Gravitation Question 15
Question:The radii of two planets are respectively $ [R_{1}] $ and $ [R_{2}] $ and their densities are respectively $ [{\rho_{1}}] $ and $ [{\rho_{2}}] $ . The ratio of the accelerations due to gravity at their surfaces is [MP PET 1994]
Options:
A) $ [g_{1}:g_{2}=\frac{{\rho_{1}}}{R_{1}^{2}}:\frac{{\rho_{2}}}{R_{2}^{2}}] $
B) $ [g_{1}:g_{2}=R_{1}R_{2}:{\rho_{1}}{\rho_{2}}] $
C) $ [g_{1}:g_{2}=R_{1}{\rho_{2}}:R_{2}{\rho_{1}}] $
D) $ [g_{1}:g_{2}=R_{1}{\rho_{1}}:R_{2}{\rho_{2}}] $
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Answer:
Correct Answer: D
Solution:
$ [g=\frac{4}{3}\pi \rho GR] $ $ [\therefore ] $
$ [\frac{g_{1}}{g_{2}}=\frac{R_{1}{\rho_{1}}}{R_{2}{\rho_{2}}}] $
