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: Understanding the Concept
Rotational kinetic energy is \(K=\tfrac12I\omega^2\) and angular momentum is \(L=I\omega\).

Step 2: Key Formula or Approach
Eliminate \(\omega\): \(K=\dfrac{L^2}{2I}\), so \(L=\sqrt{2IK}\).

Step 3: Detailed Explanation
Both bodies have the same \(K\), so \(L\propto\sqrt I\).
\[ \frac{L_A}{L_B}=\sqrt{\frac{I_A}{I_B}} \]

Final Answer:
The ratio is \(\sqrt{I_A/I_B}\), option (C). \[ \boxed{\sqrt{\dfrac{I_A}{I_B}}\ \text{(C)}} \]