---
title: "A physical pendulum consists of a uniform solid disk of mass \\(M\\) and radius \\(R\\) pivoted about a frictionless horizontal axle passing perpendicularly through a point on its outer rim. A simple pendulum consists of a small point-like bob of mass \\(M\\) suspended from a light string of length \\(R\\). Both pendulums oscillate in vertical planes with small angular amplitudes. What is the ratio of the period of oscillation of the disk pendulum to the period of oscillation of the simple pendulum, \\(\\dfrac{T_{\\text{disk}}}{T_{\\text{simple}}}\\)?"
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url: "https://nerd-notes.com/ubq/120969/"
date_modified: "2026-08-23T04:44:52+00:00"
---

# A physical pendulum consists of a uniform solid disk of mass \(M\) and radius \(R\) pivoted about a frictionless horizontal axle passing perpendicularly through a point on its outer rim. A simple pendulum consists of a small point-like bob of mass \(M\) suspended from a light string of length \(R\). Both pendulums oscillate in vertical planes with small angular amplitudes. What is the ratio of the period of oscillation of the disk pendulum to the period of oscillation of the simple pendulum, \(\dfrac{T_{\text{disk}}}{T_{\text{simple}}}\)?

A physical pendulum consists of a uniform solid disk of mass \(M\) and radius \(R\) pivoted about a frictionless horizontal axle passing perpendicularly through a point on its outer rim. A simple pendulum consists of a small point-like bob of mass \(M\) suspended from a light string of length \(R\). Both pendulums oscillate in vertical planes with small angular amplitudes. What is the ratio of the period of oscillation of the disk pendulum to the period of oscillation of the simple pendulum, \(\dfrac{T_{\text{disk}}}{T_{\text{simple}}}\)?

![A side-by-side comparison diagram of two pendulums. On the left, a solid circular disk of radius \(R\) has a small circular pivot point on its topmost rim. A vertical dashed line passes through this top pivot down to the center of the disk labeled \(R\). On the right, a simple pendulum consists of a horizontal line representing a ceiling, a thin straight vertical line of length \(R\) extending downward from a fixed point on the ceiling, and a small shaded circle representing a bob of mass \(M\) at its bottom end. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460292-bB9lmh.jpg)

- **A.** \(\sqrt{\dfrac{1}{2}}\)
- **B.** \(\sqrt{\dfrac{3}{2}}\)
- **C.** \(\sqrt{2}\)
- **D.** \(\dfrac{3}{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120969/*