---
title: "A uniform thin rod of mass \\(M\\) and length \\(L\\) is pivoted about a frictionless horizontal axis passing through one of its ends. The rod is displaced by a small angle \\(\\theta\\) from the vertical and released from rest. Which of the following expressions represents the period \\(T\\) of small-angle oscillations of the rod?"
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url: "https://nerd-notes.com/ubq/120982/"
date_modified: "2026-08-23T04:44:56+00:00"
---

# A uniform thin rod of mass \(M\) and length \(L\) is pivoted about a frictionless horizontal axis passing through one of its ends. The rod is displaced by a small angle \(\theta\) from the vertical and released from rest. Which of the following expressions represents the period \(T\) of small-angle oscillations of the rod?

A uniform thin rod of mass \(M\) and length \(L\) is pivoted about a frictionless horizontal axis passing through one of its ends. The rod is displaced by a small angle \(\theta\) from the vertical and released from rest. Which of the following expressions represents the period \(T\) of small-angle oscillations of the rod?

![A vertical dashed reference line extends downward from a fixed horizontal ceiling. A uniform thin rectangular rod of length \(L\) and mass \(M\) is attached to the ceiling at a small circular pivot at its top end. The rod is shown tilted to the right by a small angle \(\theta\) relative to the vertical dashed line. A curved arrow labeled \(\theta\) indicates the angular displacement from the vertical dashed line to the centerline of the rod. A small filled circle at the geometric center of the rod marks the center of mass, located a distance \(L/2\) from the pivot. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460295-dhdf7P.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120982/*