---
title: "A rigid wheel with rotational inertia \\(I = MR^2\\) is mounted on a fixed, frictionless horizontal axle and consists of two concentric spools of radii \\(R\\) and \\(2R\\).  In Scenario 1, a light cord is wrapped around the inner spool of radius \\(R\\) and attached to a hanging block of mass \\(M\\).  In Scenario 2, the cord is instead wrapped around the outer spool of radius \\(2R\\) and attached to the same block of mass \\(M\\), leaving the inner spool empty.  If both systems are released from rest, what is the ratio of the vertical displacement of the block in Scenario 2 to that in Scenario 1 after an identical time interval \\(\\Delta t\\)?"
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/120819/"
date_modified: "2026-08-23T04:43:28+00:00"
---

# A rigid wheel with rotational inertia \(I = MR^2\) is mounted on a fixed, frictionless horizontal axle and consists of two concentric spools of radii \(R\) and \(2R\).

In Scenario 1, a light cord is wrapped around the inner spool of radius \(R\) and attached to a hanging block of mass \(M\).

In Scenario 2, the cord is instead wrapped around the outer spool of radius \(2R\) and attached to the same block of mass \(M\), leaving the inner spool empty.

If both systems are released from rest, what is the ratio of the vertical displacement of the block in Scenario 2 to that in Scenario 1 after an identical time interval \(\Delta t\)?

A rigid wheel with rotational inertia \(I = MR^2\) is mounted on a fixed, frictionless horizontal axle and consists of two concentric spools of radii \(R\) and \(2R\).

In Scenario 1, a light cord is wrapped around the inner spool of radius \(R\) and attached to a hanging block of mass \(M\).

In Scenario 2, the cord is instead wrapped around the outer spool of radius \(2R\) and attached to the same block of mass \(M\), leaving the inner spool empty.

If both systems are released from rest, what is the ratio of the vertical displacement of the block in Scenario 2 to that in Scenario 1 after an identical time interval \(\Delta t\)?

![Two side-by-side grayscale diagrams labeled Scenario 1 on the left and Scenario 2 on the right. Each diagram depicts a front view of a compound pulley consisting of a smaller inner circle of radius \(R\) and a larger concentric outer circle of radius \(2R\) sharing a central fixed axle dot. In Scenario 1, a vertical line representing a cord extends downward from the right edge of the inner circle to a suspended square block labeled \(M\); an arrow from the center to the inner rim is labeled \(R\). In Scenario 2, a vertical cord extends downward from the right edge of the outer circle to an identical suspended square block labeled \(M\); an arrow from the center to the outer rim is labeled \(2R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460208-iDdE98.jpg)

- **A.** \(\dfrac{4}{5}\)
- **B.** \(\dfrac{8}{5}\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120819/*