---
title: "A thin, uniform square plate with side length \\(L\\) is mounted on a fixed, frictionless pivot at its central point \\(P\\). Four forces act along the outer edges of the plate: a force of magnitude \\(3F\\) directed to the right along the top edge, a force of magnitude \\(2F\\) directed upward along the right edge, a force of magnitude \\(F\\) directed to the left along the bottom edge, and a force of magnitude \\(4F\\) directed downward along the left edge. Which of the following correctly identifies the net torque exerted on the plate about the pivot \\(P\\) and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/120798/"
date_modified: "2026-08-23T04:43:24+00:00"
---

# A thin, uniform square plate with side length \(L\) is mounted on a fixed, frictionless pivot at its central point \(P\). Four forces act along the outer edges of the plate: a force of magnitude \(3F\) directed to the right along the top edge, a force of magnitude \(2F\) directed upward along the right edge, a force of magnitude \(F\) directed to the left along the bottom edge, and a force of magnitude \(4F\) directed downward along the left edge. Which of the following correctly identifies the net torque exerted on the plate about the pivot \(P\) and provides the correct physical justification?

A thin, uniform square plate with side length \(L\) is mounted on a fixed, frictionless pivot at its central point \(P\). Four forces act along the outer edges of the plate: a force of magnitude \(3F\) directed to the right along the top edge, a force of magnitude \(2F\) directed upward along the right edge, a force of magnitude \(F\) directed to the left along the bottom edge, and a force of magnitude \(4F\) directed downward along the left edge. Which of the following correctly identifies the net torque exerted on the plate about the pivot \(P\) and provides the correct physical justification?

![A square outline representing a plate viewed face-on, with its center marked by a small filled dot labeled P. A horizontal arrow labeled 3F lies along the top edge pointing rightward. A vertical arrow labeled 2F lies along the right edge pointing upward. A horizontal arrow labeled F lies along the bottom edge pointing leftward. A vertical arrow labeled 4F lies along the left edge pointing downward. A vertical dashed line segment extends from the central point P upward to the top edge and is labeled L/2. A horizontal dimension line spanning the bottom edge is labeled L. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460204-XYXT3s.jpg)

- **A.** The net torque has magnitude \(FL\) directed counterclockwise because the forces on the left and right edges produce a total counterclockwise torque of \(3FL\) while the forces on the top and bottom edges produce a total clockwise torque of \(2FL\).
- **B.** The net torque has magnitude \(2FL\) directed counterclockwise because each force acts at a distance of \(L\) from the central pivot, producing \(6FL\) of counterclockwise torque and \(4FL\) of clockwise torque.
- **C.** The net torque is zero because the forces acting in the positive coordinate directions (\(3F\) rightward and \(2F\) upward) exactly balance the forces acting in the negative coordinate directions (\(F\) leftward and \(4F\) downward).
- **D.** The net torque has magnitude \(5FL\) directed counterclockwise because the torque contributions from all four forces act constructively in the same rotational sense about the central pivot.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120798/*