Gravitation Question 105
Question: 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 planet and star is proportional to $ [{{R}^{-\frac{5}{2}}}] $ , then $ [T^{2}] $ is proportional to[IIT 1989; RPMT 1997]
Options:
A) $ [R^{3}] $
B)$ [{{R}^{7/2}}] $
C) $ [{{R}^{5/2}}] $
D) $ [{{R}^{3/2}}] $
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Answer:
Correct Answer: B
Solution:
For revolution of planet centripetal force is provided by gravitational force of attraction $ [m{{\omega }^{2}}R\propto {{R}^{-5/2}}] $ Þ$ [\frac{1}{T^{2}}\propto {{R}^{-7/2}}] $ $ [\Rightarrow T^{2}\propto {{R}^{7/2}}] $
