# Two planets have same average density but their radii are $R_1$ and $R_2$. If acceleration due to gravity on these planets are $g_1$ and $g_2$ respectively.

$a)\; \frac{g_1}{g_2}=\frac{R_1}{R_2} \\ b) \;\frac{g_1}{g_2}=\frac{R_2}{R_1} \\ c)\;\frac{g_1}{g_2}=\frac{{R_1}^2}{{R_2}^2} \\ d)\;\frac{g_1}{g_2}=\frac{{R_1}^3}{{R_2}^3}$

$g=\large\frac{4}{3}$$\pi \rho GR$
If $\rho$ is constant their
$\large\frac{g_1}{g_2}=\frac{R_1}{R_2}$
Hence a is the correct answer.

edited Feb 17, 2014 by meena.p