---
title: "A long vertical cylinder of length L and cross-sectional area A is lowered into a deep tank of fluid. The density of the fluid increases linearly with depth z below the surface (z = 0) according to the equation rho(z) = rho_0 + bz, where rho_0 and b are positive constants. The cylinder is lowered slowly such that its axis remains vertical. Let h represent the depth of the bottom of the cylinder below the surface. Which of the following graphs best represents the buoyant force F_B exerted on the cylinder as a function of h for h > 0?"
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url: "https://nerd-notes.com/ubq/111297/"
date_modified: "2026-04-10T04:07:04+00:00"
---

# A long vertical cylinder of length L and cross-sectional area A is lowered into a deep tank of fluid. The density of the fluid increases linearly with depth z below the surface (z = 0) according to the equation rho(z) = rho_0 + bz, where rho_0 and b are positive constants. The cylinder is lowered slowly such that its axis remains vertical. Let h represent the depth of the bottom of the cylinder below the surface. Which of the following graphs best represents the buoyant force F_B exerted on the cylinder as a function of h for h > 0?

A long vertical cylinder of length L and cross-sectional area A is lowered into a deep tank of fluid. The density of the fluid increases linearly with depth z below the surface (z = 0) according to the equation rho(z) = rho_0 + bz, where rho_0 and b are positive constants. The cylinder is lowered slowly such that its axis remains vertical. Let h represent the depth of the bottom of the cylinder below the surface. Which of the following graphs best represents the buoyant force F_B exerted on the cylinder as a function of h for h > 0?

![A vertical cylinder of length L and area A is partially submerged in a fluid tank. The bottom of the cylinder is at depth h. A vertical axis z points downward from the surface at z=0. The fluid is shaded with a gradient that gets darker with depth to indicate increasing density.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775794024-e4X8rP.jpg)

- **A.** A graph that is a single straight line with a constant positive slope for all values of h.
- **B.** A graph that is concave up for 0 < h < L and horizontal for h > L.
- **C.** A graph that is concave up for 0 < h < L and a straight line with a constant positive slope for h > L.
- **D.** A graph that is concave down for 0 < h < L and a straight line with a constant positive slope for h > L.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111297/*