---
title: "A uniform horizontal boom of mass \\(M\\) and length \\(L\\) is attached to a vertical wall by a frictionless pivot at its left end. A light tie-rod is connected between the right end of the boom and the wall above the pivot, making an angle \\(\\theta\\) with the horizontal boom, where \\(0 < \\theta < 90^\\circ\\). Let \\(T\\) be the tension in the tie-rod and \\(F_H\\) be the magnitude of the horizontal force exerted by the pivot on the boom. Which of the following correctly describes the behavior of \\(T\\) and \\(F_H\\) in the theoretical limits \\(\\theta \\to 0^\\circ\\) and \\(\\theta \\to 90^\\circ\\)?"
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url: "https://nerd-notes.com/ubq/124350/"
date_modified: "2026-09-28T14:04:56+00:00"
---

# A uniform horizontal boom of mass \(M\) and length \(L\) is attached to a vertical wall by a frictionless pivot at its left end. A light tie-rod is connected between the right end of the boom and the wall above the pivot, making an angle \(\theta\) with the horizontal boom, where \(0 < \theta < 90^\circ\). Let \(T\) be the tension in the tie-rod and \(F_H\) be the magnitude of the horizontal force exerted by the pivot on the boom. Which of the following correctly describes the behavior of \(T\) and \(F_H\) in the theoretical limits \(\theta \to 0^\circ\) and \(\theta \to 90^\circ\)?

A uniform horizontal boom of mass \(M\) and length \(L\) is attached to a vertical wall by a frictionless pivot at its left end. A light tie-rod is connected between the right end of the boom and the wall above the pivot, making an angle \(\theta\) with the horizontal boom, where \(0 < \theta < 90^\circ\). Let \(T\) be the tension in the tie-rod and \(F_H\) be the magnitude of the horizontal force exerted by the pivot on the boom. Which of the following correctly describes the behavior of \(T\) and \(F_H\) in the theoretical limits \(\theta \to 0^\circ\) and \(\theta \to 90^\circ\)?

![A schematic diagram showing a horizontal boom supported by a vertical wall and a tie-rod. On the left, a vertical wall is represented by a vertical line with hash marks to its left. A horizontal rectangular boom of length \(L\) and mass \(M\) extends to the right from the wall. The left end of the boom is attached to the wall at a pivot indicated by a small open circle. A straight thin line segment representing a tie-rod connects the right end of the boom to an anchor point on the vertical wall directly above the pivot. The angle between the horizontal boom and the inclined tie-rod is labeled with an arc and the symbol \(\theta\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604295-i5oVsI.jpg)

- **A.** As \(\theta \to 0^\circ\), \(T \to \infty\) and \(F_H \to 0\); as \(\theta \to 90^\circ\), \(T \to Mg\) and \(F_H \to 0\).
- **B.** As \(\theta \to 0^\circ\), \(T \to \infty\) and \(F_H \to \infty\); as \(\theta \to 90^\circ\), \(T \to Mg\) and \(F_H \to 0\).
- **C.** As \(\theta \to 0^\circ\), \(T \to \infty\) and \(F_H \to 0\); as \(\theta \to 90^\circ\), \(T \to \dfrac{Mg}{2}\) and \(F_H \to 0\).
- **D.** As \(\theta \to 0^\circ\), \(T \to \infty\) and \(F_H \to \infty\); as \(\theta \to 90^\circ\), \(T \to \dfrac{Mg}{2}\) and \(F_H \to 0\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124350/*