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Question

Two bodies with moments of inertia $I_{1}$ and $I_{2}$ ( $I_{1} > I_{2}$ ) have equal angular momenta. If their kinetic energies of rotation are $E_{1}$ and $E_{2}$ respectively, then

A

E_{1} = E_{2}

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B

E_{1} < E_{2}

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C

E_{1} > E_{2}

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D

E_{1} \geq E_{2}

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Solution

The correct option is C $E_{1} < E_{2}$
Angular momentum, $L = I w$
Given: $L_{1} = L_{2} ⟹ I_{1} w_{1} = I_{2} w_{2}$
$\frac{w_{1}}{w_{2}} = \frac{I_{2}}{I_{1}}$
Rotational K.E, $E = \frac{1}{2} I w^{2}$
$\frac{E_{1}}{E_{2}} = (\frac{I_{2}}{I_{1}})^{2} \frac{I_{1}}{I_{2}} = \frac{I_{2}}{I_{1}} < 1$

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