---
title: "A particle moves along the x-axis in a region where its potential energy is given by the function \\(U(x) = \\dfrac{a}{x^2} – \\dfrac{b}{x}\\), where \\(a\\) and \\(b\\) are positive constants and \\(x > 0\\). At what position \\(x\\) is the particle in stable equilibrium?"
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url: "https://nerd-notes.com/ubq/117534/"
date_modified: "2026-08-04T07:48:54+00:00"
---

# A particle moves along the x-axis in a region where its potential energy is given by the function \(U(x) = \dfrac{a}{x^2} – \dfrac{b}{x}\), where \(a\) and \(b\) are positive constants and \(x > 0\). At what position \(x\) is the particle in stable equilibrium?

A particle moves along the x-axis in a region where its potential energy is given by the function \(U(x) = \dfrac{a}{x^2} - \dfrac{b}{x}\), where \(a\) and \(b\) are positive constants and \(x > 0\). At what position \(x\) is the particle in stable equilibrium?

- **A.** \(x = \dfrac{a}{b}\)
- **B.** \(x = \dfrac{2a}{b}\)
- **C.** \(x = \dfrac{b}{2a}\)
- **D.** \(x = \dfrac{a}{2b}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117534/*