---
title: "A uniform solid cylinder of mass \\(M\\) and radius \\(R\\) is mounted on a fixed, horizontal, frictionless axle through its center. A light, inextensible cord is wrapped around the outer rim of the cylinder and attached to a block of mass \\(m\\). The block is released from rest, causing the cylinder to rotate as the cord unwinds without slipping. Which of the following expressions gives the downward acceleration \\(a\\) of the block, and what are the limiting values of \\(a\\) and the cord tension \\(T\\) as \\(M \\to \\infty\\) and as \\(M \\to 0\\)?"
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url: "https://nerd-notes.com/ubq/124330/"
date_modified: "2026-09-28T14:04:53+00:00"
---

# A uniform solid cylinder of mass \(M\) and radius \(R\) is mounted on a fixed, horizontal, frictionless axle through its center. A light, inextensible cord is wrapped around the outer rim of the cylinder and attached to a block of mass \(m\). The block is released from rest, causing the cylinder to rotate as the cord unwinds without slipping. Which of the following expressions gives the downward acceleration \(a\) of the block, and what are the limiting values of \(a\) and the cord tension \(T\) as \(M \to \infty\) and as \(M \to 0\)?

A uniform solid cylinder of mass \(M\) and radius \(R\) is mounted on a fixed, horizontal, frictionless axle through its center. A light, inextensible cord is wrapped around the outer rim of the cylinder and attached to a block of mass \(m\). The block is released from rest, causing the cylinder to rotate as the cord unwinds without slipping. Which of the following expressions gives the downward acceleration \(a\) of the block, and what are the limiting values of \(a\) and the cord tension \(T\) as \(M \to \infty\) and as \(M \to 0\)?

![A schematic diagram showing a solid circular disk of radius \(R\) mounted on a central horizontal axle, viewed from the side. The disk is centered in the upper-left region of the frame, with a small central dark circle indicating the axle. A thin vertical line representing a light cord extends tangentially downward from the rightmost edge of the disk. At the lower end of the cord hangs a small rectangular block labeled \(m\). The disk is labeled \(M\) near its center. A horizontal dashed line indicates the fixed axle support. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604292-RX3WeB.jpg)

- **A.** \(a = \dfrac{g}{1 + \dfrac{M}{2m}}\); as \(M \to \infty\), \(a \to 0\) and \(T \to mg\); as \(M \to 0\), \(a \to g\) and \(T \to 0\)
- **B.** \(a = \dfrac{g}{1 + \dfrac{M}{2m}}\); as \(M \to \infty\), \(a \to 0\) and \(T \to mg\); as \(M \to 0\), \(a \to g\) and \(T \to mg\)
- **C.** \(a = \dfrac{g}{1 + \dfrac{M}{m}}\); as \(M \to \infty\), \(a \to 0\) and \(T \to mg\); as \(M \to 0\), \(a \to g\) and \(T \to 0\)
- **D.** \(a = \dfrac{g}{1 + \dfrac{M}{m}}\); as \(M \to \infty\), \(a \to 0\) and \(T \to 0\); as \(M \to 0\), \(a \to g\) and \(T \to mg\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124330/*