---
title: "A solid sphere and a hollow sphere, both with mass \\(M\\) and radius \\(R\\), are released from rest at the top of a ramp inclined at an angle \\(\\theta\\) above the horizontal. Both spheres roll without slipping as they move down the ramp. Which of the following correctly compares the translational accelerations of the centers of mass of the spheres and provides a correct justification?"
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url: "https://nerd-notes.com/ubq/110861/"
date_modified: "2026-04-09T00:07:29+00:00"
---

# A solid sphere and a hollow sphere, both with mass \(M\) and radius \(R\), are released from rest at the top of a ramp inclined at an angle \(\theta\) above the horizontal. Both spheres roll without slipping as they move down the ramp. Which of the following correctly compares the translational accelerations of the centers of mass of the spheres and provides a correct justification?

A solid sphere and a hollow sphere, both with mass \(M\) and radius \(R\), are released from rest at the top of a ramp inclined at an angle \(\theta\) above the horizontal. Both spheres roll without slipping as they move down the ramp. Which of the following correctly compares the translational accelerations of the centers of mass of the spheres and provides a correct justification?

![Two spheres, one solid and one hollow, are positioned at the top of an inclined plane. The incline makes an angle theta with the horizontal. Both spheres have the same radius R. Arrows indicate the direction of motion down the ramp.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775693249-coujTL.jpg)

- **A.** The acceleration of the solid sphere is greater because it has a smaller rotational inertia, and thus a smaller frictional force is required to provide the torque for rolling.
- **B.** The acceleration of the hollow sphere is greater because its mass is distributed further from the center, which allows gravity to exert a greater torque on it.
- **C.** The acceleration of the solid sphere is greater because it has a smaller rotational inertia, which requires a larger frictional force to maintain the rolling condition.
- **D.** The accelerations are equal because both spheres have the same mass and experience the same component of the gravitational force parallel to the incline.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110861/*