The speed of rolling of a ring of mass $M$ changes from $V$to $3\ V$. What is the change in its kinetic energy

A solid sphere of mass $m$ and radius $R$ is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation $E_{sphere}/E_{cylinder}$ will be

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are $0.1 \;kg - m ^{2}$ and $10\; rad \,s^{-1}$ respectively while those for the second one are $0.2 \;kg - m ^{2}$ and $5\; rad \,s ^{-1}$ respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is ...........$J$

One end of rod of length $L$ is on horizontal plane. It is inclined at angle $\alpha$ to  horizontal plane. When released its angular velocity after coming to horizontal plane is 

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

The total kinetic energy of a body of mass $10\ kg$ and radius $0.5\ m$ moving with a velocity of $2\ m/s$ without slipping is $32.8\ joule$.  The radius of gyration of the body is  .......... $m$