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

we know that g = {𝐺𝑀 \over 𝑅^2}  or  M = {𝑔𝑅^2 \over 𝐺}

⟹ Average density of the earth,    D = {𝑀𝑎𝑠𝑠 \over 𝑉𝑜𝑙𝑢𝑚𝑒} = {𝑔𝑅^2 \over 𝐺 ×𝑉𝑒}

(Where V e is the volume of the earth)

Or,                                                    D = {𝑔𝑅^2 \over 𝐺{4\over3}πR^3} = {3g \over 4 πGR}