---
title: "A solid cube of mass \\( M \\) and density \\( \\rho_c \\) is held completely submerged in a container of liquid with density \\( \\rho_l \\). The density of the cube is less than the density of the liquid (\\( \\rho_c < \\rho_l \\)). To keep the cube from rising to the surface, it is tethered to the bottom of the container by a thin, vertical string of negligible mass. Which of the following is a correct expression for the magnitude of the tension \\( T \\) in the string?"
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url: "https://nerd-notes.com/ubq/109401/"
date_modified: "2026-03-21T23:49:20+00:00"
---

# A solid cube of mass \( M \) and density \( \rho_c \) is held completely submerged in a container of liquid with density \( \rho_l \). The density of the cube is less than the density of the liquid (\( \rho_c < \rho_l \)). To keep the cube from rising to the surface, it is tethered to the bottom of the container by a thin, vertical string of negligible mass. Which of the following is a correct expression for the magnitude of the tension \( T \) in the string?

A solid cube of mass \( M \) and density \( \rho_c \) is held completely submerged in a container of liquid with density \( \rho_l \). The density of the cube is less than the density of the liquid (\( \rho_c < \rho_l \)). To keep the cube from rising to the surface, it is tethered to the bottom of the container by a thin, vertical string of negligible mass. Which of the following is a correct expression for the magnitude of the tension \( T \) in the string?

![A clear rectangular beaker is filled with a shaded liquid. A solid cube is positioned in the center of the liquid, fully submerged. A thin vertical line represents a string connecting the center of the bottom face of the cube to the center of the bottom of the beaker. A small arrow labeled g points downward next to the beaker.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774136960-OXhsWK.jpg)

- **A.** \( T = Mg \left( \dfrac{\rho_l}{\rho_c} - 1 \right) \)
- **B.** \( T = Mg \left( 1 - \dfrac{\rho_c}{\rho_l} \right) \)
- **C.** \( T = Mg \left( \dfrac{\rho_l}{\rho_c} + 1 \right) \)
- **D.** \( T = Mg \left( \dfrac{\rho_c}{\rho_l} \right) \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109401/*