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Question

If the mass of earth and radius suddenly become 2 times and 1/4th of the present value, the length of the day becomes:

A
24h
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B
6h
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C
3/2h
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D
3h
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Solution

The correct option is D 3h
If mass of earth becomes 2 times and radius of earth becomes 14 of the present value moment of inertia of earth I=25mR2 becomes 18 of the present value. As no external torque acting on the earth its angular momentum L=Iw=I2πT remains constant. As I becomes 18 of present value so length of the day T becomes 18 of present day or 3 hours.
Correct option (D).

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