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Rotational Work and Energy

Two bodies ro...

Question

Two bodies rotating with the same angular momentum have M.I. $I_{1} a n d I_{2}$ respectively such as $I_{1} > I_{2}$ respectively, then

A

E_{2} > E_{1}

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B

E_{1} > E_{2}

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C

E_{2} = E_{1}

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D

E_{1} = 2 E_{2}

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Solution

The correct option is A $E_{2} > E_{1}$
As the angular momentum of two bodies is given to be same or $I_{1} ω_{1} = I_{2} ω_{2} o r I_{1}^{2} ω_{1}^{2} = I_{2}^{2} ω_{2}^{2}$
or $I_{1} (\frac{1}{2} I_{1} ω_{1}^{2}) = I_{2} (\frac{1}{2} I_{2} ω_{2}^{2})$
or $I_{1} E_{1} = I_{2} E_{2}$
As per the question,
$I_{1} > I_{2}$
$∴ E_{2} > E_{1} .$

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