---
title: "Four uniform, symmetric objects—a thin hoop, a solid cylinder, a thin spherical shell, and a solid sphere—are released from rest simultaneously from the top of an inclined plane of vertical height \\(h\\). All four objects roll down the incline to the bottom without slipping. Which of the following correctly ranks the translational speeds of the centers of mass of the objects, \\(v\\), at the bottom of the incline?"
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url: "https://nerd-notes.com/ubq/120903/"
date_modified: "2026-08-23T04:44:12+00:00"
---

# Four uniform, symmetric objects—a thin hoop, a solid cylinder, a thin spherical shell, and a solid sphere—are released from rest simultaneously from the top of an inclined plane of vertical height \(h\). All four objects roll down the incline to the bottom without slipping. Which of the following correctly ranks the translational speeds of the centers of mass of the objects, \(v\), at the bottom of the incline?

Four uniform, symmetric objects—a thin hoop, a solid cylinder, a thin spherical shell, and a solid sphere—are released from rest simultaneously from the top of an inclined plane of vertical height \(h\). All four objects roll down the incline to the bottom without slipping. Which of the following correctly ranks the translational speeds of the centers of mass of the objects, \(v\), at the bottom of the incline?

![A right-angled triangular incline rests on flat horizontal ground, sloping downward to the right. A vertical dimension line on the left edge is labeled \(h\). A single circular body is positioned at the top edge of the slope. A clockwise curved arrow on the circular body indicates rotation, and a straight arrow parallel to the incline points down the slope. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460251-S9drwk.jpg)

- **A.** \(v_{\text{hoop}} > v_{\text{shell}} > v_{\text{cylinder}} > v_{\text{sphere}}\)
- **B.** \(v_{\text{sphere}} > v_{\text{shell}} > v_{\text{cylinder}} > v_{\text{hoop}}\)
- **C.** \(v_{\text{sphere}} > v_{\text{cylinder}} > v_{\text{shell}} > v_{\text{hoop}}\)
- **D.** \(v_{\text{cylinder}} > v_{\text{sphere}} > v_{\text{shell}} > v_{\text{hoop}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120903/*