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Question

Two artificial satellites P and Q are revolving round the earth in circular orbits. If the ratio of their radii is 1:4 and ratio of their masses is 3:1 then the ratio of their time periods will be

A
18
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B
8
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C
4
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D
3
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Solution

The correct option is C 18
The time period of a satellite is given by T=2π(r3GM)0.5 i.e. T=K(r)1.5 because remaining are constant in this case here.
So, for the first satellite T1=Kr11.5
similarly foe the second satellite T2=Kr21.5.
Given that r1r2=14.
Taking the ratio of timeperiods, we get T1T2=Kr11.5Kr11.5=(14)1.5=18

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