Gravitation Question 3

Question: Two planets have the same average density but their radii are $ [R_{1}] $ and $ [R_{2}] $ . If acceleration due to gravity on these planets be $ [g_{1}] $ and $ [g_{2}] $ respectively, then [AIIMS 1985]

Options:

A) $ [\frac{g_{1}}{g_{2}}=\frac{R_{1}}{R_{2}}] $

B) $ [\frac{g_{1}}{g_{2}}=\frac{R_{2}}{R_{1}}] $

C) $ [\frac{g_{1}}{g_{2}}=\frac{R_{1}^{2}}{R_{2}^{2}}] $

D) $ [\frac{g_{1}}{g_{2}}=\frac{R_{1}^{3}}{R_{2}^{3}}] $

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Answer:

Correct Answer: A

Solution:

$ [g=\frac{4}{3}\pi \rho GR] $ . If $ [\rho ] $ = constant then $ [\frac{g_{1}}{g_{2}}=\frac{R_{1}}{R_{2}}] $



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