Rotational Motion Questions

A solid cylinder of mass $2\text{kg}$ and radius $4\text{cm}$ rotating about its axis at the rate of $3\text{rpm}$. The torque required to stop after $2\pi$ revolutions is:

A solid cylinder of mass $2\text{kg}$ and radius $50\text{cm}$ rolls up an inclined plane of angle of inclination $30^{\circ }$. The centre of mass of the cylinder has a speed of $4\text{m/s}$. The distance travelled by the cylinder on the inclined surface will be ($g=10{\text{m/s}}^2$):

A particle of mass $5m$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $m$ each move along mutually perpendicular directions with speed $v$ each. The energy released during the process is: