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Question
Calculate the average density of the earth in terms of g, G and R
Solution
Let the earth be a sphere of radius R.
Now Density, ρ = `"Mass"/"Volume" = "M"/"V"`
From Newton's law of gravitation
g = "G""M"/"R"^2` or M= ("gR"^2)/"G"`
Volume of earth, V = `4/3π"R"^3`
∴ ρ = `"gR"^2/"G" xx 3/(4π"R"^3)`
= `(3"g")/(4π"RG")`
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