---
title: "A flexible, uniform cord of mass \\(M\\) and length \\(L\\) hangs symmetrically at rest over a small frictionless peg, with equal lengths of \\(\\dfrac{L}{2}\\) hanging vertically on each side. The cord is given an infinitesimal nudge and begins to slide off the peg. In terms of \\(g\\) and \\(L\\), what is the speed of the cord at the instant its trailing end completely leaves the peg?"
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url: "https://nerd-notes.com/ubq/120672/"
date_modified: "2026-08-23T04:42:37+00:00"
---

# A flexible, uniform cord of mass \(M\) and length \(L\) hangs symmetrically at rest over a small frictionless peg, with equal lengths of \(\dfrac{L}{2}\) hanging vertically on each side. The cord is given an infinitesimal nudge and begins to slide off the peg. In terms of \(g\) and \(L\), what is the speed of the cord at the instant its trailing end completely leaves the peg?

A flexible, uniform cord of mass \(M\) and length \(L\) hangs symmetrically at rest over a small frictionless peg, with equal lengths of \(\dfrac{L}{2}\) hanging vertically on each side. The cord is given an infinitesimal nudge and begins to slide off the peg. In terms of \(g\) and \(L\), what is the speed of the cord at the instant its trailing end completely leaves the peg?

![A small circular peg is mounted horizontally. A uniform flexible cord hangs over the top of the peg, extending straight downward in two equal vertical segments on the left and right sides. A horizontal dashed line passes through the peg center to indicate the reference level y = 0. A downward vertical arrow indicates the positive y-direction. Two vertical dimension arrows indicate that each hanging side has length L/2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460156-qIyM6z.jpg)

- **A.** \(\sqrt{\dfrac{gL}{6}}\)
- **B.** \(\sqrt{\dfrac{gL}{4}}\)
- **C.** \(\sqrt{\dfrac{gL}{3}}\)
- **D.** \(\sqrt{\dfrac{gL}{2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120672/*