---
title: "A block of mass \\(2m\\) labeled block A rests on a fixed ramp inclined at an angle of \\(30^\\circ\\) above the horizontal. Block A is connected by a light, inextensible string that passes over a frictionless, massless pulley to a hanging block of mass \\(2m\\) labeled block B. The coefficient of static friction between block A and the ramp is \\(\\mu_s = \\dfrac{\\sqrt{3}}{2}\\), and the coefficient of kinetic friction is \\(\\mu_k = \\dfrac{\\sqrt{3}}{6}\\). In Case 1, the system is released from rest, while in Case 2, block A is given an initial upward velocity along the ramp. Which of the following correctly compares the magnitude of the system acceleration and the string tension for Case 1 and Case 2?"
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url: "https://nerd-notes.com/ubq/120615/"
date_modified: "2026-08-23T04:41:59+00:00"
---

# A block of mass \(2m\) labeled block A rests on a fixed ramp inclined at an angle of \(30^\circ\) above the horizontal. Block A is connected by a light, inextensible string that passes over a frictionless, massless pulley to a hanging block of mass \(2m\) labeled block B. The coefficient of static friction between block A and the ramp is \(\mu_s = \dfrac{\sqrt{3}}{2}\), and the coefficient of kinetic friction is \(\mu_k = \dfrac{\sqrt{3}}{6}\). In Case 1, the system is released from rest, while in Case 2, block A is given an initial upward velocity along the ramp. Which of the following correctly compares the magnitude of the system acceleration and the string tension for Case 1 and Case 2?

A block of mass \(2m\) labeled block A rests on a fixed ramp inclined at an angle of \(30^\circ\) above the horizontal. Block A is connected by a light, inextensible string that passes over a frictionless, massless pulley to a hanging block of mass \(2m\) labeled block B. The coefficient of static friction between block A and the ramp is \(\mu_s = \dfrac{\sqrt{3}}{2}\), and the coefficient of kinetic friction is \(\mu_k = \dfrac{\sqrt{3}}{6}\). In Case 1, the system is released from rest, while in Case 2, block A is given an initial upward velocity along the ramp. Which of the following correctly compares the magnitude of the system acceleration and the string tension for Case 1 and Case 2?

![A right triangle represents a fixed incline with a horizontal base and a 30-degree inclined surface rising from left to right. At the top apex on the right, an ideal circular pulley is mounted. A rectangular block labeled A rests on the inclined surface. A straight line representing a string extends from the top edge of block A parallel to the incline, passes over the top apex pulley, and extends vertically downward. A second rectangular block labeled B hangs freely from the vertical section of the string. A coordinate angle arc at the lower-left corner of the incline is labeled 30^\circ. No other labels, lines, text, or arrows appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460119-DFkXUb.jpg)

- **A.** | Case 1 Acceleration | Case 1 Tension | Case 2 Acceleration | Case 2 Tension | |---|---|---|---| | \(0\) | \(2mg\) | \(\dfrac{1}{8}g\) | \(\dfrac{7}{4}mg\) |
- **B.** | Case 1 Acceleration | Case 1 Tension | Case 2 Acceleration | Case 2 Tension | |---|---|---|---| | \(\dfrac{1}{8}g\) | \(\dfrac{7}{4}mg\) | \(\dfrac{1}{8}g\) | \(\dfrac{7}{4}mg\) |
- **C.** | Case 1 Acceleration | Case 1 Tension | Case 2 Acceleration | Case 2 Tension | |---|---|---|---| | \(0\) | \(mg\) | \(\dfrac{3}{8}g\) | \(\dfrac{5}{4}mg\) |
- **D.** | Case 1 Acceleration | Case 1 Tension | Case 2 Acceleration | Case 2 Tension | |---|---|---|---| | \(0\) | \(\dfrac{3}{2}mg\) | \(\dfrac{1}{4}g\) | \(\dfrac{3}{2}mg\) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120615/*