---
title: "A student investigates the motion of a conical pendulum consisting of a small bob of mass \\(m\\) attached to a light string of length \\(L\\). The bob moves at a constant speed in a horizontal circular path such that the string makes a constant angle \\(\\theta\\) with the vertical. The student measures the period of revolution \\(T\\) for several different values of \\(\\theta\\) while keeping \\(L\\) constant. In order to produce a linear graph whose slope \\(S\\) can be used to determine the acceleration due to gravity \\(g\\), which quantities should be plotted on the vertical and horizontal axes, and what is the correct expression for \\(g\\) in terms of \\(S\\) and \\(L\\)?"
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url: "https://nerd-notes.com/ubq/120593/"
date_modified: "2026-08-23T04:41:46+00:00"
---

# A student investigates the motion of a conical pendulum consisting of a small bob of mass \(m\) attached to a light string of length \(L\). The bob moves at a constant speed in a horizontal circular path such that the string makes a constant angle \(\theta\) with the vertical. The student measures the period of revolution \(T\) for several different values of \(\theta\) while keeping \(L\) constant. In order to produce a linear graph whose slope \(S\) can be used to determine the acceleration due to gravity \(g\), which quantities should be plotted on the vertical and horizontal axes, and what is the correct expression for \(g\) in terms of \(S\) and \(L\)?

A student investigates the motion of a conical pendulum consisting of a small bob of mass \(m\) attached to a light string of length \(L\). The bob moves at a constant speed in a horizontal circular path such that the string makes a constant angle \(\theta\) with the vertical. The student measures the period of revolution \(T\) for several different values of \(\theta\) while keeping \(L\) constant. In order to produce a linear graph whose slope \(S\) can be used to determine the acceleration due to gravity \(g\), which quantities should be plotted on the vertical and horizontal axes, and what is the correct expression for \(g\) in terms of \(S\) and \(L\)?

![A schematic of a conical pendulum. A horizontal ceiling support line is drawn at the top. A vertical dashed centerline extends downward from the attachment point. A solid straight segment representing the string of length \(L\) extends downward and to the right at an angle \(\theta\) relative to the vertical dashed line. At the end of the string is a small solid circular bob of mass \(m\). A horizontal dashed ellipse indicates the circular path traced by the bob, with a horizontal dashed line from the vertical centerline to the bob indicating the radius \(r\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460106-ELBd4i.jpg)

- **A.** Vertical axis: \(T^2\); Horizontal axis: \(\sin\theta\); Value of \(g\): \(\dfrac{4\pi^2 L}{S}\)
- **B.** Vertical axis: \(T^2\); Horizontal axis: \(\dfrac{1}{\cos\theta}\); Value of \(g\): \(\dfrac{4\pi^2 L}{S}\)
- **C.** Vertical axis: \(T^2\); Horizontal axis: \(\cos\theta\); Value of \(g\): \(4\pi^2 L S\)
- **D.** Vertical axis: \(T^2\); Horizontal axis: \(\cos\theta\); Value of \(g\): \(\dfrac{4\pi^2 L}{S}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120593/*