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Question

A geostationary satellite is orbiting the earth at a height $$6R$$ above the surface of the earth, where $$R$$ is the radius of earth. The time period of another satellite revolving around earth at a height $$2.5 R$$ from earth's surface is :


A
122 hr
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B
12 hr
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C
62 hr
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D
6 hr
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Solution

The correct option is C $$6\sqrt{2}$$ hr
Time period is related to orbit radius as
$$T^2\propto R^3$$
$$\Rightarrow \dfrac {T_1^2}{T_2^2}=\dfrac {R_1^3}{R_2^3}$$
Given $$R_1=7R$$ and $$R_2=3.5R$$
$$\Rightarrow \dfrac {T_1^2}{T_2^2}= \left(\dfrac {7R}{3.5R}\right)^3=8$$
$$\Rightarrow T_2=\dfrac {T_1}{\sqrt {8}}=\dfrac {24}{2\sqrt 2}=6\sqrt2$$ hours
Option C.

Physics

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