---
title: "A uniform rigid beam of length \\(L\\) and weight \\(W\\) is attached to a vertical wall by a frictionless pivot at its left end and held in a horizontal orientation. A support cable is attached to the beam at a distance \\(\\dfrac{L}{4}\\) from the pivot and connects to the wall at an angle \\(\\theta\\) above the beam. A sensor measures the vertical force exerted by the pivot on the beam and records a value directed downward. Which of the following provides the correct physical explanation for this observation?"
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url: "https://nerd-notes.com/ubq/120807/"
date_modified: "2026-08-23T04:43:25+00:00"
---

# A uniform rigid beam of length \(L\) and weight \(W\) is attached to a vertical wall by a frictionless pivot at its left end and held in a horizontal orientation. A support cable is attached to the beam at a distance \(\dfrac{L}{4}\) from the pivot and connects to the wall at an angle \(\theta\) above the beam. A sensor measures the vertical force exerted by the pivot on the beam and records a value directed downward. Which of the following provides the correct physical explanation for this observation?

A uniform rigid beam of length \(L\) and weight \(W\) is attached to a vertical wall by a frictionless pivot at its left end and held in a horizontal orientation. A support cable is attached to the beam at a distance \(\dfrac{L}{4}\) from the pivot and connects to the wall at an angle \(\theta\) above the beam. A sensor measures the vertical force exerted by the pivot on the beam and records a value directed downward. Which of the following provides the correct physical explanation for this observation?

![A schematic diagram showing a vertical wall on the left with hatch marks behind it. A horizontal beam of uniform thickness extends horizontally to the right from a circular pivot on the wall. A straight line representing a cable connects a point on the top edge of the beam at distance \(L/4\) from the pivot to an anchor point on the wall directly above the pivot. An angle arc at the beam-cable junction is labeled \(\theta\). A solid black dot on the beam at distance \(L/2\) from the wall marks the center of mass. A horizontal double-headed dimension arrow beneath the beam spans the entire length labeled \(L\), and a shorter dimension arrow indicates the cable attachment at \(L/4\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460205-H7tEYb.jpg)

- **A.** Because the cable is attached closer to the pivot than the beam's center of mass, its vertical component of tension must exceed the beam's total weight to maintain rotational equilibrium, requiring a downward vertical reaction force at the pivot to satisfy translational equilibrium.
- **B.** Because the beam's center of mass lies to the right of the cable attachment, gravity exerts a clockwise torque about the cable that must be balanced by an upward force from the pivot, but the pivot pulls downward because it acts as a rigid anchor resisting upward beam deflection.
- **C.** Because the cable pulls upward and to the left, the horizontal component of the tension creates a downward static friction force against the wall that exceeds the upward normal force supplied by the pivot pin.
- **D.** Because the right segment of the beam is three times longer than the left segment, the downward force at the pivot arises solely from the shear stress required to support the cantilevered right portion regardless of the cable's vertical tension.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120807/*