---
title: "Two identical uniform solid cylinders, A and B, are released from rest from the same vertical height at the top of two identical inclined planes of angle \\(\\theta\\). Cylinder A rolls down its incline without slipping, while cylinder B slides down its incline on a frictionless surface without rotating.  Which row in the table correctly compares the center-of-mass speeds, \\(v_A\\) and \\(v_B\\), of the cylinders at the bottom of the inclines and their elapsed travel times, \\(t_A\\) and \\(t_B\\), to reach the bottom?  | Option | Center-of-Mass Speed at Bottom | Travel Time to Reach Bottom | | :—: | :—: | :—: | | (A) | \\(v_A < v_B\\) | \\(t_A  v_B\\) | \\(t_A < t_B\\) | | (C) | \\(v_A  t_B\\) | | (D) | \\(v_A > v_B\\) | \\(t_A > t_B\\) |"
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url: "https://nerd-notes.com/ubq/124456/"
date_modified: "2026-09-28T14:05:37+00:00"
---

# Two identical uniform solid cylinders, A and B, are released from rest from the same vertical height at the top of two identical inclined planes of angle \(\theta\). Cylinder A rolls down its incline without slipping, while cylinder B slides down its incline on a frictionless surface without rotating.

Which row in the table correctly compares the center-of-mass speeds, \(v_A\) and \(v_B\), of the cylinders at the bottom of the inclines and their elapsed travel times, \(t_A\) and \(t_B\), to reach the bottom?

| Option | Center-of-Mass Speed at Bottom | Travel Time to Reach Bottom |
| :—: | :—: | :—: |
| (A) | \(v_A < v_B\) | \(t_A  v_B\) | \(t_A < t_B\) |
| (C) | \(v_A  t_B\) |
| (D) | \(v_A > v_B\) | \(t_A > t_B\) |

Two identical uniform solid cylinders, A and B, are released from rest from the same vertical height at the top of two identical inclined planes of angle \(\theta\). Cylinder A rolls down its incline without slipping, while cylinder B slides down its incline on a frictionless surface without rotating.

Which row in the table correctly compares the center-of-mass speeds, \(v_A\) and \(v_B\), of the cylinders at the bottom of the inclines and their elapsed travel times, \(t_A\) and \(t_B\), to reach the bottom?

| Option | Center-of-Mass Speed at Bottom | Travel Time to Reach Bottom |
| :---: | :---: | :---: |
| (A) | \(v_A < v_B\) | \(t_A < t_B\) |
| (B) | \(v_A > v_B\) | \(t_A < t_B\) |
| (C) | \(v_A < v_B\) | \(t_A > t_B\) |
| (D) | \(v_A > v_B\) | \(t_A > t_B\) |

![Two identical right-triangular wedges sit side by side on a horizontal ground line, each with an incline angle \(\theta\) at the lower right and a vertical left side of height \(H\). On the left incline, labeled Rough surface, a circular disk labeled A rests at the top of the ramp, with a small clockwise curved arrow around its center indicating rolling motion down the ramp. On the right incline, labeled Frictionless surface, an identical circular disk labeled B rests at the top of the ramp without any curved arrows. A vertical dashed line with double-headed dimension arrows indicates the vertical height \(H\) of each incline. An angle arc at the base of each incline is labeled \(\theta\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604337-9wrekf.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124456/*