Gravitation Question 58
Question: Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth.If the ratio of densities of earth $ [({\rho_{e}})] $ and moon $ [({\rho_{m}})] $ is $ [\left( \frac{{\rho_{e}}}{{\rho_{m}}} \right)=\frac{5}{3}] $ then radius of moon Rm in terms of Re will be [MP PMT 2003]
Options:
A) $ [\frac{5}{18}R_{e}] $
B) $ [\frac{1}{6}R_{e}] $
C) $ [\frac{3}{18}R_{e}] $
D) $ [\frac{1}{2\sqrt{3}}R_{e}] $
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Answer:
Correct Answer: A
Solution:
$ [g=\frac{4}{3}\pi G\rho R] $ $ [\Rightarrow ,,g\propto \rho R,\Rightarrow ,\frac{g_{e}}{g_{m}}=\frac{{\rho_{e}}}{{\rho_{m}}}\times \frac{R_{e}}{R_{m}}] $ $ [\Rightarrow ,,\frac{6}{1}=\frac{5}{3}\times \frac{R_{e}}{R_{m}},\Rightarrow ,,R_{m}=\frac{5}{18}R_{e}] $
