---
title: "A small block of mass \\( M \\) is attached to a string of length \\( L \\) and is whirled in a horizontal circle at a constant speed \\( v \\) on a frictionless tabletop. The tension in the string is measured to be \\( T \\). The student then increases the speed of the block to \\( 2v \\). To keep the tension in the string equal to its original value \\( T \\), the student must adjust the length of the string. How should the length of the string be changed?"
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url: "https://nerd-notes.com/ubq/113125/"
date_modified: "2026-05-05T04:25:59+00:00"
---

# A small block of mass \( M \) is attached to a string of length \( L \) and is whirled in a horizontal circle at a constant speed \( v \) on a frictionless tabletop. The tension in the string is measured to be \( T \). The student then increases the speed of the block to \( 2v \). To keep the tension in the string equal to its original value \( T \), the student must adjust the length of the string. How should the length of the string be changed?

A small block of mass \( M \) is attached to a string of length \( L \) and is whirled in a horizontal circle at a constant speed \( v \) on a frictionless tabletop. The tension in the string is measured to be \( T \). The student then increases the speed of the block to \( 2v \). To keep the tension in the string equal to its original value \( T \), the student must adjust the length of the string. How should the length of the string be changed?

![A top-down view of a block of mass M moving in a circular path of radius L on a horizontal surface. A string connects the block to a central pivot point. A velocity vector v is shown tangent to the circle at the block's position.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1777955158-DOpyxt.jpg)

- **A.** The length must be increased to \( 2L \) because the tension is directly proportional to the speed of the block.
- **B.** The length must be increased to \( 4L \) because the tension is directly proportional to the square of the speed of the block.
- **C.** The length must be decreased to \( L/2 \) because the tension is inversely proportional to the length of the string.
- **D.** The length must be decreased to \( L/4 \) because the tension is inversely proportional to the square of the length of the string.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113125/*