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Q.

If the earth were to suddenly contract to half of its present radius without any change in its mass, the duration (in hrs.) of the new day will be nearly

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a

12

b

24

c

14

d

6

answer is C.

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Detailed Solution

The total angular momentum of the earth will be conserved.

$I_{1} ω_{1} = I_{2} ω_{2}$

$\frac{2}{5} M R^{2} \times \frac{2 π}{24} = \frac{2}{5} M {(\frac{R}{2})}^{2} \frac{2 π}{T^{1}}$

$∴ T^{1} = \frac{24}{4} = 6 h o u r s$

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If the earth were to suddenly contract to half of its present radius without any change in its mass, the duration (in hrs.) of the new day will be nearly