Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through...

Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through its center (Fig. 13-8). Also assume we can position an apple anywhere along the tunnel or outside the sphere. Let F_R be the magnitude of the gravitational force on the apple when it is located at the planet\"s surface. How far from the surface is there a point where the magnitude of the gravitational force on the apple is ½ F_R if we move the apple (a) away from the planet and (b) into the tunnel?

Fig. 13.8 A capsule of mass m faIls from rest through a tunnel that connects Earth\"s south and north poles. When the capsule is at distance r from Earth\"s center, the portion of Earth\"s mass that is contained in a sphere of that radius is M_ins.

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