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If the distance between sun and planet is r then force of attraction varies as F\propto \frac{1}{r^{n}}        . How will the orbital velocity v varies as:

Option: 1

V\propto \frac{1}{\sqrt{r^n}}


Option: 2

V\propto \frac{1}{\sqrt{r^{n+1}}}


Option: 3

V\propto \frac{1}{\sqrt{r^{n-1}}}


Option: 4

 V \propto{\sqrt{r^{n-1}}}


Answers (1)

best_answer

As we learn

Relation of force of attraction to the orbital velocity -

F\alpha \frac{1}{r^{n}}

v\alpha \frac{1}{\sqrt{r^{n}-1}}

V\rightarrow Orbital velocity

r\rightarrow Distance between sun and planet

- wherein

F= Force of attraction of sun to the planet.

 

 When a planet revolve around the sun then gravitational force = centripetal force

\frac{GMm}{r^{n}} = \frac{mv^2}{r}

v = \sqrt{\frac{GM}{r^{n-1}}}

v\propto \frac{1}{\sqrt{r^{n-1}}}

 

Posted by

Shailly goel

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