Question

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio:

• A. 1:4
• B. \(\sqrt 2\) :1
• C. 4:1
• D. 1:\(\sqrt 2\)

Answer 1

The Correct Option is D

KE= \(\frac{1}{2}\)I \(\omega\)² = \(\frac{1}{2}\, \frac{L^2}{I}\) 

KE₁ = KE₂ 

\(\frac{1}{2}\, \frac{L^2}{I_1}\) = \(\frac{1}{2}\, \frac{L^2}{I_2}\) 

\(\frac{L^2}{1}\)=\(\frac{L^2_2}{2}\)

\(\frac{L_1}{L_2}\) =\(\frac{1}{\sqrt 2}\)

1:\(\sqrt 2\)​ 

Therefore, the correct option is (D): 1:\(\sqrt 2\)​