R and r are the radii of the earth and moo

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$R$ 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

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

$\frac{R}{r}\frac{{{\rho _m}}}{{{\rho _e}}}$

$R$ 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

$g = \frac{4}{3}\pi \rho GR$

$⇒$ $g \propto r\rho $

$\frac{{{g_e}}}{{{g_m}}} = \frac{R}{r} \times \frac{{{\rho _e}}}{{{\rho _m}}}$