Three objects, $A :$ (a solid sphere), $B :$ (a thin circular disk) and $C :$ (a circular ring), each have the same mass $M$ and radius $R.$ They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work $(W)$ required to bring them to rest, would satisfy the relation

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  

For the pivoted slender rod of length $l$ as shown in figure, the angular velocity as the bar reaches the vertical position after being released in the horizontal position 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)

Two discs of moment of inertia $I_1$ and $I_2$ and angular speeds ${\omega _1}\,{\rm{and }}{\omega _2}$ are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same axis the rotational $KE$ of system will be 

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