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Question

Mass remaining the same if the earth shrinks until its radius becomes half of its value, then the duration of new day would be

A
18 hrs
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B
6 hrs
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C
48 hrs
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D
12 hrs
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Solution

The correct option is B 6 hrs
Given: mass remaining the same if the earth shrinks until its radius becomes half of its value,
To find the duration of new day
Solution:
Since no external torque acts on the object, conservation of momentum can be applied to this problem.
Apply conservation of momentum, by considering earth as a solid sphere,
I1ω1=I2ω2
Since earth is a solid sphere
I1=25MR2
Hence
I1I2=25MR225M(R2)2I1I2=4
We know,
ω2ω1=T1T2I1I2=ω2ω1=4
Substituting
T1=24,
we have
ω2ω1=T1T24=24T2T2=6hrs
Hence the duration of new day is 6hours

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