Rotational Motion Question 59
Question: Two bodies have their moments of inertia $ l $ and $ 2l $ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:
[AIPMT (S) 2005]
Options:
A) 1 : 2
B) $ \sqrt{2}:1 $
C) 2 : 1
D) $ 1:\sqrt{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
- As said, $ {{(KE)} _{rot}} $ remains same. i.e., $ \frac{1}{2}I _1\omega _1^{2}=\frac{1}{2}I _2\omega _2^{2} $
$ \Rightarrow $ $ \frac{1}{2I _1}{{(I _1{\omega_1})}^{2}}=\frac{1}{2I _2}{{(I _2{\omega_2})}^{2}} $
$ \Rightarrow $ $ \frac{L_1^{2}}{I _1}=\frac{L_2^{2}}{I _2} $
$ \Rightarrow $ $ \frac{L _1}{L _2}=\sqrt{\frac{I _1}{I _2}} $ but $ I _1=I,I _2=2I $
$ \therefore $ $ \frac{L _1}{L _2}=\sqrt{\frac{I}{2I}}=\frac{1}{\sqrt{2}} $ or $ L _1:L _2=1:\sqrt{2} $
