---
title: "A block of mass \\(M\\) is placed on a rough horizontal table with coefficient of static friction \\(\\mu_s\\). The block is connected to a vertical wall by a horizontal ideal spring with spring constant \\(k\\). On the opposite side, the block is connected to a light string that passes over a frictionless pulley to a hanging mass \\(m\\), as shown in the diagram. The spring is stretched a distance \\(x\\) from its equilibrium length. Which of the following expressions represents the maximum value of \\(x\\) for which the block of mass \\(M\\) will remain in equilibrium?"
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url: "https://nerd-notes.com/ubq/109774/"
date_modified: "2026-03-26T05:49:51+00:00"
---

# A block of mass \(M\) is placed on a rough horizontal table with coefficient of static friction \(\mu_s\). The block is connected to a vertical wall by a horizontal ideal spring with spring constant \(k\). On the opposite side, the block is connected to a light string that passes over a frictionless pulley to a hanging mass \(m\), as shown in the diagram. The spring is stretched a distance \(x\) from its equilibrium length. Which of the following expressions represents the maximum value of \(x\) for which the block of mass \(M\) will remain in equilibrium?

A block of mass \(M\) is placed on a rough horizontal table with coefficient of static friction \(\mu_s\). The block is connected to a vertical wall by a horizontal ideal spring with spring constant \(k\). On the opposite side, the block is connected to a light string that passes over a frictionless pulley to a hanging mass \(m\), as shown in the diagram. The spring is stretched a distance \(x\) from its equilibrium length. Which of the following expressions represents the maximum value of \(x\) for which the block of mass \(M\) will remain in equilibrium?

![A block of mass M sits on a horizontal surface. To its left, it is attached to a horizontal spring which is fixed to a vertical wall. To its right, it is attached to a string that goes over a pulley at the edge of the table. A mass m hangs vertically from the string. The spring is shown in a stretched state.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774504191-LRnqur.jpg)

- **A.** \(x = \dfrac{mg + \mu_s Mg}{k}\)
- **B.** \(x = \dfrac{mg - \mu_s Mg}{k}\)
- **C.** \(x = \dfrac{\mu_s Mg - mg}{k}\)
- **D.** \(x = \dfrac{mg}{k}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109774/*