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 hourConservation of angular momentum dictates that angular momentum before and aftef contradiction must be the same.I1w1=I2w2I=25Mr2→ Momentum of intertia of earthw=2πT→ Angular velocity of earth =2πdayLet r2 and T2 be the new radius and new day durationTherefore,r12T1=r22T2∴T2=r22r12T1When earth contracts, r2=1nr1∴T2=(1nr1)2r21T1T2=1n2T1T1=24hours∴T2=24n2hours

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