It can be shown that for a uniform sphere the force of gravity at a point inside

Question

It can be shown that for a uniform sphere the force of gravity at a point inside the sphere depends only on the mass closer to the center than that point. The net force of gravity due to points outside the radius of the point cancels.

How far would you have to drill into the Earth, to reach a point where your weight is reduced by 6.0 ? Approximate the Earth as a uniform sphere. It can be shown that for a uniform sphere the force of gravity at a point inside the sphere depends only on the mass closer to the center than that point. The net force of gravity due to points outside the radius of the point cancels.

Explanation / Answer

g=GM/R^2 g'=Gm/r^2 Where m is the effective mass m=(4/3)*pi*r^3*density As we go into the earth g'/g=r/R 94/100=r/6400 r=6016 km Depth=384 km

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