---
title: "Two small conducting spheres, \\(A\\) and \\(B\\), each of mass \\(m\\), are placed on a frictionless insulating surface separated by a distance \\(d\\) in a vacuum. Sphere \\(A\\) carries a net charge of \\(+q\\), and sphere \\(B\\) carries a net charge of \\(+3q\\). The spheres are released from rest simultaneously. Which of the following correctly compares the magnitudes of the initial accelerations \\(a_A\\) and \\(a_B\\) of the two spheres immediately after release, and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/117931/"
date_modified: "2026-08-04T08:02:37+00:00"
---

# Two small conducting spheres, \(A\) and \(B\), each of mass \(m\), are placed on a frictionless insulating surface separated by a distance \(d\) in a vacuum. Sphere \(A\) carries a net charge of \(+q\), and sphere \(B\) carries a net charge of \(+3q\). The spheres are released from rest simultaneously. Which of the following correctly compares the magnitudes of the initial accelerations \(a_A\) and \(a_B\) of the two spheres immediately after release, and provides the correct physical justification?

Two small conducting spheres, \(A\) and \(B\), each of mass \(m\), are placed on a frictionless insulating surface separated by a distance \(d\) in a vacuum. Sphere \(A\) carries a net charge of \(+q\), and sphere \(B\) carries a net charge of \(+3q\). The spheres are released from rest simultaneously. Which of the following correctly compares the magnitudes of the initial accelerations \(a_A\) and \(a_B\) of the two spheres immediately after release, and provides the correct physical justification?

![A horizontal line segment representing a distance d connects two small spheres. The left sphere is labeled A with charge +q and mass m. The right sphere is labeled B with charge +3q and mass m. Both spheres lie along the same horizontal line with no other objects present. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830557-8J268t.jpg)

- **A.** \(a_A = \dfrac{1}{3}a_B\), because sphere \(B\) has three times the charge of sphere \(A\) and therefore experiences three times the electrostatic force.
- **B.** \(a_A = 3a_B\), because sphere \(A\) is located in the electric field created by sphere \(B\), which is three times stronger than the field created by sphere \(A\).
- **C.** \(a_A = a_B\), because by Newton's third law the two spheres exert electrostatic forces of equal magnitude on each other, and both spheres have equal mass.
- **D.** \(a_A = a_B\), because the electric potential energy of the system is shared equally, causing the total charge \(4q\) to perform equal work on each sphere.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117931/*