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  4. Two rotating bodies A and B of masses m and 2m with momenta of inertia IA and IB (IB > IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then -

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Q. Two rotating bodies $A$ and $B$ of masses $m$ and $2m$ with momenta of inertia $I_A$ and $I_B (I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then -

NEETNEET 2016System of Particles and Rotational Motion

Solution:

$K.E_{A} = K.E_{B}$
$ \frac{1}{2} I_{A} \omega^{2}_{A} = \frac{1}{2} I_{B} \omega^{2}_{B} $
$ \frac{\omega_{A}}{\omega_{B} } = \sqrt{\frac{I_{B}}{I_{A}}} $ .....(i)
$ L_{A} =I_{A}\omega_{A} L_{B} = I_{B} \omega_{B} $
$ \frac{L_{A}}{L_{B}} = \frac{I_{A}}{I_{B}} \times\frac{\omega_{A}}{\omega_{B}} = \frac{I_{A}}{I_{B}} \times \sqrt{\frac{I_{A}}{I_{B}}} $
$ = \sqrt{\frac{I_{A}}{I_{B}}} < 1 $
$ \left[L_{A} < L_{B}\right] $