---
title: "A container of mass \\(M_{\\text{tank}}\\) filled with a liquid of mass \\(M_{\\text{liq}}\\) rests on an electronic scale. A small, rigid model submarine of mass \\(M_{\\text{sub}}\\) and fixed volume \\(V_0\\) is completely submerged in the liquid and held in place by a taut, light vertical string anchored to the bottom of the container. Initially, the liquid has uniform density \\(\\rho_1\\), where \\(\\rho_1 V_0 > M_{\\text{sub}}\\), and the system is in static equilibrium. The liquid is then uniformly heated, decreasing its density to \\(\\rho_2\\), where \\(\\rho_2 V_0 > M_{\\text{sub}}\\) still holds, while the volume of the submarine and the total mass of the liquid remain unchanged. How do the tension in the string and the normal force exerted by the scale on the container after heating compare to their initial values before heating?"
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url: "https://nerd-notes.com/ubq/122775/"
date_modified: "2026-09-28T11:02:53+00:00"
---

# A container of mass \(M_{\text{tank}}\) filled with a liquid of mass \(M_{\text{liq}}\) rests on an electronic scale. A small, rigid model submarine of mass \(M_{\text{sub}}\) and fixed volume \(V_0\) is completely submerged in the liquid and held in place by a taut, light vertical string anchored to the bottom of the container. Initially, the liquid has uniform density \(\rho_1\), where \(\rho_1 V_0 > M_{\text{sub}}\), and the system is in static equilibrium. The liquid is then uniformly heated, decreasing its density to \(\rho_2\), where \(\rho_2 V_0 > M_{\text{sub}}\) still holds, while the volume of the submarine and the total mass of the liquid remain unchanged. How do the tension in the string and the normal force exerted by the scale on the container after heating compare to their initial values before heating?

A container of mass \(M_{\text{tank}}\) filled with a liquid of mass \(M_{\text{liq}}\) rests on an electronic scale. A small, rigid model submarine of mass \(M_{\text{sub}}\) and fixed volume \(V_0\) is completely submerged in the liquid and held in place by a taut, light vertical string anchored to the bottom of the container. Initially, the liquid has uniform density \(\rho_1\), where \(\rho_1 V_0 > M_{\text{sub}}\), and the system is in static equilibrium. The liquid is then uniformly heated, decreasing its density to \(\rho_2\), where \(\rho_2 V_0 > M_{\text{sub}}\) still holds, while the volume of the submarine and the total mass of the liquid remain unchanged. How do the tension in the string and the normal force exerted by the scale on the container after heating compare to their initial values before heating?

![A schematic drawing of a laboratory apparatus. At the bottom, a horizontal rectangular platform representing an electronic scale supports a cylindrical container labeled M_{\text{tank}}. Inside the container, liquid of mass M_{\text{liq}} fills the container up to a horizontal line indicating the fluid surface. Completely submerged within the liquid is a rigid oval shape representing a model submarine labeled M_{\text{sub}} and V_0. A single vertical straight solid line representing a taut string connects the center of the container bottom to the bottom of the submarine. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790593373-XwD418.jpg)

- **A.** The tension in the string increases, and the normal force on the container increases.
- **B.** The tension in the string decreases, and the normal force on the container remains unchanged.
- **C.** The tension in the string decreases, and the normal force on the container decreases.
- **D.** The tension in the string increases, and the normal force on the container remains unchanged.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/122775/*