---
title: "A sphere starts from rest and rolls down an incline of height \\( H = 1.0 \\) \\( \\text{m} \\) at an angle of \\( 25^\\circ \\) with the horizontal, as shown above. The radius of the sphere \\( R = 15 \\) \\( \\text{cm} \\), and its mass \\( m = 1.0 \\) \\( \\text{kg} \\). The moment of inertia for a sphere is \\( \\frac{2}{5}mR^2 \\). What is the speed of the sphere when it reaches the bottom of the plane?"
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url: "https://nerd-notes.com/ubq/81048/"
date_modified: "2025-04-14T03:32:09+00:00"
---

# A sphere starts from rest and rolls down an incline of height \( H = 1.0 \) \( \text{m} \) at an angle of \( 25^\circ \) with the horizontal, as shown above. The radius of the sphere \( R = 15 \) \( \text{cm} \), and its mass \( m = 1.0 \) \( \text{kg} \). The moment of inertia for a sphere is \( \frac{2}{5}mR^2 \). What is the speed of the sphere when it reaches the bottom of the plane?

A sphere starts from rest and rolls down an incline of height \( H = 1.0 \) \( \text{m} \) at an angle of \( 25^\circ \) with the horizontal, as shown above. The radius of the sphere \( R = 15 \) \( \text{cm} \), and its mass \( m = 1.0 \) \( \text{kg} \). The moment of inertia for a sphere is \( \frac{2}{5}mR^2 \). What is the speed of the sphere when it reaches the bottom of the plane?

![Diagram](https://nerd-notes.com/wp-content/uploads/2025/03/sphererollingdownaramproblem1.png)

- **A.** \( 3.7 \) \( \text{m/s} \)
- **B.** \( 0.0090 \) \( \text{m/s} \)
- **C.** \( 0.15 \) \( \text{m/s} \)
- **D.** \( 4.4 \) \( \text{m/s} \)
- **E.** \( 2.9 \) \( \text{m/s} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/81048/*