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  • The mean radius of the earth is R, its angular speed about its own axis is and the acceleration due to gravity at

The mean radius of the earth is R, its angular speed about its own axis is \omega and the acceleration due to gravity at the earth surface is g. The cube of radius of orbit of ‘geostationary satellite’ will be:A

Option: 1

\mathrm{\left(R^2 g / \omega\right) .}


Option: 2

\mathrm{\left(R^2 \omega / g\right) .}


Option: 3

\mathrm{\left(R g / \omega^2\right) .}


Option: 4

\mathrm{\left(R^2 g / \omega^2\right) .}


Answers (1)

best_answer

\mathrm{\begin{aligned} \mathrm{mr} \omega^2= & \frac{\mathrm{GMm}}{r^2} \Rightarrow r \omega^2=\frac{G M}{r^2} \\ & \Rightarrow r^3=\frac{G M}{\omega^2}=\frac{G M}{R^2} \cdot \frac{R^2}{\omega^2} \\ & \Rightarrow r^3=g \frac{R^2}{\omega^2} . \end{aligned}}

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Rakesh

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