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  • Imagine a light planet revolving around a very massive star in a circular orbit of radius with a peri

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

Option: 1

\mathrm{R}^3


 


Option: 2

\mathrm{R^{7 / 2}}
 


Option: 3

\mathrm{\mathrm{R}^{3 / 2}}
 


Option: 4

\mathrm{\mathrm{R}^{3.75}}


Answers (1)

best_answer

\mathrm{ m R \omega^2=F_{g r} }

\mathrm{ \Rightarrow m R \omega^2=\frac{k}{R^{5 / 2}} }

\mathrm{ \omega^2=\frac{k}{m R^{7 / 2}} \quad \Rightarrow \quad \omega \propto \frac{1}{R^{7 / 4}} }

\mathrm{\Rightarrow T \propto R^{7 / 4} \quad \Rightarrow \quad T^2 \propto R^{7 / 2} }

Hence option 2 is correct.


 

Posted by

Sayak

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