---
title: "An Atwood machine consists of two blocks of masses \\(m_1\\) and \\(m_2\\) (where \\(m_2 > m_1\\)) connected by a light string that passes over a uniform solid cylindrical disk pulley of mass \\(M\\) and radius \\(R\\). The pulley is mounted on a frictionless horizontal axle, and the string does not slip on the pulley as the system accelerates from rest. What is the difference between the tensions in the two vertical segments of the string, \\(T_2 – T_1\\), in terms of the given quantities and fundamental constants?"
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url: "https://nerd-notes.com/ubq/120800/"
date_modified: "2026-08-23T04:43:24+00:00"
---

# An Atwood machine consists of two blocks of masses \(m_1\) and \(m_2\) (where \(m_2 > m_1\)) connected by a light string that passes over a uniform solid cylindrical disk pulley of mass \(M\) and radius \(R\). The pulley is mounted on a frictionless horizontal axle, and the string does not slip on the pulley as the system accelerates from rest. What is the difference between the tensions in the two vertical segments of the string, \(T_2 – T_1\), in terms of the given quantities and fundamental constants?

An Atwood machine consists of two blocks of masses \(m_1\) and \(m_2\) (where \(m_2 > m_1\)) connected by a light string that passes over a uniform solid cylindrical disk pulley of mass \(M\) and radius \(R\). The pulley is mounted on a frictionless horizontal axle, and the string does not slip on the pulley as the system accelerates from rest. What is the difference between the tensions in the two vertical segments of the string, \(T_2 - T_1\), in terms of the given quantities and fundamental constants?

![A schematic diagram showing an Atwood machine. At the top, a horizontal line represents a ceiling from which a vertical bracket extends downward to hold the center axle of a circular disk pulley labeled with mass M and radius R. A string hangs vertically from the left edge of the pulley supporting a square block labeled m_1, with an upward arrow along the string labeled T_1. From the right edge of the pulley, the string hangs vertically downward supporting a larger square block labeled m_2, with an upward arrow along the string labeled T_2. No other lines, labels, or coordinate axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460204-qCYT4U.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120800/*