This is a possible simulacrum of a final exam question. I need a numerical and w

Question

This is a possible simulacrum of a final exam question. I need a numerical and well delineated answer please. 2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density p 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, mou may make use of results derived in class for a thin spherical shell.) b) Find the difference in the gravitational potential enerky of the mas, between the centre of the earth and the earth's surface.

Explanation / Answer

a) g = GM/r2

But effective mass of earth which is responsible for gravity decreases as the depth increases. Here Me is effective mass and Re is effective radius

g = GMe/ Re2 ................( also mass = density x volume, )

So g = G 4 pi x density R /3

At depth h it is given by

g = G 4 x pi x ( R-h)3x density /3 ( R-h)2

Dividing voth equations we get we get g1 = g ( 1 - h/R)

b) Gravitational potential at a depth r is given by

So no put r = 0 and r =R

V1 = -GM/2R

V2 = -GM/3R

V1-V2 = GM/6R

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