Gravitation Question 108
Question:Suppose the gravitational force varies inversely as the $ [n^{th}] $ power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to [AIEEE 2004]
Options:
A) $ [{{R}^{\left( \frac{n+1}{2} \right)}}] $
B) $ [{{R}^{\left( \frac{n-1}{2} \right)}}] $
C) $ [R^{n}] $
D) $ [{{R}^{\left( \frac{n-2}{2} \right)}}] $
Show Answer
Answer:
Correct Answer: A
Solution:
$ [m{{\omega }^{2}}R\propto \frac{1}{R^{n}}] $ Þ $ [m\left( \frac{4{{\pi }^{2}}}{T^{2}} \right)R\propto \frac{1}{R^{n}}] $ Þ $ [T^{2}\propto {{R}^{n+1}}] $ $ [T\propto {{R}^{\left( \frac{n+1}{2} \right)}}] $
