A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their centre of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is correct?

The rotational kinetic energy of a rigid body is given by the formula K = (1/2)I̩², where I is the moment of inertia and ̩ is the angular velocity. For a thin ring of mass M and radius R, the mass is concentrated at the maximum distance from the axis, resulting in a moment of inertia I_ring = MR². In contrast, for a solid thin disc of the same mass and radius, the mass is distributed from the center to the edge, yielding a lower moment of inertia I_disc = (1/2)MR². Since both bodies rotate with the same angular velocity ̩, the body with the higher moment of inertia possesses greater kinetic energy. Consequently, the ring has twice the kinetic energy of the disc because its mass is distributed further from the axis of rotation.