---
title: "A uniform ladder of mass \\(M\\) and length \\(L\\) leans against a frictionless vertical wall, making an angle \\(\\theta\\) with the rough horizontal floor. The coefficient of static friction between the ladder and the floor is \\(\\mu_s\\). Which of the following expressions represents the minimum value of \\(\\mu_s\\) required to prevent the ladder from slipping?"
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url: "https://nerd-notes.com/ubq/120785/"
date_modified: "2026-08-23T04:43:22+00:00"
---

# A uniform ladder of mass \(M\) and length \(L\) leans against a frictionless vertical wall, making an angle \(\theta\) with the rough horizontal floor. The coefficient of static friction between the ladder and the floor is \(\mu_s\). Which of the following expressions represents the minimum value of \(\mu_s\) required to prevent the ladder from slipping?

A uniform ladder of mass \(M\) and length \(L\) leans against a frictionless vertical wall, making an angle \(\theta\) with the rough horizontal floor. The coefficient of static friction between the ladder and the floor is \(\mu_s\). Which of the following expressions represents the minimum value of \(\mu_s\) required to prevent the ladder from slipping?

![A vertical wall on the right and a horizontal ground line meet at a right angle. A straight uniform bar representing a ladder of length \(L\) is inclined with its upper end against the wall and its lower end on the ground. An angle arc is drawn between the ground and the ladder, labeled \(\theta\). A small filled circle at the midpoint of the ladder indicates its center of mass. No forces, vectors, numerical values, or extra lines appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460201-u0mGkI.jpg)

- **A.** \(\dfrac{\tan\theta}{2}\)
- **B.** \(\tan\theta\)
- **C.** \(\dfrac{1}{\tan\theta}\)
- **D.** \(\dfrac{1}{2\tan\theta}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120785/*