---
title: "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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url: "https://nerd-notes.com/ubq/124048/"
date_modified: "2026-09-28T13:30:16+00:00"
---

# 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 \(r \ge 0\)?

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 \(r \ge 0\)?

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124048/*