kinetic energy is

Explain work done by torque.

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