---
title: "A technician uses a wrench to loosen a bolt. In the first attempt, the technician applies a force of magnitude \\(F\\) at a distance \\(r\\) from the center of the bolt, such that the force makes an angle of \\(30^{\\circ}\\) with the wrench handle. In the second attempt, the technician applies a force of the same magnitude \\(F\\) at a distance \\(2r\\) from the center of the bolt such that the force is perpendicular to the wrench handle. What is the ratio of the magnitude of the torque produced in the second attempt to the magnitude of the torque produced in the first attempt?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/111618/"
date_modified: "2026-04-13T23:21:19+00:00"
---

# A technician uses a wrench to loosen a bolt. In the first attempt, the technician applies a force of magnitude \(F\) at a distance \(r\) from the center of the bolt, such that the force makes an angle of \(30^{\circ}\) with the wrench handle. In the second attempt, the technician applies a force of the same magnitude \(F\) at a distance \(2r\) from the center of the bolt such that the force is perpendicular to the wrench handle. What is the ratio of the magnitude of the torque produced in the second attempt to the magnitude of the torque produced in the first attempt?

A technician uses a wrench to loosen a bolt. In the first attempt, the technician applies a force of magnitude \(F\) at a distance \(r\) from the center of the bolt, such that the force makes an angle of \(30^{\circ}\) with the wrench handle. In the second attempt, the technician applies a force of the same magnitude \(F\) at a distance \(2r\) from the center of the bolt such that the force is perpendicular to the wrench handle. What is the ratio of the magnitude of the torque produced in the second attempt to the magnitude of the torque produced in the first attempt?

![Two diagrams showing a wrench on a bolt. Diagram 1: The wrench handle is horizontal to the right. A force vector F is applied at distance r from the pivot at a 30-degree angle above the horizontal handle. Diagram 2: The same wrench handle. A force vector F is applied at distance 2r from the pivot, pointing vertically upward, forming a 90-degree angle with the handle.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1776122478-gchP56.jpg)

- **A.** 1
- **B.** 2
- **C.** 4
- **D.** 8

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111618/*