Question

Two bodies A and B have moment of inertia \(I_A\) and \(I_B\), and angular momenta \(L_A\) and \(L_B\) respectively. Both of them have same kinetic energy of rotation. So the ratio \(L_A\) to \(L_B\) is

• A. \(\frac{I_A}{I_B}\)
• B. \(\frac{I_A^2}{I_B^2}\)
• C. \(\sqrt{\frac{I_A}{I_B}}\)
• D. \(\sqrt{\frac{I_B}{I_A}}\)

Hint:

Use \(K=\dfrac{L^2}{2I}\) so \(L=\sqrt{2IK}\).

Answer 1

The Correct Option is C

Step 1: Write the equal-energy condition
$\dfrac{L_A^2}{2I_A}=\dfrac{L_B^2}{2I_B}$.

Step 2: Rearrange
$\dfrac{L_A^2}{L_B^2}=\dfrac{I_A}{I_B}$, so $\dfrac{L_A}{L_B}=\sqrt{I_A/I_B}$, option (C).

Final Answer:
$L_A/L_B=\sqrt{I_A/I_B}$, option (C). \[ \boxed{\sqrt{I_A/I_B}} \]