---
title: "A flexible, uniform chain of total mass \\(M\\) and length \\(L\\) rests on a frictionless horizontal tabletop. Initially, a length \\(y_0\\) of the chain hangs vertically over the edge of the table, and the chain is released from rest. As the chain slides off the table, the portion on the table moves horizontally toward the edge while the hanging portion falls vertically.  What is the total work done by the gravitational force on the chain from the moment of release until the instant the entire chain leaves the horizontal tabletop?"
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url: "https://nerd-notes.com/ubq/120657/"
date_modified: "2026-08-23T04:42:30+00:00"
---

# A flexible, uniform chain of total mass \(M\) and length \(L\) rests on a frictionless horizontal tabletop. Initially, a length \(y_0\) of the chain hangs vertically over the edge of the table, and the chain is released from rest. As the chain slides off the table, the portion on the table moves horizontally toward the edge while the hanging portion falls vertically.

What is the total work done by the gravitational force on the chain from the moment of release until the instant the entire chain leaves the horizontal tabletop?

A flexible, uniform chain of total mass \(M\) and length \(L\) rests on a frictionless horizontal tabletop. Initially, a length \(y_0\) of the chain hangs vertically over the edge of the table, and the chain is released from rest. As the chain slides off the table, the portion on the table moves horizontally toward the edge while the hanging portion falls vertically.

What is the total work done by the gravitational force on the chain from the moment of release until the instant the entire chain leaves the horizontal tabletop?

![A side-view diagram showing a horizontal table surface with a smooth, rounded corner on the right. A uniform chain of total length \(L\) is depicted as a continuous thick line lying horizontally on the tabletop and bending over the right edge to hang vertically. A vertical dimension arrow spans the vertical hanging portion from the table height to the bottom tip of the chain, labeled \(y_0\). A horizontal dimension arrow spans the portion on the table, labeled \(L - y_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460150-KXq30W.jpg)

- **A.** \(\dfrac{Mg}{2}(L - y_0)\)
- **B.** \(\dfrac{Mg}{2L}(L^2 - y_0^2)\)
- **C.** \(\dfrac{Mg}{2L}(L - y_0)^2\)
- **D.** \(\dfrac{Mg}{L}(L^2 - y_0^2)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120657/*