---
title: "A rifle of mass \\(M\\) is suspended from a ceiling by two long, light vertical cords and loaded with a bullet of mass \\(m\\). When the rifle is fired, high-pressure gas from the ignited gunpowder exerts a horizontal force that accelerates the bullet down the barrel of length \\(L\\) and pushes backward on the rifle. Friction and external horizontal forces are negligible, and the bullet exits the barrel before the suspension cords deviate noticeably from the vertical. Which of the following correctly pairs the fraction of the total kinetic energy acquired by the bullet, \\(\\dfrac{K_{\\text{bullet}}}{K_{\\text{total}}}\\), with the physical reason that the work done by the gas on the bullet exceeds the work done on the rifle?"
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url: "https://nerd-notes.com/ubq/124475/"
date_modified: "2026-09-28T14:06:00+00:00"
---

# A rifle of mass \(M\) is suspended from a ceiling by two long, light vertical cords and loaded with a bullet of mass \(m\). When the rifle is fired, high-pressure gas from the ignited gunpowder exerts a horizontal force that accelerates the bullet down the barrel of length \(L\) and pushes backward on the rifle. Friction and external horizontal forces are negligible, and the bullet exits the barrel before the suspension cords deviate noticeably from the vertical. Which of the following correctly pairs the fraction of the total kinetic energy acquired by the bullet, \(\dfrac{K_{\text{bullet}}}{K_{\text{total}}}\), with the physical reason that the work done by the gas on the bullet exceeds the work done on the rifle?

A rifle of mass \(M\) is suspended from a ceiling by two long, light vertical cords and loaded with a bullet of mass \(m\). When the rifle is fired, high-pressure gas from the ignited gunpowder exerts a horizontal force that accelerates the bullet down the barrel of length \(L\) and pushes backward on the rifle. Friction and external horizontal forces are negligible, and the bullet exits the barrel before the suspension cords deviate noticeably from the vertical. Which of the following correctly pairs the fraction of the total kinetic energy acquired by the bullet, \(\dfrac{K_{\text{bullet}}}{K_{\text{total}}}\), with the physical reason that the work done by the gas on the bullet exceeds the work done on the rifle?

![A physical setup diagram showing a horizontal ceiling at the top represented by a solid horizontal line with small hatching marks above it. Suspended from the ceiling are two identical, parallel vertical dashed lines representing support cords of equal length. Attached to the bottom ends of these cords is a horizontal rifle body of mass labeled M. Inside the rifle body is a horizontal barrel of length labeled L oriented horizontally to the right. Located inside the left end of the barrel is a small solid cylindrical projectile of mass labeled m. A horizontal dashed centerline extends along the barrel axis to the right, with a horizontal arrow pointing to the right labeled with a plus x direction. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604360-cutLmi.jpg)

- **A.** Fraction: \(\dfrac{m}{m+M}\) ; Reason: The gas force acts over a greater displacement on the bullet than on the rifle.
- **B.** Fraction: \(\dfrac{m}{m+M}\) ; Reason: The gas force acts over a longer time interval on the bullet than on the rifle.
- **C.** Fraction: \(\dfrac{M}{m+M}\) ; Reason: The gas force acts over a greater displacement on the bullet than on the rifle.
- **D.** Fraction: \(\dfrac{M}{m+M}\) ; Reason: The gas force acts over a longer time interval on the bullet than on the rifle.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124475/*