---
title: "A physical pendulum consists of a uniform solid disk of mass \\(M\\) and radius \\(R\\). A small pivot hole is drilled at a distance \\(d\\) from the center of the disk, allowing it to swing freely without friction in a vertical plane. Which of the following expressions represents the pivot distance \\(d\\) that minimizes the period of small-angle oscillations?"
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url: "https://nerd-notes.com/ubq/117625/"
date_modified: "2026-08-04T07:49:22+00:00"
---

# A physical pendulum consists of a uniform solid disk of mass \(M\) and radius \(R\). A small pivot hole is drilled at a distance \(d\) from the center of the disk, allowing it to swing freely without friction in a vertical plane. Which of the following expressions represents the pivot distance \(d\) that minimizes the period of small-angle oscillations?

A physical pendulum consists of a uniform solid disk of mass \(M\) and radius \(R\). A small pivot hole is drilled at a distance \(d\) from the center of the disk, allowing it to swing freely without friction in a vertical plane. Which of the following expressions represents the pivot distance \(d\) that minimizes the period of small-angle oscillations?

![A uniform solid circular disk with center labeled C. A pivot point labeled P is positioned on the disk at a distance d above C along a vertical radial line. A dashed vertical axis passes through P. A straight radial line from center C to the outer boundary is labeled R. A curved arrow labeled \theta shows a small angular displacement of line PC from the vertical dashed axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-pendulum-fig-1785829761-4w3oV7.jpg)

- **A.** \(\dfrac{R}{4}\)
- **B.** \(\dfrac{R}{2}\)
- **C.** \(\dfrac{R}{\sqrt{3}}\)
- **D.** \(\dfrac{R}{\sqrt{2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117625/*