---
title: "A uniform thin rod of mass \\(M\\) and length \\(L\\) is suspended from a frictionless horizontal pivot located a distance \\(d\\) from the center of mass of the rod, where \\(0 < d < \\dfrac{L}{2}\\). When displaced by a small angle and released from rest, the rod oscillates as a physical pendulum. In terms of \\(L\\), at what distance \\(d\\) from the center of mass is the period of oscillation minimized?"
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url: "https://nerd-notes.com/ubq/121001/"
date_modified: "2026-08-23T04:45:05+00:00"
---

# A uniform thin rod of mass \(M\) and length \(L\) is suspended from a frictionless horizontal pivot located a distance \(d\) from the center of mass of the rod, where \(0 < d < \dfrac{L}{2}\). When displaced by a small angle and released from rest, the rod oscillates as a physical pendulum. In terms of \(L\), at what distance \(d\) from the center of mass is the period of oscillation minimized?

A uniform thin rod of mass \(M\) and length \(L\) is suspended from a frictionless horizontal pivot located a distance \(d\) from the center of mass of the rod, where \(0 < d < \dfrac{L}{2}\). When displaced by a small angle and released from rest, the rod oscillates as a physical pendulum. In terms of \(L\), at what distance \(d\) from the center of mass is the period of oscillation minimized?

![A vertical diagram showing a slender rectangular rod of total length \(L\). The rod is oriented vertically. A small solid circular dot representing the center of mass is located at the geometric center of the rod and labeled \(\text{CM}\). Above the center of mass, a small open circle representing a horizontal pivot axis passes through the rod at a distance \(d\) from the center of mass. A vertical two-headed dimension arrow spans between the center of mass and the pivot, labeled \(d\). A full-length vertical dimension line spans the entire height of the rod on the right, labeled \(L\). A dashed vertical reference line extends along the center line of the rod. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460305-Rh8yBL.jpg)

- **A.** \(\dfrac{L}{2\sqrt{3}}\)
- **B.** \(\dfrac{L}{\sqrt{6}}\)
- **C.** \(\dfrac{L}{\sqrt{3}}\)
- **D.** \(\dfrac{L}{6}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121001/*