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title: "A block of mass \\(m_1\\) rests on a frictionless horizontal tabletop and is connected by a light, non-stretching string to a suspended block of mass \\(m_2\\). The string passes over a uniform solid cylindrical pulley of mass \\(M\\) and radius \\(R\\) that rotates about a frictionless axle at its center without the string slipping. Let \\(T_1\\) denote the tension in the horizontal segment of the string attached to \\(m_1\\), and let \\(T_2\\) denote the tension in the vertical segment attached to \\(m_2\\). In the theoretical limit as the pulley mass approaches infinity (\\(M \\to \\infty\\)), which of the following correctly describes the values toward which \\(T_1\\) and \\(T_2\\) approach?"
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url: "https://nerd-notes.com/ubq/120829/"
date_modified: "2026-08-23T04:43:30+00:00"
---

# A block of mass \(m_1\) rests on a frictionless horizontal tabletop and is connected by a light, non-stretching string to a suspended block of mass \(m_2\). The string passes over a uniform solid cylindrical pulley of mass \(M\) and radius \(R\) that rotates about a frictionless axle at its center without the string slipping. Let \(T_1\) denote the tension in the horizontal segment of the string attached to \(m_1\), and let \(T_2\) denote the tension in the vertical segment attached to \(m_2\). In the theoretical limit as the pulley mass approaches infinity (\(M \to \infty\)), which of the following correctly describes the values toward which \(T_1\) and \(T_2\) approach?

A block of mass \(m_1\) rests on a frictionless horizontal tabletop and is connected by a light, non-stretching string to a suspended block of mass \(m_2\). The string passes over a uniform solid cylindrical pulley of mass \(M\) and radius \(R\) that rotates about a frictionless axle at its center without the string slipping. Let \(T_1\) denote the tension in the horizontal segment of the string attached to \(m_1\), and let \(T_2\) denote the tension in the vertical segment attached to \(m_2\). In the theoretical limit as the pulley mass approaches infinity (\(M \to \infty\)), which of the following correctly describes the values toward which \(T_1\) and \(T_2\) approach?

![A side-view diagram of a tabletop and pulley system. On a horizontal surface, a rectangular block is labeled \(m_1\). A thin horizontal line segment representing a string extends from the right side of block \(m_1\) to the top edge of a circular disk of radius \(R\) labeled \(M\), which is mounted at the right edge of the tabletop. The string wraps around the upper-right quadrant of the disk and hangs vertically downward from its right edge. A second rectangular block labeled \(m_2\) is attached to the bottom end of the vertical string segment. An arrow labeled \(T_1\) points to the right along the horizontal string segment, and an arrow labeled \(T_2\) points upward along the vertical string segment. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460210-Jw7GaR.jpg)

- **A.** \(T_1 \to m_2 g\) and \(T_2 \to m_2 g\)
- **B.** \(T_1 \to \dfrac{m_1 m_2 g}{m_1 + m_2}\) and \(T_2 \to \dfrac{m_1 m_2 g}{m_1 + m_2}\)
- **C.** \(T_1 \to 0\) and \(T_2 \to 0\)
- **D.** \(T_1 \to 0\) and \(T_2 \to m_2 g\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120829/*