Calculate the average density of earth in

Average density $=\frac{\text { Mass of earth }}{\text { Volume of earth }}=\frac{\mathrm{M}_{e}}{\frac{4}{3} \pi \mathrm{R}^{3}}$

Now $\quad g=\frac{\mathrm{GM}_{e}}{\mathrm{R}^{2}}$ or $\mathrm{M}_{e}=g \mathrm{R}^{2} / \mathrm{G} \quad \therefore$ Average density of earth $=\frac{g \mathrm{R}^{2} / \mathrm{G}}{\frac{4}{3} \pi \mathrm{R}^{3}}=\frac{3 g}{4 \pi \mathrm{GR}}$