Question

Question 21
Calculate the average density of the earth in terms of g, G and R.

Answer 1

$g=\frac{GM}{R^2}$ or $M=\frac{g\times R^2}{G}\Rightarrow$ Density D = $\frac{\text{mass}}{\text{volume}}=\frac{g\times R^2}{G\times V_e}$

(Where $V_e$ is the volume of the earth)

or $D=\frac{g\times R^2}{G\times \frac{4}{3}\pi R^3}=\frac{3g}{4\pi GR}$