Gravitation Question 208
Question: The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as [AMU 1995]
Options:
A) $ [4{{\pi }^{2}}R^{3}{{G}^{-1}}{{T}^{-2}}] $
B) $ [8{{\pi }^{2}}R^{3}{{G}^{-1}}{{T}^{-2}}] $
C) $ [12{{\pi }^{2}}R^{3}{{G}^{-1}}{{T}^{-2}}] $
D) $ [16{{\pi }^{2}}R^{3}{{G}^{-1}}{{T}^{-2}}] $
Show Answer
Answer:
Correct Answer: A
Solution:
$ [m{{\omega }^{2}}R=\frac{GMm}{R^{2}},\Rightarrow ,{{\left( \frac{2\pi }{T} \right)}^{2}}R=\frac{GM}{R^{2}}] $ $ [\Rightarrow ,M=\frac{4{{\pi }^{2}}R^{3}}{GT^{2}}] $
