---
title: "A uniform rod of length \\(L\\) and mass \\(M\\) is attached to a vertical wall by a frictionless hinge at point \\(P\\). The rod is maintained in static equilibrium in a horizontal orientation by a light cable. The cable is attached to the rod at a distance \\(d = \\dfrac{L}{3}\\) from the hinge and connects to the wall at a point vertically above \\(P\\), making an acute angle \\(\\theta\\) with the rod. Which of the following correctly pairs the direction of the vertical component with the direction of the horizontal component of the force exerted by the hinge on the rod at point \\(P\\)?"
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url: "https://nerd-notes.com/ubq/120838/"
date_modified: "2026-08-23T04:43:33+00:00"
---

# A uniform rod of length \(L\) and mass \(M\) is attached to a vertical wall by a frictionless hinge at point \(P\). The rod is maintained in static equilibrium in a horizontal orientation by a light cable. The cable is attached to the rod at a distance \(d = \dfrac{L}{3}\) from the hinge and connects to the wall at a point vertically above \(P\), making an acute angle \(\theta\) with the rod. Which of the following correctly pairs the direction of the vertical component with the direction of the horizontal component of the force exerted by the hinge on the rod at point \(P\)?

A uniform rod of length \(L\) and mass \(M\) is attached to a vertical wall by a frictionless hinge at point \(P\). The rod is maintained in static equilibrium in a horizontal orientation by a light cable. The cable is attached to the rod at a distance \(d = \dfrac{L}{3}\) from the hinge and connects to the wall at a point vertically above \(P\), making an acute angle \(\theta\) with the rod. Which of the following correctly pairs the direction of the vertical component with the direction of the horizontal component of the force exerted by the hinge on the rod at point \(P\)?

![A schematic diagram showing a horizontal uniform rod attached to a vertical surface on the left. At the left end of the rod, a small circle on the vertical surface marks the hinge at point \(P\). The rod extends horizontally to the right with total length \(L\). At a distance \(d = L/3\) from point \(P\), a straight line representing a cable extends upward and to the left, terminating at the vertical surface above point \(P\). An arc between the rod and the cable indicates an acute angle \(\theta\). A downward vertical arrow originates from the midpoint of the rod at distance \(L/2\) from the hinge and is labeled \(Mg\). A horizontal dimension line below the rod indicates the distance \(d = L/3\) from point \(P\) to the cable attachment point, and a second dimension line spans the entire rod length \(L\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460213-Fq1oBz.jpg)

- **A.** Vertical component: Upward ; Horizontal component: Toward the wall
- **B.** Vertical component: Downward ; Horizontal component: Away from the wall
- **C.** Vertical component: Upward ; Horizontal component: Away from the wall
- **D.** Vertical component: Downward ; Horizontal component: Toward the wall

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120838/*