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Question

If the earth were to suddenly contract to 1nth of its present radius without any change in its mass then the duration of the new day will be close to

A
24n hour
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B
24n hour
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C
24n2 hour
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D
24n2 hour
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Solution

The correct option is C 24n2 hour
Conservation of angular momentum dictates that angular momentum before and aftef contradiction must be the same.
I1w1=I2w2
I=25Mr2 Momentum of intertia of earth
w=2πT Angular velocity of earth =2πday
Let r2 and T2 be the new radius and new day duration
Therefore,
r12T1=r22T2
T2=r22r12T1
When earth contracts, r2=1nr1
T2=(1nr1)2r21T1
T2=1n2T1
T1=24hours
T2=24n2hours

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