Question

2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density ρ--M/V is therefore constant.) a) Find the force of gravity exerted on a point mass m located inside the earth, as a function of its distance from the earth's centre. (You may make use of results derived in class for a thin spherical shell.) b) Find the difference in the gravitational potential energy of the mass, between the centre of the earth and the earth's surface.

Answer 1

Assume the earth is a uniform sphere of mass. M and radius R p = m/v m = 4/3 pi R^3 p g = cem/R^2 (on surface) g = 4/R^2 (4/3 pi R^3 p] = 4/3 pi R4 p mass of earth in radius 'r' m^1 = 4/3 pi r^3 p = > g' = 4 m^1/R^2 g^1 = 4/3 pi r4p force of quantity F = mg^1 = 4/3 pi r cr pm \r\n G.P.E at counter of earth V_cont = m V_center uc = m [-3gm/2R] = -3gm/2R G.P.E at surface U_s = -Gmm/R delta U = Gmm/2R