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}}] $



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