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Question

A satellite of mass m revolves round the earth of mass M in a circular orbit of radius r with an angular velocity ω. If the angular velocity is ω/8 then the radius of the orbit will be

A
4r
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B
2r
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C
8r
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D
r
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Solution

The correct option is A 4r
The time period of revolution of a satellite and radius of circular orbit is related as

T2R3

And, using ω=2πT, we get

ω21R3

(ω1ω2)2=(R2R1)3

Here, ω1=ω; ω2=ω/8; R1=r

R2=(ωω/8)2/3r=4r

Hence, option (a) is correct.
Key Concept: The time period of revolution of a satellite and radius of circular orbit is related as T2R3


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