Question

The angular momentum of a rotating body is 'L'. When the frequency of rotating body is tripled and its kinetic energy is made one-third, the new angular momentum becomes

• A. \(9L\)
• B. \(6L\)
• C. \(\frac{L}{3}\)
• D. \(\frac{L}{9}\)

Hint:

Use K = (1/2) L w and remember that the moment of inertia must change.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
For rotation, \(L = I\omega\) and \(K = \frac12 I\omega^2 = \frac12 L\omega\). Both \(I\) and \(\omega\) can change here, so use the form that links \(K\), \(L\) and \(\omega\).

Step 2: Key Formula or Approach:
\(K = \frac12 L\omega\), so \(L = \frac{2K}{\omega}\). The frequency is proportional to \(\omega\).

Step 3: Detailed Explanation:
New \(\omega = 3\omega\) and new \(K = \frac K3\).
\[ L' = \frac{2(K/3)}{3\omega} = \frac19\cdot\frac{2K}{\omega} = \frac{L}{9} \]
If \(I\) stayed fixed, tripling \(\omega\) would give \(3L\) and \(9K\), which does not match the stated \(K' = \frac K3\). So the moment of inertia must have changed, and the answer is \(\frac L9\).

Final Answer:
The new angular momentum is \(\frac{L}{9}\), option (D). \[ \boxed{\frac{L}{9}} \]