---
title: "Two small spheres, \\(A\\) and \\(B\\), each of mass \\(m\\), are suspended from a ceiling by light insulating strings of equal length attached to a common point. Sphere \\(A\\) carries a charge of \\(+q\\), and sphere \\(B\\) carries a charge of \\(+3q\\). The spheres repel each other and come to rest in electrostatic equilibrium. Which of the following correctly compares the tensions \\(T_A\\) and \\(T_B\\) in the strings supporting spheres \\(A\\) and \\(B\\), respectively, and provides a correct justification?"
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url: "https://nerd-notes.com/ubq/117904/"
date_modified: "2026-08-04T08:02:30+00:00"
---

# Two small spheres, \(A\) and \(B\), each of mass \(m\), are suspended from a ceiling by light insulating strings of equal length attached to a common point. Sphere \(A\) carries a charge of \(+q\), and sphere \(B\) carries a charge of \(+3q\). The spheres repel each other and come to rest in electrostatic equilibrium. Which of the following correctly compares the tensions \(T_A\) and \(T_B\) in the strings supporting spheres \(A\) and \(B\), respectively, and provides a correct justification?

Two small spheres, \(A\) and \(B\), each of mass \(m\), are suspended from a ceiling by light insulating strings of equal length attached to a common point. Sphere \(A\) carries a charge of \(+q\), and sphere \(B\) carries a charge of \(+3q\). The spheres repel each other and come to rest in electrostatic equilibrium. Which of the following correctly compares the tensions \(T_A\) and \(T_B\) in the strings supporting spheres \(A\) and \(B\), respectively, and provides a correct justification?

![Two small spheres labeled A and B hang from light insulating strings attached to a single pivot point on a horizontal line representing a ceiling. Sphere A hangs to the left and sphere B hangs to the right. A vertical dashed reference line extends downward from the pivot point. The string for sphere A forms an angle \(\theta_A\) with the dashed vertical line, and the string for sphere B forms an angle \(\theta_B\) with the dashed vertical line. Sphere A is labeled +q and mass m. Sphere B is labeled +3q and mass m. No other labels, text, or arrows appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830550-cLgt8o.jpg)

- **A.** \(T_B = 3T_A\), because sphere \(B\) carries three times the charge of sphere \(A\) and therefore experiences three times as much electrostatic repulsive force.
- **B.** \(T_B > T_A\), because sphere \(B\) deflects to a larger angle from the vertical than sphere \(A\) due to its greater charge.
- **C.** \(T_B = T_A\), because the electric field created by sphere \(A\) at the location of sphere \(B\) is equal in magnitude to the electric field created by sphere \(B\) at the location of sphere \(A\).
- **D.** \(T_B = T_A\), because Newton's third law requires the electrostatic force on sphere \(B\) to equal the electrostatic force on sphere \(A\), and both spheres experience equal gravitational forces.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117904/*