---
title: "A porous composite cube of total volume \\(V\\) consists of a solid matrix material with uniform density \\(\\rho_s\\) and internal hollow voids that occupy a volume fraction \\(f\\) of the total volume, where \\(0 < f  (1-f)\\rho_s\\)) and floats in static equilibrium. Which of the following expressions correctly represents the fraction of the cube’s total volume that is submerged below the surface of the liquid?"
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url: "https://nerd-notes.com/ubq/119044/"
date_modified: "2026-08-18T04:47:08+00:00"
---

# A porous composite cube of total volume \(V\) consists of a solid matrix material with uniform density \(\rho_s\) and internal hollow voids that occupy a volume fraction \(f\) of the total volume, where \(0 < f  (1-f)\rho_s\)) and floats in static equilibrium. Which of the following expressions correctly represents the fraction of the cube’s total volume that is submerged below the surface of the liquid?

A porous composite cube of total volume \(V\) consists of a solid matrix material with uniform density \(\rho_s\) and internal hollow voids that occupy a volume fraction \(f\) of the total volume, where \(0 < f < 1\). The mass of the gas within the voids is negligible. The cube is placed in a container filled with a liquid of density \(\rho_L\) (where \(\rho_L > (1-f)\rho_s\)) and floats in static equilibrium. Which of the following expressions correctly represents the fraction of the cube's total volume that is submerged below the surface of the liquid?

![A schematic showing a square-faced cube partially submerged in a liquid container. The interior of the cube shows several small circular void spaces uniformly distributed across its cross-section. A horizontal line across the container indicates the liquid surface. A portion of the cube sits above the liquid surface, while the remaining portion sits submerged below. A vertical downward arrow labeled F_g originates from the center of mass of the cube, and a vertical upward arrow labeled F_B originates from the center of the submerged portion. Labels show density \rho_s for the solid matrix material, void fraction f, and density \rho_L for the liquid. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787028428-FrDy9m.jpg)

- **A.** \(\dfrac{f \rho_s}{\rho_L}\)
- **B.** \(\dfrac{\rho_s}{(1 - f)\rho_L}\)
- **C.** \(\dfrac{(1 + f)\rho_s}{\rho_L}\)
- **D.** \(\dfrac{(1 - f)\rho_s}{\rho_L}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119044/*