---
title: "Two blocks of masses \\(m_1\\) and \\(m_2\\), with \\(m_1 > m_2\\), are connected by a light, inextensible string that passes over a uniform solid disk pulley of mass \\(M\\) and radius \\(R\\). The pulley is mounted on a frictionless horizontal axle, and the string does not slip along the pulley rim as the system accelerates from rest. The tensions in the string segments attached to \\(m_1\\) and \\(m_2\\) are \\(T_1\\) and \\(T_2\\), respectively. In terms of \\(m_1\\), \\(m_2\\), \\(M\\), and fundamental constants, what is the magnitude of the difference in string tensions, \\(T_1 – T_2\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120833/"
date_modified: "2026-08-23T04:43:31+00:00"
---

# Two blocks of masses \(m_1\) and \(m_2\), with \(m_1 > m_2\), are connected by a light, inextensible string that passes over a uniform solid disk pulley of mass \(M\) and radius \(R\). The pulley is mounted on a frictionless horizontal axle, and the string does not slip along the pulley rim as the system accelerates from rest. The tensions in the string segments attached to \(m_1\) and \(m_2\) are \(T_1\) and \(T_2\), respectively. In terms of \(m_1\), \(m_2\), \(M\), and fundamental constants, what is the magnitude of the difference in string tensions, \(T_1 – T_2\)?

Two blocks of masses \(m_1\) and \(m_2\), with \(m_1 > m_2\), are connected by a light, inextensible string that passes over a uniform solid disk pulley of mass \(M\) and radius \(R\). The pulley is mounted on a frictionless horizontal axle, and the string does not slip along the pulley rim as the system accelerates from rest. The tensions in the string segments attached to \(m_1\) and \(m_2\) are \(T_1\) and \(T_2\), respectively. In terms of \(m_1\), \(m_2\), \(M\), and fundamental constants, what is the magnitude of the difference in string tensions, \(T_1 - T_2\)?

![A schematic diagram showing an Atwood machine. At the top center, a solid circular disk representing a pulley of radius \(R\) and mass \(M\) is mounted on a fixed horizontal axle through its center. A thin vertical line extends upward from the center of the disk to a horizontal hatched ceiling surface. A continuous string passes over the top perimeter of the disk. From the left rim of the disk, a vertical string segment hangs downward and connects to a rectangular block labeled \(m_1\). From the right rim of the disk, a second vertical string segment hangs downward and connects to a smaller rectangular block labeled \(m_2\). Upward tension arrows labeled \(T_1\) and \(T_2\) are drawn along the left and right string segments, respectively. A curved arrow indicating counterclockwise rotation is near the disk. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460211-YuUMRs.jpg)

- **A.** \(\dfrac{M(m_1 - m_2)g}{2(m_1 + m_2) + M}\)
- **B.** \(\dfrac{M(m_1 - m_2)g}{m_1 + m_2 + M}\)
- **C.** \(\dfrac{M(m_1 - m_2)g}{2(m_1 + m_2)}\)
- **D.** \(\dfrac{2M(m_1 - m_2)g}{2(m_1 + m_2) + M}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120833/*