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The Principle

If earth sudd...

Question

If earth suddenly shrinks and its radius becomes half, then what will be the duration of a day?

A

3 hour

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B

6 hour

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C

9 hour

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D

12 hour

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Solution

The correct option is B 6 hour
From conservation of angular momentum,
$I_{1} ω_{1} = I_{2} ω_{2}$
$\frac{2}{5} M R^{2} \times \frac{2 π}{24} = \frac{2}{5} M \times {(\frac{R}{2})}^{2} \times \frac{2 π}{T}$
$T = 6 hours$

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