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  • A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity <img alt="\mathrm{\frac{3\pi

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity \mathrm{\frac{3\pi }{Gd}} represents:

Option: 1

\mathrm{T}


Option: 2

\mathrm{T}^2


Option: 3

\mathrm{T}^3


Option: 4

\sqrt{T}


Answers (1)

best_answer

\begin{aligned} \mathrm{T}^2 & =\frac{4 \pi^2}{\mathrm{GM}}\left(\mathrm{R}^3\right) \\ \mathrm{T}^2 & =\frac{4 \pi^2 \times \mathrm{R}^3}{\mathrm{Gd}\left(\frac{4}{3} \pi \mathrm{R}^3\right)} \\ \mathrm{T}^2 & =\frac{3 \pi}{\mathrm{Gd}} \end{aligned}

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Rakesh

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