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 5.5 ? Approximate the Earth as a uniform sphere.

Express your answer using two significant figures.

Answer 1

Reduced by 5.5 m/s^2 (from 9.8 m/s^2), or by a factor of 5.5?

When you have clarified how much you want to reduce g, drill to a value of R for which M/R^2 (which is proportional to density*R) is reduced by the same factor.

Answer 2

No by 5.5%.

Answer 3

To reduce the value of g by 5.5%, reduce the distance from the center of the Earth by 5.5%. That will mean going down about 350 km.