AP Physics C: Mechanics
3.3 Potential Energy
A hypothetical planet is modeled as a uniform solid sphere of mass \(M\) and radius \(R\). A narrow radial tunnel passes through the planet from its center to its surface, allowing a small test mass \(m\) to move freely along the radial coordinate \(r\). Taking the gravitational potential energy of the planet-mass system to be zero at infinite separation (\(U(\infty) = 0\)), which of the following graphs best represents the gravitational potential energy \(U\) of the system as a function of distance \(r\) from the center of the planet for \(r \ge 0\)?
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