Question

The moments of inertia of two freely rotating bodies $ A $ and $ B $ are $ I_A $ and $ I_B $ respectively. $ I_A > I_B $ and their angular momenta are equal. If $ K_a $ and $ K_b $ are their kinetic energies, then

• A. $ K_A = K_B $
• B. $ K_A \ne K_B $
• C. $ K_A < K_B $
• D. $ K_A > 2K_B $

Answer 1

Answer: (C)

Kinetic energy $E=\frac{L^{2}}{2 I}$
If angular momenta are equal, then $E \propto \frac{1}{I}$
Kinetic energy $E=K$ (given in problem)
If $I_{A}>I_{B}$ then $K_{A}< K_{B}$