---
title: "A small sphere of mass \\(m\\) is attached to an ideal string of length \\(R\\) and whirled in a vertical circle. When the sphere is at the highest point of its path, it has a speed \\(v_0\\) and the tension in the string has a magnitude \\(T\\). The speed of the sphere is then increased such that the new speed at the highest point is \\(2v_0\\). What is the new magnitude of the tension in the string when the sphere is at the highest point with this new speed?"
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url: "https://nerd-notes.com/ubq/114645/"
date_modified: "2026-07-03T04:46:46+00:00"
---

# A small sphere of mass \(m\) is attached to an ideal string of length \(R\) and whirled in a vertical circle. When the sphere is at the highest point of its path, it has a speed \(v_0\) and the tension in the string has a magnitude \(T\). The speed of the sphere is then increased such that the new speed at the highest point is \(2v_0\). What is the new magnitude of the tension in the string when the sphere is at the highest point with this new speed?

A small sphere of mass \(m\) is attached to an ideal string of length \(R\) and whirled in a vertical circle. When the sphere is at the highest point of its path, it has a speed \(v_0\) and the tension in the string has a magnitude \(T\). The speed of the sphere is then increased such that the new speed at the highest point is \(2v_0\). What is the new magnitude of the tension in the string when the sphere is at the highest point with this new speed?

![A side-view diagram showing a small sphere of mass m attached to a string of length R. The sphere is at the top of a vertical circle, which is indicated by a dashed circular path. A horizontal velocity vector labeled v_0 points to the right from the sphere. Two downward arrows from the sphere represent the force of gravity mg and the tension force T.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1783054005-9QWGE4.jpg)

- **A.** \(4T - 3mg\)
- **B.** \(4T\)
- **C.** \(4T + 3mg\)
- **D.** \(4T + 4mg\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114645/*