A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true ?
The ring has higher kinetic energy
The disc has higher kinetic energy
The ring and the disc have the same kinetic energy
Kinetic energies of both the bodies are zero since they are not in linear motion
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-2 – 2019
The moment of inertia of a thin ring about an axis through its center and perpendicular to its plane is I_ring = M * R². The moment of inertia of a thin disc about an axis through its center and perpendicular to its plane is I_disc = (1/2) * M * R². Since I_ring > I_disc (M*R² is greater than (1/2)*M*R²), and ω is the same for both, the rotational kinetic energy of the ring is higher than that of the disc (KE_ring = (1/2)*I_ring*ω² > KE_disc = (1/2)*I_disc*ω²).