---
title: "A student performs an experiment to determine the local acceleration due to gravity, projects, using a simple pendulum. For several trials, the student measures the length, \\(L\\), of the string from the pivot to the top of a spherical bob of radius \\(R\\). The student records the period, \\(T\\), of the pendulum for small-angle oscillations and plots \\(T^2\\) on the vertical axis as a function of \\(L\\) on the horizontal axis. The resulting best-fit line is given by the equation \\(T^2 = 4.05L + 0.12\\), where \\(T\\) is in seconds and \\(L\\) is in meters. Which of the following is a correct interpretation of the data?"
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/110766/"
date_modified: "2026-04-07T22:29:30+00:00"
---

# A student performs an experiment to determine the local acceleration due to gravity, projects, using a simple pendulum. For several trials, the student measures the length, \(L\), of the string from the pivot to the top of a spherical bob of radius \(R\). The student records the period, \(T\), of the pendulum for small-angle oscillations and plots \(T^2\) on the vertical axis as a function of \(L\) on the horizontal axis. The resulting best-fit line is given by the equation \(T^2 = 4.05L + 0.12\), where \(T\) is in seconds and \(L\) is in meters. Which of the following is a correct interpretation of the data?

A student performs an experiment to determine the local acceleration due to gravity, projects, using a simple pendulum. For several trials, the student measures the length, \(L\), of the string from the pivot to the top of a spherical bob of radius \(R\). The student records the period, \(T\), of the pendulum for small-angle oscillations and plots \(T^2\) on the vertical axis as a function of \(L\) on the horizontal axis. The resulting best-fit line is given by the equation \(T^2 = 4.05L + 0.12\), where \(T\) is in seconds and \(L\) is in meters. Which of the following is a correct interpretation of the data?

![A graph with the horizontal axis labeled 'Length L (m)' and the vertical axis labeled 'Period Squared T^2 (s^2)'. A series of points are plotted in a linear arrangement. A solid line of best fit passes through the points. The line starts at a positive value on the vertical axis (0.12) when L is zero and has a constant positive slope. A label next to the line reads 'T^2 = 4.05L + 0.12'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775600970-Z67dY1.jpg)

- **A.** The value of \(g\) is approximately \(9.75 \text{ m/s}^2\), and the positive y-intercept is consistent with the fact that the effective length of the pendulum is \(L + R\).
- **B.** The value of \(g\) is approximately \(4.05 \text{ m/s}^2\), and the positive y-intercept indicates a systematic error in the stopwatch calibration.
- **C.** The value of \(g\) is approximately \(9.75 \text{ m/s}^2\), and the positive y-intercept indicates that the mass of the bob was too large for the small-angle approximation to be valid.
- **D.** The value of \(g\) is approximately \(0.10 \text{ m/s}^2\), and the positive y-intercept indicates that the student should have plotted \(T\) versus \(\sqrt{L}\) to eliminate the intercept.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110766/*