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Rotational Work and Energy

Two bodies wi...

Question

Two bodies with moment of inertias $I_{1}$ and $I_{2}$ $(I_{1} > I_{2})$ have equal angular momenta. If K.E. of rotation are $E_{1}$ and $E_{2}$ 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 $E_{1} < E_{2}$
$L_{1} = L_{2}$
$⟹ I_{1} w_{1} = I_{2} w_{2}$ ................(1)
Rotational K.E, $E = \frac{1}{2} I w^{2}$
$\frac{E_{1}}{E_{2}} = \frac{I_{1} w_{1}^{2}}{I_{2} w_{2}^{2}} = \frac{I_{1}}{I_{2}} \times \frac{I_{2}^{2}}{I_{1}^{2}}$
$⟹ \frac{E_{1}}{E_{2}} = \frac{I_{2}}{I_{1}}$
$I_{2} < I_{1} ⟹ E_{1} < E_{2}$

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