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title: "A cylindrical oceanographic probe of mass \\(M\\), height \\(H\\), and uniform cross-sectional area \\(A\\) floats vertically across the horizontal boundary between two immiscible seawater layers. The upper layer has density \\(\\rho_1\\) and the lower layer has density \\(\\rho_2\\), where \\(\\rho_1 < \\rho_2\\). A warm plume from a hydrothermal vent reduces the density of the upper layer to a lower value \\(\\rho_1'\\), while the density \\(\\rho_2\\) of the lower layer remains unchanged. Which of the following claims correctly describes the change in the depth \\(h_2\\) of the probe submerged in the lower layer, and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/119064/"
date_modified: "2026-08-18T04:47:18+00:00"
---

# A cylindrical oceanographic probe of mass \(M\), height \(H\), and uniform cross-sectional area \(A\) floats vertically across the horizontal boundary between two immiscible seawater layers. The upper layer has density \(\rho_1\) and the lower layer has density \(\rho_2\), where \(\rho_1 < \rho_2\). A warm plume from a hydrothermal vent reduces the density of the upper layer to a lower value \(\rho_1'\), while the density \(\rho_2\) of the lower layer remains unchanged. Which of the following claims correctly describes the change in the depth \(h_2\) of the probe submerged in the lower layer, and provides the correct physical justification?

A cylindrical oceanographic probe of mass \(M\), height \(H\), and uniform cross-sectional area \(A\) floats vertically across the horizontal boundary between two immiscible seawater layers. The upper layer has density \(\rho_1\) and the lower layer has density \(\rho_2\), where \(\rho_1 < \rho_2\). A warm plume from a hydrothermal vent reduces the density of the upper layer to a lower value \(\rho_1'\), while the density \(\rho_2\) of the lower layer remains unchanged. Which of the following claims correctly describes the change in the depth \(h_2\) of the probe submerged in the lower layer, and provides the correct physical justification?

![A vertical rectangle representing a cylindrical probe of height H sits oriented vertically across a horizontal dashed line that divides two fluid regions. The upper region is labeled with density \rho_1 and the lower region is labeled with density \rho_2. The probe's vertical segment in the upper region is labeled h_1 and its vertical segment in the lower region is labeled h_2. A single downward vector arrow labeled Mg extends from the center of the rectangle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787028438-qyRM47.jpg)

- **A.** The depth \(h_2\) decreases because the reduced density of the upper layer lowers the total pressure at the interface, allowing the lower fluid to exert a greater net upward pressure that lifts the probe.
- **B.** The depth \(h_2\) increases because the decreased density of the upper layer provides less buoyant force per unit volume submerged in that layer, requiring a greater volume of the probe to be displaced in the denser lower layer to balance the probe's weight.
- **C.** The depth \(h_2\) increases because the total buoyant force acting on the probe must increase to overcome the reduced upward support from the less dense upper layer.
- **D.** The depth \(h_2\) remains unchanged because the total weight of the probe and the density of the lower fluid layer \(\rho_2\) are both constant.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119064/*