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}}] $
Show Answer
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}}] $
