Question

Find the acceleration due to gravity 'g' in terms of mean density of the Earth 'd'. Assume it to be a
perfect sphere.​

Answer 1

Let us take earth to be a sphere of radius R and  density d. 

Then the mass of the earth M is given by,

M = 4/3 π R³ d. According to law of gravitation the force on a body of mass m, near the surface of earth is given by,

F = G (mM/R²), in magnitude, and acting along the line joining the centre of the earth and the centre of the body. Let this force produce an acceleration g in the body of mass m. Then

G (mM/R²) = mg, or g = G M/R² = 4π/3 G R d.

Acceleration due to gravity is proportional to mean density of earth, and its radius.