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The Principle

The moments o...

Question

The moments of inertia of two freely rotating bodies A and B are $I_{A}$ and $I_{B}$ respectively. $I_{A} > I_{B}$ and theor angular momenta are equal. If $K_{A}$ and $K_{B}$ are their kinetic energies, then.

A

K_{A} = K_{B}

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B

K_{A} \neq K_{B}

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C

K_{A} < K_{B}

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D

K_{A} = 2 K_{B}

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Solution

The correct options are
B $K_{A} \neq K_{B}$
C $K_{A} < K_{B}$
Kinetic energy $E = \frac{L^{2}}{2 I}$
If angular momenta are equal, then $E \propto \frac{1}{I}$
Kinetic energy $E = K$ (given in problem)
If $I_{A} > I_{B}$ then $K_{A} < K_{B}$

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