---
title: "A uniform solid cylinder of mass \\(M\\) and radius \\(R\\) is mounted on a frictionless horizontal axle through its central axis and is initially at rest. At time \\(t = 0\\), a time-dependent force \\(F(t) = F_0 e^{-kt}\\) is applied tangentially to the outer rim of the cylinder, where \\(F_0\\) and \\(k\\) are positive constants. Which of the following expressions represents the angular speed of the cylinder as \\(t \\to \\infty\\)?"
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url: "https://nerd-notes.com/ubq/117617/"
date_modified: "2026-08-04T07:49:20+00:00"
---

# A uniform solid cylinder of mass \(M\) and radius \(R\) is mounted on a frictionless horizontal axle through its central axis and is initially at rest. At time \(t = 0\), a time-dependent force \(F(t) = F_0 e^{-kt}\) is applied tangentially to the outer rim of the cylinder, where \(F_0\) and \(k\) are positive constants. Which of the following expressions represents the angular speed of the cylinder as \(t \to \infty\)?

A uniform solid cylinder of mass \(M\) and radius \(R\) is mounted on a frictionless horizontal axle through its central axis and is initially at rest. At time \(t = 0\), a time-dependent force \(F(t) = F_0 e^{-kt}\) is applied tangentially to the outer rim of the cylinder, where \(F_0\) and \(k\) are positive constants. Which of the following expressions represents the angular speed of the cylinder as \(t \to \infty\)?

![A perspective view of a uniform solid cylinder mounted horizontally on a thin cylindrical axle along its central axis. The cylinder has mass M and radius R, with a dashed radial line labeled R extending from the center of the circular face to the top edge. At the top edge of the cylinder, a single straight arrow pointing horizontally to the right represents a tangential force, labeled F(t) = F_0 e^{-kt}. A curved arrow around the central axle indicates rotation labeled \omega. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829759-XUh062.jpg)

- **A.** \(\dfrac{F_0}{2 M R k}\)
- **B.** \(\dfrac{F_0}{M R k}\)
- **C.** \(\dfrac{2 F_0}{M R k}\)
- **D.** \(\dfrac{5 F_0}{2 M R k}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117617/*