---
title: "A small ball of mass \\(m\\) travels horizontally with speed \\(v\\) on a frictionless surface. It strikes the bottom end of a uniform rod of mass \\(M\\) and length \\(L\\) that is suspended vertically from a frictionless pivot at its top end. The ball sticks to the rod, and the ball-rod system begins to rotate about the pivot. Which of the following correctly compares the linear momentum of the ball-rod system immediately before the collision, \\(p_i\\), to the linear momentum of the system immediately after the collision, \\(p_f\\), and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/111691/"
date_modified: "2026-04-14T22:37:14+00:00"
---

# A small ball of mass \(m\) travels horizontally with speed \(v\) on a frictionless surface. It strikes the bottom end of a uniform rod of mass \(M\) and length \(L\) that is suspended vertically from a frictionless pivot at its top end. The ball sticks to the rod, and the ball-rod system begins to rotate about the pivot. Which of the following correctly compares the linear momentum of the ball-rod system immediately before the collision, \(p_i\), to the linear momentum of the system immediately after the collision, \(p_f\), and provides the correct physical justification?

A small ball of mass \(m\) travels horizontally with speed \(v\) on a frictionless surface. It strikes the bottom end of a uniform rod of mass \(M\) and length \(L\) that is suspended vertically from a frictionless pivot at its top end. The ball sticks to the rod, and the ball-rod system begins to rotate about the pivot. Which of the following correctly compares the linear momentum of the ball-rod system immediately before the collision, \(p_i\), to the linear momentum of the system immediately after the collision, \(p_f\), and provides the correct physical justification?

![A vertical uniform rod of length L is attached to a pivot P at the top end. A small ball of mass m is moving horizontally to the right with velocity v toward the bottom end of the rod. A dashed line shows the ball's path toward the tip of the rod.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1776206234-BamTNn.jpg)

- **A.** \(p_f = p_i\), because the pivot is frictionless and the collision occurs entirely within the ball-rod system.
- **B.** \(p_f < p_i\), because the collision is perfectly inelastic, and the loss of mechanical energy results in a corresponding loss of linear momentum.
- **C.** \(p_f > p_i\), because the pivot must exert a horizontal force in the direction of the ball's motion to keep the top of the rod fixed.
- **D.** \(p_f < p_i\), because the pivot must exert a horizontal force in the direction opposite to the ball's motion to resist the rotation of the rod.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111691/*