---
title: "Three small spheres, labeled 1, 2, and 3, are aligned along a straight, frictionless horizontal track. Sphere 1 has mass \\(m\\), sphere 2 has mass \\(2m\\), and sphere 3 has mass \\(m\\). Initially, spheres 2 and 3 are at rest. Sphere 1 is launched toward sphere 2 with an initial speed \\(v_0\\). All collisions are head-on and perfectly elastic. After all collisions have taken place, which of the following correctly ranks the final speeds \\(v_1\\), \\(v_2\\), and \\(v_3\\) of the spheres?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120750/"
date_modified: "2026-08-23T04:42:59+00:00"
---

# Three small spheres, labeled 1, 2, and 3, are aligned along a straight, frictionless horizontal track. Sphere 1 has mass \(m\), sphere 2 has mass \(2m\), and sphere 3 has mass \(m\). Initially, spheres 2 and 3 are at rest. Sphere 1 is launched toward sphere 2 with an initial speed \(v_0\). All collisions are head-on and perfectly elastic. After all collisions have taken place, which of the following correctly ranks the final speeds \(v_1\), \(v_2\), and \(v_3\) of the spheres?

Three small spheres, labeled 1, 2, and 3, are aligned along a straight, frictionless horizontal track. Sphere 1 has mass \(m\), sphere 2 has mass \(2m\), and sphere 3 has mass \(m\). Initially, spheres 2 and 3 are at rest. Sphere 1 is launched toward sphere 2 with an initial speed \(v_0\). All collisions are head-on and perfectly elastic. After all collisions have taken place, which of the following correctly ranks the final speeds \(v_1\), \(v_2\), and \(v_3\) of the spheres?

![A horizontal line represents a frictionless track. On the track are three circles in a line from left to right. The leftmost circle is labeled 1 with mass label m above it, and a horizontal arrow labeled v_0 points right from its center. The middle circle is slightly larger, labeled 2 with mass label 2m above it. The rightmost circle is the same size as the first, labeled 3 with mass label m above it. Spheres 2 and 3 have no velocity arrows. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460179-h41dTU.jpg)

- **A.** \(v_3 > v_2 > v_1\)
- **B.** \(v_3 > v_1 > v_2\)
- **C.** \(v_1 = v_3 > v_2\)
- **D.** \(v_2 > v_1 > v_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120750/*