---
title: "Two unequal masses, \\(m_1\\) and \\(m_2\\) with \\(m_1 > m_2\\), are released from rest in deep space and interact solely through their mutual gravitational attraction. An observer in an inertial reference frame observes that both masses accelerate toward each other with different, time-dependent accelerations. Which of the following best explains why the center of mass of the two-mass system does not accelerate despite the individual masses experiencing non-zero accelerations?"
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url: "https://nerd-notes.com/ubq/124221/"
date_modified: "2026-09-28T14:04:14+00:00"
---

# Two unequal masses, \(m_1\) and \(m_2\) with \(m_1 > m_2\), are released from rest in deep space and interact solely through their mutual gravitational attraction. An observer in an inertial reference frame observes that both masses accelerate toward each other with different, time-dependent accelerations. Which of the following best explains why the center of mass of the two-mass system does not accelerate despite the individual masses experiencing non-zero accelerations?

Two unequal masses, \(m_1\) and \(m_2\) with \(m_1 > m_2\), are released from rest in deep space and interact solely through their mutual gravitational attraction. An observer in an inertial reference frame observes that both masses accelerate toward each other with different, time-dependent accelerations. Which of the following best explains why the center of mass of the two-mass system does not accelerate despite the individual masses experiencing non-zero accelerations?

- **A.** The mutual gravitational force is conservative, which ensures that all potential energy is converted entirely into internal kinetic energy of the particles without performing net external work on the system.
- **B.** The mutual gravitational forces induce individual accelerations that have equal magnitudes and opposite directions, so the direct vector sum of the two accelerations cancels out at every point in time.
- **C.** The more massive object exerts a proportionately greater gravitational force on the smaller object, which compensates for their different inertial masses and maintains the position of the center of mass.
- **D.** The mutual gravitational forces form an action-reaction pair with equal magnitudes and opposite directions, ensuring that the net external force on the system is zero and the mass-weighted sum of accelerations vanishes.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124221/*