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

Two point masses of $0.3\ kg$ and $0.7\ kg$ are fixed at the ends of a rod of length $1.4\ m$  and of negligible mass. The rod is set rotating about an axis perpendicular  to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of  

A smooth tube of certain mass closed at both ends is rotated in a gravity free space and released. The two balls shown in figure moves towards the ends of the tube and stay there. Then which statement is incorrect about this whole system

A uniform cylinder of radius $R$ is spinned with angular velocity  $\omega$ about its axis and then placed into a corner. The coefficient of friction between the cylinder and planes is $μ$. The number of turns taken by the cylinder before stopping is given by

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50 \,\%$ of its translational kinetic energy. The body is :

A uniform sphere of mass $500\; g$ rolls without slipping on a plane horizontal surface with its centre moving at a speed of $5.00\; \mathrm{cm} / \mathrm{s}$. Its kinetic energy is