---
title: "A uniform beam of mass \\(M\\) and length \\(L\\) is attached to a vertical wall by a pivot hinge at one end. The beam is held in a horizontal position by a cable attached to the other end of the beam at an angle \\(\\theta = 30^{\\circ}\\) relative to the beam, as shown in the figure. A student claims that because the beam is in equilibrium, the hinge does not exert any force on the beam. Which of the following correctly identifies whether the student’s claim is correct and provides a valid justification?  Consider the axis of rotation to be at the hinge."
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/111530/"
date_modified: "2026-04-12T02:41:52+00:00"
---

# A uniform beam of mass \(M\) and length \(L\) is attached to a vertical wall by a pivot hinge at one end. The beam is held in a horizontal position by a cable attached to the other end of the beam at an angle \(\theta = 30^{\circ}\) relative to the beam, as shown in the figure. A student claims that because the beam is in equilibrium, the hinge does not exert any force on the beam. Which of the following correctly identifies whether the student’s claim is correct and provides a valid justification?

Consider the axis of rotation to be at the hinge.

A uniform beam of mass \(M\) and length \(L\) is attached to a vertical wall by a pivot hinge at one end. The beam is held in a horizontal position by a cable attached to the other end of the beam at an angle \(\theta = 30^{\circ}\) relative to the beam, as shown in the figure. A student claims that because the beam is in equilibrium, the hinge does not exert any force on the beam. Which of the following correctly identifies whether the student's claim is correct and provides a valid justification?

Consider the axis of rotation to be at the hinge.

![A horizontal beam of length L is attached to a vertical wall on the left side by a hinge. A cable is attached to the right end of the beam and goes up and to the left, attaching to the wall at a point above the hinge. The cable makes an angle theta of 30 degrees with the horizontal beam. The beam's weight Mg is shown as a vector acting downward from the center of the beam (L/2).](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775961712-nT2VEy.jpg)

- **A.** The claim is correct because the sum of the torques about the hinge is zero, which implies that the hinge does not need to exert a force to maintain equilibrium.
- **B.** The claim is incorrect because the vertical component of the tension in the cable only supports half of the beam's weight, so the hinge must exert an upward vertical force of \(Mg/2\) to satisfy translational equilibrium.
- **C.** The claim is incorrect because the hinge must exert a clockwise torque to counteract the counterclockwise torque produced by the tension in the cable.
- **D.** The claim is correct because the horizontal component of the tension is balanced by the beam's internal compression, leaving no net external force for the hinge to provide.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111530/*