Two bodies have their moments of inertia I and 2 I respectively about their axis of rotation. If the

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6.System of Particles and Rotational Motion

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Two bodies have their moments of inertia $I$ and $2 I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio

A

$1:2$

B

$ \sqrt 2 :1$

C

$2:1$

D

$1 : \sqrt 2 $

(AIPMT-2005)

Solution

$KE =\frac{1}{2} I \omega^2=\frac{1}{2} \frac{ L ^2}{I}$

$KE _1= KE _2$

$\frac{1}{2} \frac{ L ^2}{ I _1}=\frac{1}{2} \frac{L_2^2}{I_2}$

$\frac{L_1^2}{I}=\frac{L_2^2}{2}$

$\frac{L_1}{L_2}=\frac{1}{\sqrt{2}}$

$1: \sqrt{2}$

Standard 11

Physics

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