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Question

The mean radius of earth is R, and its angular speed on its axis is ω. What will be the radius of orbit of a geostationary satellite?

A
(2R2gω2)1/3
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B
(R2gω2)1/3
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C
(R2g3ω2)1/3
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D
(R2g5ω2)1/3
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Solution

The correct option is B (R2gω2)1/3

Time period of rotation of earth=2πω
(Duration of one day)

Geostationary satellite has same time period, T=2πω.

Let r be the radius of orbit of satellite.

So, the time period of satellite =2πr3/2GMearth

As, g=GMearthR2

T=2πr3/2Rg

Since, T=2πω

2πr3/2Rg=2πω

r3/2=Rωg

r=(R2gω2)1/3

Hence, option (b) is the correct answer.

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