Question

Assume earth to be a uniform sphere of radius R, mass m, desntiy ρ₀ . g is acceleration due to gravity on surface of earth. If earth is replaced by a sphere of same radius having a density variation as

p = p₀   0 ≤ r ≤ R/2

p = p₀ r  R/2 ≤ r ≤ R

The value of acceleration due to gravity on the surface would be

(1) g

(2) g/g

(3) -0.83 g

(4) g/g [1+5.625R]

Answer 1

(4) g/g [1+5.625R]

We know for present earth

g = GM/R² ---(1)

Let M₁ and M₂ be mass of part of earth of radius R/2 and the part of earth radius varying from R/2 to R respectively. Then

g’ = Acceleration due to gravity on surface of new earth = GM'/R₂