Rotational Motion Question 204
Question: Two bodies have their moments of inertia I and 21 respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio
Options:
A) 2:1
B) 1:2
C) $\sqrt{2}:1$
D) $1:\sqrt{2}$
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Answer:
Correct Answer: D
Solution:
[d]
$K=\frac{L^{2}}{2I}\Rightarrow L^{2}=2KI\Rightarrow L=\sqrt{2KI}$
$\frac{L _{1}}{L _{2}}=\sqrt{\frac{K _{1}}{K _{2}}.\frac{I _{1}}{I _{2}}}=\sqrt{\frac{K}{K}.\frac{I}{2I}=}\frac{1}{\sqrt{2}}$
$\Rightarrow L _{1}:L _{2}=1:\sqrt{2}$
