Acceleration due to gravity on the surface of moon is$1.67{\text{ms}}^{-2}$ . If the mass of earth is 80 times that of moon then the ratio of radii of earth to the moon is

We have $g=\frac{GM}{R^2}$ 

Where M is the mass of the planet, R is the radius and Gis the gravitational constant.

$g\propto \frac{M}{R^2}$

$\Rightarrow R\propto \sqrt{\frac{M}{g}}$

We can get $\frac{R_E}{R_M}=\frac{\sqrt{\frac{M_E}{g_E}}}{\sqrt{\frac{M_{moon}}{g_{moon}}}}=\sqrt{\frac{M_E}{M_{moon}}\times \frac{g_{moon}}{g_{earth}}}$

$=\sqrt{80\times \frac{1.67}{10}}=\sqrt{13.36}=3.65$

$\therefore R_E:R_M=3.65$