---
title: "A uniform horizontal beam of mass \\(M\\) and length \\(L\\) is attached to a vertical wall by a pivot at its left end. The beam is held in static equilibrium by a light cable attached to the beam at a distance of \\(\\dfrac{3}{4}L\\) from the wall, making an angle \\(\\theta\\) with the horizontal beam. In terms of \\(M\\) and \\(g\\), what is the vertical component of the force exerted by the pivot on the beam?"
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url: "https://nerd-notes.com/ubq/124298/"
date_modified: "2026-09-28T14:04:41+00:00"
---

# A uniform horizontal beam of mass \(M\) and length \(L\) is attached to a vertical wall by a pivot at its left end. The beam is held in static equilibrium by a light cable attached to the beam at a distance of \(\dfrac{3}{4}L\) from the wall, making an angle \(\theta\) with the horizontal beam. In terms of \(M\) and \(g\), what is the vertical component of the force exerted by the pivot on the beam?

A uniform horizontal beam of mass \(M\) and length \(L\) is attached to a vertical wall by a pivot at its left end. The beam is held in static equilibrium by a light cable attached to the beam at a distance of \(\dfrac{3}{4}L\) from the wall, making an angle \(\theta\) with the horizontal beam. In terms of \(M\) and \(g\), what is the vertical component of the force exerted by the pivot on the beam?

![A schematic showing a horizontal beam connected to a vertical wall. On the left, a vertical hatched line represents a wall. A small circle on the wall represents a pivot attached to the left end of a uniform horizontal rectangular beam of length \(L\). At the beam's midpoint, a downward arrow labeled \(Mg\) indicates the center of mass at a distance \(L/2\) from the pivot. At a distance \(3L/4\) from the pivot, a straight line representing a cable extends upward and to the left to anchor to the vertical wall, forming an angle \(\theta\) with the horizontal beam. Dimension lines below the beam indicate the distance from the pivot to the center of mass as \(L/2\) and from the pivot to the cable attachment point as \(3L/4\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604281-4w4s50.jpg)

- **A.** \(\dfrac{1}{4}Mg\)
- **B.** \(\dfrac{1}{3}Mg\)
- **C.** \(\dfrac{1}{2}Mg\)
- **D.** \(\dfrac{2}{3}Mg\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124298/*