---
title: "A thin, uniform rod of length \\(L\\) and total mass \\(M\\) lies along the \\(x\\)-axis, centered at the origin. A point \\(P\\) is located on the \\(y\\)-axis at coordinates \\((0, d)\\), where \\(d > 0\\).  Which of the following expressions represents the correct integral setup to determine the magnitude of the net gravitational field at point \\(P\\) due to the rod?"
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url: "https://nerd-notes.com/ubq/120575/"
date_modified: "2026-08-23T04:41:40+00:00"
---

# A thin, uniform rod of length \(L\) and total mass \(M\) lies along the \(x\)-axis, centered at the origin. A point \(P\) is located on the \(y\)-axis at coordinates \((0, d)\), where \(d > 0\).

Which of the following expressions represents the correct integral setup to determine the magnitude of the net gravitational field at point \(P\) due to the rod?

A thin, uniform rod of length \(L\) and total mass \(M\) lies along the \(x\)-axis, centered at the origin. A point \(P\) is located on the \(y\)-axis at coordinates \((0, d)\), where \(d > 0\).

Which of the following expressions represents the correct integral setup to determine the magnitude of the net gravitational field at point \(P\) due to the rod?

![A Cartesian coordinate system with a horizontal x-axis and a vertical y-axis intersecting at the origin labeled O. A thick horizontal line segment representing a rod of length L is centered on the origin along the x-axis, spanning from x = -L/2 on the left to x = L/2 on the right, with both endpoints labeled on the axis. On the positive y-axis, a single black dot labeled P is plotted at a vertical distance labeled d above the origin. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460100-CdgAVP.jpg)

- **A.** \(g = \dfrac{GM}{L} \int_{-L/2}^{L/2} \dfrac{1}{x^2 + d^2} \, dx\)
- **B.** \(g = \dfrac{GMd}{L} \int_{0}^{L/2} \dfrac{1}{(x^2 + d^2)^{3/2}} \, dx\)
- **C.** \(g = \dfrac{2GM}{L} \int_{0}^{L/2} \dfrac{x}{(x^2 + d^2)^{3/2}} \, dx\)
- **D.** \(g = \dfrac{2GMd}{L} \int_{0}^{L/2} \dfrac{1}{(x^2 + d^2)^{3/2}} \, dx\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120575/*