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  • Suppose the gravitational force varies inversely as the nth power of distance then the time period of

Suppose the gravitational force varies inversely as the nth power of distance then the time period \mathrm{T}of a satellite revolving in a circular orbit of radius \mathrm{r} around the earth is proportional to

Option: 1

\mathrm{r^{\frac{n+1}{2}}}


Option: 2

\mathrm{r^{\frac{n-1}{2}}}


Option: 3

\mathrm{\frac{1}{\sqrt r^{n}-1}}


Option: 4

\mathrm{\frac{1}{\sqrt r^{n}+1}}


Answers (1)

best_answer

\mathrm{ \frac{G M m}{r^n}=m r\left(\frac{2 \pi}{T}\right)^2 }

\mathrm{ T^2=\frac{4 \pi^2 r^{n+1}}{G M} \Rightarrow T \propto r^{\frac{n+1}{2}}}

Hence option 1 is correct.

 

Posted by

Divya Prakash Singh

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