---
title: "A student conducts three trials where a small ball is attached to a light string of length \\(L\\) and swung in a vertical circle. In each trial, the ball is launched from the bottom of the loop with a specific launch speed \\(v_0\\). The table below shows the mass of the ball and the launch speed for each trial.  | Case | Mass | Launch Speed \\(v_0\\) | | :— | :— | :— | | 1 | \\(M\\) | \\(\\sqrt{7gL}\\) | | 2 | \\(2M\\) | \\(\\sqrt{6gL}\\) | | 3 | \\(M\\) | \\(\\sqrt{6gL}\\) |  Which of the following correctly ranks the tension \\(T\\) in the string when the ball is at the top of the loop for the three cases?"
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url: "https://nerd-notes.com/ubq/109867/"
date_modified: "2026-04-04T01:39:58+00:00"
---

# A student conducts three trials where a small ball is attached to a light string of length \(L\) and swung in a vertical circle. In each trial, the ball is launched from the bottom of the loop with a specific launch speed \(v_0\). The table below shows the mass of the ball and the launch speed for each trial.

| Case | Mass | Launch Speed \(v_0\) |
| :— | :— | :— |
| 1 | \(M\) | \(\sqrt{7gL}\) |
| 2 | \(2M\) | \(\sqrt{6gL}\) |
| 3 | \(M\) | \(\sqrt{6gL}\) |

Which of the following correctly ranks the tension \(T\) in the string when the ball is at the top of the loop for the three cases?

A student conducts three trials where a small ball is attached to a light string of length \(L\) and swung in a vertical circle. In each trial, the ball is launched from the bottom of the loop with a specific launch speed \(v_0\). The table below shows the mass of the ball and the launch speed for each trial.

| Case | Mass | Launch Speed \(v_0\) |
| :--- | :--- | :--- |
| 1 | \(M\) | \(\sqrt{7gL}\) |
| 2 | \(2M\) | \(\sqrt{6gL}\) |
| 3 | \(M\) | \(\sqrt{6gL}\) |

Which of the following correctly ranks the tension \(T\) in the string when the ball is at the top of the loop for the three cases?

![A ball of mass m is at the bottom of a vertical circular path of radius L. A velocity vector v_0 points horizontally to the right. The circular path is indicated by a dashed line. The position at the top of the circle is also shown with a dashed circle representing the ball at that location.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1775266797-e0ewPG.jpg)

- **A.** \(T_1 = T_2 > T_3\)
- **B.** \(T_2 > T_1 > T_3\)
- **C.** \(T_1 > T_2 > T_3\)
- **D.** \(T_2 > T_3 > T_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109867/*