It can be shown that for a uniform sphere the force of gravi

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 3.5 % ? Approximate the Earth as a uniform sphere. Express your answer using two significant figures.

Solution

R = 6.371 * 10⁶ m

0.965 (G M m / R²) = G M m / r²

0.965 / R² = 1 / r²

r² = R² / 0.965

= ( 6.371 * 10⁶ m )² / (0.965)

r = 6.49 * 10⁶ m