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  • Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star i

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to \mathrm{R^{-5 / 2} \text {, then } T^2} is proportional to:

Option: 1

\mathrm{R^3}


Option: 2

\mathrm{R^{7 / 2}}


Option: 3

\mathrm{R^{3 / 2}}


Option: 4

\mathrm{R^{3.75}}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \mathrm{mR} \omega^2=\mathrm{F}_{\mathrm{gr}} \\ \Rightarrow & \mathrm{mR} \omega^2=\frac{\mathrm{k}}{\mathrm{R}^{5 / 2}} \\ \Rightarrow & \omega^2=\frac{\mathrm{k}}{\mathrm{m} \mathrm{R}^{7 / 2}} \\ \Rightarrow & \mathrm{T}^2 \propto \mathrm{R}^{7 / 2} \end{aligned}}

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Ritika Kankaria

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