Gravitation Question 275
Question:If $ [g\propto \frac{1}{R^{3}}] $ (instead of $ [\frac{1}{R^{2}}),] $ then the relation between time period of a satellite near earth’s surface and radius R will be[RPMT 2002]
Options:
A) $ [T^{2}\propto R^{3}] $
B) $ [T\propto R^{2}] $
C) $ [T^{2}\propto R] $
D) $ [T\propto R] $
Show Answer
Answer:
Correct Answer: B
Solution:
Gravitational force provides the required centripetal force $ [m{{\omega }^{2}}R=\frac{GMm}{R^{3}}] $ $ [\Rightarrow ] $ $ [\frac{4{{\pi }^{2}}}{T^{2}}=\frac{GM}{R^{4}}] $ $ [\Rightarrow ] $ $ [T\propto R^{2}] $
