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

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

Option: 1

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


Option: 2

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


Option: 3

\mathrm{\left(\mathrm{Rg} / \omega^2\right)}


Option: 4

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


Answers (1)

best_answer

\mathrm{\begin{aligned} & m r \omega^2=\frac{G M m}{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}}

Hence (D) is correct.

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manish

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