If the earth suddenly shrinks to half its present radius without any change in its mass, the duration of a day on earth will become: MCQ with Answer and Explanation

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If the earth suddenly shrinks to half its present radius without any change in its mass, the duration of a day on earth will become:

A. 6 hours

B. 48 hours

C. 24 hours

D. 12 hours

Answer: Option A

Solution (By JKExamLibrary)

By conservation of angular momentum: I1w1 = I2w2. Moment of inertia of a solid sphere is 2/5 MR^2. So, (R1^2) * (2pi/T1) = (R2^2) * (2pi/T2). If radius halves, R2 = R1/2. R1^2 / T1 = (R1/2)^2 / T2. T2 = T1 / 4. A day is 24 hours, so 24/4 = exactly 6 hours.

This question belongs to: Science Physics

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