Question

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

July 30, 2024

Answer

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 = ${𝑔𝑅^2 \over 𝐺{4\over3}πR^3}$ = ${3g \over 4 πGR}$

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