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NEET 2005

Exam: NEET
Year: 2005
Subject: Physics
Chapter: Rotational Motion

NEET 2005 · Physics · Rotational Motion

Two bodies have their moments of inertia l and 2 l respectively...

Two bodies have their moments of inertia

l

and

2 l

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 $1: \sqrt{2}$

Correct answer

D. $1: \sqrt{2}$

Step-by-step solution

K.E. rotation

K=\frac{1}{2} I \omega^2

Angular momenta

L=100\therefore \quad K=\frac{L^2}{2}

Here

K_1+K_2, I_1=I_1, I_2=21

\therefore \quad

\frac{L_1}{L_2}=\sqrt{\frac{2 I_1 K_1}{2 I_2 K_2}}

\begin{aligned}& =\sqrt{\frac{I_1}{I_2}}=\sqrt{\frac{I}{2 I}}\\ & =\frac{1}{\sqrt{2}} \end{aligned}

$$

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