---
title: "A solid sphere and a thin-walled hollow cylinder, both with mass \\(M\\) and radius \\(R\\), are released from rest at the top of an incline of height \\(H\\). Both objects roll down the incline without slipping. At the bottom of the incline, the translational speed of the center of mass for the solid sphere is \\(v_S\\) and the translational speed of the center of mass for the hollow cylinder is \\(v_C\\).  Which of the following correctly compares the two speeds and provides a valid justification?"
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url: "https://nerd-notes.com/ubq/111295/"
date_modified: "2026-04-10T04:06:26+00:00"
---

# A solid sphere and a thin-walled hollow cylinder, both with mass \(M\) and radius \(R\), are released from rest at the top of an incline of height \(H\). Both objects roll down the incline without slipping. At the bottom of the incline, the translational speed of the center of mass for the solid sphere is \(v_S\) and the translational speed of the center of mass for the hollow cylinder is \(v_C\).

Which of the following correctly compares the two speeds and provides a valid justification?

A solid sphere and a thin-walled hollow cylinder, both with mass \(M\) and radius \(R\), are released from rest at the top of an incline of height \(H\). Both objects roll down the incline without slipping. At the bottom of the incline, the translational speed of the center of mass for the solid sphere is \(v_S\) and the translational speed of the center of mass for the hollow cylinder is \(v_C\).

Which of the following correctly compares the two speeds and provides a valid justification?

![An inclined plane forming a triangle with a horizontal base. At the top of the incline, a solid sphere and a thin hoop are positioned side-by-side. The vertical height from the base to the top of the incline is labeled H. Dashed lines indicate the path of both objects moving down the ramp.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775793986-S18mwF.jpg)

- **A.** \(v_S > v_C\) because the sphere has a smaller rotational inertia, resulting in a smaller fraction of total mechanical energy being converted into rotational kinetic energy.
- **B.** \(v_S > v_C\) because the sphere has a larger rotational inertia, allowing it to resist the torque from friction more effectively as it rolls down the ramp.
- **C.** \(v_C > v_S\) because the cylinder's mass is distributed further from the axis of rotation, giving it more angular momentum to maintain its motion.
- **D.** \(v_C = v_S\) because both objects start with the same gravitational potential energy \(MgH\) and energy is conserved during the rolling motion.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111295/*