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Question

If the radius of earth shrinks by 0.2% without any change in its mass, its angular velocity:

A
increases by 0.4%
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B
increases by 0.1%
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C
decreases by 0.4%
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D
decreases by 0.1%
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Solution

The correct option is A increases by 0.4%
R=R(10.002)

Using conservation of angular momentum

25MR2ωi=25MR2(10.002)2ωf

ωi=ωf(10.002)2

ωf=ωi(10.002)2

ωf=ωi(1+0.004)

i.e. wf is increased by 0.4%

We used (1+a)n=1an

if a1

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