Question

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

• A. \(\frac{1}{9} L\)
• B. \(\frac{1}{3} L\)
• C. \(6 L\)
• D. \(9 L\)

Hint:

Remember $K.E. = \frac{1}{2} L \omega$, which is analogous to $K.E. = \frac{1}{2} p v$ in linear motion.

Answer 1

The Correct Option is A

Step 1: Formulae
$K.E. = \frac{1}{2} L \omega \implies L = \frac{2 K.E.}{\omega}$.

Step 2: Changes
$K.E.' = \frac{1}{3} K.E.$ and $\omega' = 3\omega$ (since frequency is tripled).

Step 3: New Angular Momentum
$L' = \frac{2 (K.E./3)}{3\omega} = \frac{1}{9} \left( \frac{2 K.E.}{\omega} \right) = \frac{1}{9} L$.
Final Answer: (A)