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title: "A uniform thin rod of mass \\(M\\) and length \\(L\\) is attached to a frictionless horizontal pivot at its left end. The rod is held horizontally at rest and then released from rest at time \\(t = 0\\). Which of the following correctly describes the vertical force exerted by the pivot on the rod immediately after release, and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/124293/"
date_modified: "2026-09-28T14:04:41+00:00"
---

# A uniform thin rod of mass \(M\) and length \(L\) is attached to a frictionless horizontal pivot at its left end. The rod is held horizontally at rest and then released from rest at time \(t = 0\). Which of the following correctly describes the vertical force exerted by the pivot on the rod immediately after release, and provides the correct justification?

A uniform thin rod of mass \(M\) and length \(L\) is attached to a frictionless horizontal pivot at its left end. The rod is held horizontally at rest and then released from rest at time \(t = 0\). Which of the following correctly describes the vertical force exerted by the pivot on the rod immediately after release, and provides the correct justification?

![A horizontal rectangular bar representing a rod of length \(L\) and mass \(M\). The left end of the bar is attached to a fixed circular hinge mounted on a hatched support. A horizontal dimension line above the bar spans its full length and is labeled \(L\). A small solid dot marks the center of the bar, with a horizontal dimension line below spanning from the left end to the dot, labeled \(\dfrac{L}{2}\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604280-DReDK4.jpg)

- **A.** The vertical force exerted by the pivot on the rod is directed downward with magnitude \(\dfrac{1}{2}Mg\) because the acceleration of the rod's free end is \(\dfrac{3}{2}g\) downward.
- **B.** The vertical force exerted by the pivot on the rod is directed upward with magnitude \(\dfrac{1}{4}Mg\) because the acceleration of the rod's center of mass is \(\dfrac{3}{4}g\) downward.
- **C.** The vertical force exerted by the pivot on the rod is directed upward with magnitude \(\dfrac{1}{2}Mg\) because the center of mass is located at the rod's midpoint.
- **D.** The vertical force exerted by the pivot on the rod is zero because the rod falls freely under the sole influence of gravity immediately after release.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124293/*