---
title: "A uniform horizontal beam of length \\(L\\) and mass \\(M\\) rests on two vertical supports. Support 1 is located at the left end (\\(x = 0\\)) and Support 2 is located at the right end (\\(x = L\\)). A piece of machinery of mass \\(2M\\) is placed on top of the beam at \\(x = \\dfrac{1}{4}L\\). Which of the following correctly states the magnitude of the upward force exerted by Support 1 on the beam and provides the valid physical justification?"
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url: "https://nerd-notes.com/ubq/120778/"
date_modified: "2026-08-23T04:43:18+00:00"
---

# A uniform horizontal beam of length \(L\) and mass \(M\) rests on two vertical supports. Support 1 is located at the left end (\(x = 0\)) and Support 2 is located at the right end (\(x = L\)). A piece of machinery of mass \(2M\) is placed on top of the beam at \(x = \dfrac{1}{4}L\). Which of the following correctly states the magnitude of the upward force exerted by Support 1 on the beam and provides the valid physical justification?

A uniform horizontal beam of length \(L\) and mass \(M\) rests on two vertical supports. Support 1 is located at the left end (\(x = 0\)) and Support 2 is located at the right end (\(x = L\)). A piece of machinery of mass \(2M\) is placed on top of the beam at \(x = \dfrac{1}{4}L\). Which of the following correctly states the magnitude of the upward force exerted by Support 1 on the beam and provides the valid physical justification?

![A horizontal rectangular beam of length L spans horizontally from left to right. At the far left end at x = 0, a triangular support labeled Support 1 touches the bottom of the beam. At the far right end at x = L, an identical triangular support labeled Support 2 touches the bottom of the beam. A square block labeled 2M rests on top of the beam at a position one-fourth of the length from the left end. A horizontal dimension line directly below the beam spans the full length labeled L. A horizontal dimension line above the beam spans from the left end to the center of the block labeled L/4. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460198-qfE0jN.jpg)

- **A.** The upward force exerted by Support 1 is \(\dfrac{3}{2}Mg\), because a static object distributes the total gravitational weight equally to both supports regardless of the position of the load.
- **B.** The upward force exerted by Support 1 is \(\dfrac{3}{2}Mg\), because the net external torque is strictly equal to zero only when calculated about the center of mass of the system.
- **C.** The upward force exerted by Support 1 is \(2Mg\), because the beam is in rotational equilibrium, requiring the net external torque about any arbitrary pivot point to equal zero.
- **D.** The upward force exerted by Support 1 is \(\dfrac{5}{2}Mg\), because the machinery acts entirely on Support 1 and only the beam's own weight is shared equally between the supports.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120778/*