---
title: "A particle moves in a conservative force field where its potential energy as a function of radial distance \\(r\\) from the origin is given by \\(U(r) = -\\dfrac{C}{r^6}\\), where \\(C\\) is a positive constant. Which of the following expressions represents the radial force vector \\(\\vec{F}(r)\\) exerted on the particle?"
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url: "https://nerd-notes.com/ubq/117543/"
date_modified: "2026-08-04T07:48:58+00:00"
---

# A particle moves in a conservative force field where its potential energy as a function of radial distance \(r\) from the origin is given by \(U(r) = -\dfrac{C}{r^6}\), where \(C\) is a positive constant. Which of the following expressions represents the radial force vector \(\vec{F}(r)\) exerted on the particle?

A particle moves in a conservative force field where its potential energy as a function of radial distance \(r\) from the origin is given by \(U(r) = -\dfrac{C}{r^6}\), where \(C\) is a positive constant. Which of the following expressions represents the radial force vector \(\vec{F}(r)\) exerted on the particle?

- **A.** \(\vec{F}(r) = -\dfrac{C}{5r^5}\hat{r}\)
- **B.** \(\vec{F}(r) = -\dfrac{6C}{r^7}\hat{r}\)
- **C.** \(\vec{F}(r) = \dfrac{6C}{r^7}\hat{r}\)
- **D.** \(\vec{F}(r) = -\dfrac{6C}{r^5}\hat{r}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117543/*