Gravitation Question 46
Question: R and r are the radii of the earth and moon respectively. $ [{\rho_{e}}] $ and $ [{\rho_{m}}] $ are the densities of earth and moon respectively. The ratio of the accelerations due to gravity on the surfaces of earth and moon is [EAMCET 2000]
Options:
A) $ [\frac{R}{r}\frac{{\rho_{e}}}{{\rho_{m}}}] $
B) $ [\frac{r}{R}\frac{{\rho_{e}}}{{\rho_{m}}}] $
C) $ [\frac{r}{R}\frac{{\rho_{m}}}{{\rho_{e}}}] $
D) $ [\frac{R}{r}\frac{{\rho_{e}}}{{\rho_{m}}}] $
Show Answer
Answer:
Correct Answer: A
Solution:
$ [g=\frac{4}{3}\pi \rho GR] $
$ [g\propto r\rho ] $
$ [\frac{g_{e}}{g_{m}}=\frac{R}{r}\times \frac{{\rho_{e}}}{{\rho_{m}}}] $
