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title: "A cart of mass \\(M\\) rests on a frictionless, horizontal track. A light, rigid rod of length \\(L\\) has a small bob of mass \\(m\\) attached to one end, and its other end is connected to the cart by a frictionless pivot. The rod is initially held vertically upright at rest and then released, falling in the vertical plane containing the track until it reaches the horizontal orientation. Which of the following correctly describes the magnitude of the cart’s horizontal displacement, \\(|\\Delta x_c|\\), and the path of the bob relative to the track in the limits \\(M \\gg m\\) and \\(M \\ll m\\)?"
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url: "https://nerd-notes.com/ubq/124263/"
date_modified: "2026-09-28T14:04:34+00:00"
---

# A cart of mass \(M\) rests on a frictionless, horizontal track. A light, rigid rod of length \(L\) has a small bob of mass \(m\) attached to one end, and its other end is connected to the cart by a frictionless pivot. The rod is initially held vertically upright at rest and then released, falling in the vertical plane containing the track until it reaches the horizontal orientation. Which of the following correctly describes the magnitude of the cart’s horizontal displacement, \(|\Delta x_c|\), and the path of the bob relative to the track in the limits \(M \gg m\) and \(M \ll m\)?

A cart of mass \(M\) rests on a frictionless, horizontal track. A light, rigid rod of length \(L\) has a small bob of mass \(m\) attached to one end, and its other end is connected to the cart by a frictionless pivot. The rod is initially held vertically upright at rest and then released, falling in the vertical plane containing the track until it reaches the horizontal orientation. Which of the following correctly describes the magnitude of the cart's horizontal displacement, \(|\Delta x_c|\), and the path of the bob relative to the track in the limits \(M \gg m\) and \(M \ll m\)?

![A horizontal line represents a flat track. Resting on the track is a rectangular box representing a cart labeled M, supported by two small circular wheels touching the track. A small circular pivot is located at the center of the top surface of the cart. Attached to this pivot is a straight vertical line segment of length L, labeled L. At the upper tip of the vertical segment is a solid shaded circle representing a bob, labeled m. A curved dashed arrow curves downward and to the right from the bob toward the horizontal level of the cart's top surface. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604274-MVAsjj.jpg)

- **A.** For \(M \gg m\), \(|\Delta x_c| \to L\) with the bob falling vertically; for \(M \ll m\), \(|\Delta x_c| \to 0\) with the bob following a circular arc of radius \(L\).
- **B.** For \(M \gg m\), \(|\Delta x_c| \to 0\) with the bob following a circular arc of radius \(L\); for \(M \ll m\), \(|\Delta x_c| \to L\) with the bob falling vertically.
- **C.** For \(M \gg m\), \(|\Delta x_c| \to 0\) with the bob following a circular arc of radius \(L\); for \(M \ll m\), \(|\Delta x_c| \to \infty\) with the bob accelerating horizontally.
- **D.** For \(M \gg m\), \(|\Delta x_c| \to 0\) with the bob following a circular arc of radius \(L\); for \(M \ll m\), \(|\Delta x_c| \to \dfrac{L}{2}\) with the bob and cart sharing displacement equally.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124263/*