---
title: "A cylindrical container of cross-sectional area \\(A\\) containing water of density \\(\\rho_w\\) rests on a table.  In State 1, a wooden block of mass \\(m\\) floats in static equilibrium, resulting in a total water surface height \\(h_1\\) above the base and a water pressure \\(P_1\\) at the bottom surface of the container.  In State 2, the wooden block is removed and replaced by a metal block of the same mass \\(m\\) and density \\(\\rho_m > \\rho_w\\) that sinks and rests on the bottom, resulting in a total water surface height \\(h_2\\) and a water pressure \\(P_2\\) at the bottom surface (away from the contact area of the metal block).  Which of the following correctly compares the water heights and the water pressures at the bottom in the two states?"
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url: "https://nerd-notes.com/ubq/122762/"
date_modified: "2026-09-28T11:02:51+00:00"
---

# A cylindrical container of cross-sectional area \(A\) containing water of density \(\rho_w\) rests on a table.

In State 1, a wooden block of mass \(m\) floats in static equilibrium, resulting in a total water surface height \(h_1\) above the base and a water pressure \(P_1\) at the bottom surface of the container.

In State 2, the wooden block is removed and replaced by a metal block of the same mass \(m\) and density \(\rho_m > \rho_w\) that sinks and rests on the bottom, resulting in a total water surface height \(h_2\) and a water pressure \(P_2\) at the bottom surface (away from the contact area of the metal block).

Which of the following correctly compares the water heights and the water pressures at the bottom in the two states?

A cylindrical container of cross-sectional area \(A\) containing water of density \(\rho_w\) rests on a table.

In State 1, a wooden block of mass \(m\) floats in static equilibrium, resulting in a total water surface height \(h_1\) above the base and a water pressure \(P_1\) at the bottom surface of the container.

In State 2, the wooden block is removed and replaced by a metal block of the same mass \(m\) and density \(\rho_m > \rho_w\) that sinks and rests on the bottom, resulting in a total water surface height \(h_2\) and a water pressure \(P_2\) at the bottom surface (away from the contact area of the metal block).

Which of the following correctly compares the water heights and the water pressures at the bottom in the two states?

![A grayscale line diagram showing two identical open cylindrical containers side by side on a flat horizontal surface. The left container is labeled State 1 and has a vertical height line on the left with a double-headed arrow spanning from the base to the liquid surface labeled h_1. Inside State 1, a square block labeled m floats partially submerged at the surface of the water, and a dot on the container floor is labeled P_1. The right container is labeled State 2 and has a vertical height line on the right with a double-headed arrow spanning from the base to the liquid surface labeled h_2, drawn noticeably lower than h_1. Inside State 2, a square block of the same size labeled m rests flat on the bottom of the container, completely submerged, and a dot on the container floor to the side of the block is labeled P_2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790593371-WDrIh4.jpg)

- **A.** \(h_2 = h_1\) and \(P_2 = P_1\)
- **B.** \(h_2 < h_1\) and \(P_2 < P_1\)
- **C.** \(h_2 < h_1\) and \(P_2 = P_1\)
- **D.** \(h_2 > h_1\) and \(P_2 > P_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/122762/*