Question

Acceleration due to gravity on the moon is $1/6th$ of the acceleration due to gravity on the earth. If the ratio of densities of the earth and the moon is $5/3$, then radius on the moon in terms of radius of earth will be

Answer 1

We know $g=\frac{4\pi G\rho r}{3}=K\rho r$

Given, $g_m=\frac{1}{6}{g}_e$

$\Rightarrow$ $\frac{g_m}{g_e}=\frac{{\rho }_m{r}_m}{{\rho }_e{r}_e}=\frac{1}{6}$

Also ${\rho }_m=\frac{3}{5}{\rho }_e$

So, $\frac{3r_m}{5r_e}=\frac{1}{6}$

$\Rightarrow r_m=\frac{5r_e}{18}$