---
title: "A solid ball of mass \\( M \\) and radius \\( R \\) has rotational inertia \\( \\frac{2}{5} M R^{2} \\) about its center. It rolls without slipping along a level surface at speed \\( v \\) just before it begins rolling up an inclined plane.Which of the following expressions correctly represents the maximum vertical height the solid ball can ascend to when it rolls up the incline without slipping?"
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/91447/"
date_modified: "2025-05-08T03:40:07+00:00"
---

# A solid ball of mass \( M \) and radius \( R \) has rotational inertia \( \frac{2}{5} M R^{2} \) about its center. It rolls without slipping along a level surface at speed \( v \) just before it begins rolling up an inclined plane.Which of the following expressions correctly represents the maximum vertical height the solid ball can ascend to when it rolls up the incline without slipping?

A solid ball of mass \( M \) and radius \( R \) has rotational inertia \( \frac{2}{5} M R^{2} \) about its center. It rolls without slipping along a level surface at speed \( v \) just before it begins rolling up an inclined plane. Which of the following expressions correctly represents the maximum vertical height the solid ball can ascend to when it rolls up the incline without slipping?

- **A.** \[ \frac{v^{2}}{5g} \]
- **B.** \[ \frac{2v^{2}}{5g} \]
- **C.** \[ \frac{v^{2}}{2g} \]
- **D.** \[ \frac{7v^{2}}{10g} \]

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/91447/*