---
title: "A solid cube is held completely submerged in a container filled with a certain oil of density \\( \\rho \\). The cube is then removed and held completely submerged in a container filled with a concentrated syrup of density \\( 3\\rho \\). If \\( F_{oil} \\) is the magnitude of the buoyant force exerted on the cube by the oil and \\( F_{syrup} \\) is the magnitude of the buoyant force exerted on the cube by the syrup, what is the ratio \\( \\dfrac{F_{syrup}}{F_{oil}} \\)?"
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url: "https://nerd-notes.com/ubq/111293/"
date_modified: "2026-04-10T04:06:25+00:00"
---

# A solid cube is held completely submerged in a container filled with a certain oil of density \( \rho \). The cube is then removed and held completely submerged in a container filled with a concentrated syrup of density \( 3\rho \). If \( F_{oil} \) is the magnitude of the buoyant force exerted on the cube by the oil and \( F_{syrup} \) is the magnitude of the buoyant force exerted on the cube by the syrup, what is the ratio \( \dfrac{F_{syrup}}{F_{oil}} \)?

A solid cube is held completely submerged in a container filled with a certain oil of density \( \rho \). The cube is then removed and held completely submerged in a container filled with a concentrated syrup of density \( 3\rho \). If \( F_{oil} \) is the magnitude of the buoyant force exerted on the cube by the oil and \( F_{syrup} \) is the magnitude of the buoyant force exerted on the cube by the syrup, what is the ratio \( \dfrac{F_{syrup}}{F_{oil}} \)?

![Two identical containers are shown side-by-side. The left container is labeled Oil and contains a liquid with density rho. The right container is labeled Syrup and contains a liquid with density 3 rho. In each container, an identical grey cube is shown fully submerged at the same depth. Arrows labeled F_oil and F_syrup point upward from the center of each cube respectively.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775793985-CBRF3A.jpg)

- **A.** \( \dfrac{1}{3} \)
- **B.** \( 1 \)
- **C.** \( 3 \)
- **D.** \( 9 \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111293/*