---
title: "A U-tube open to the atmosphere at both ends is partially filled with water of density \\( \\rho_w \\). Oil of density \\( \\rho_o \\) (where \\( \\rho_o < \\rho_w \\)) is poured into the left arm until it forms a column of height \\( L \\). The interface between the oil and water in the left arm is found to be a vertical distance \\( d \\) below the water surface in the right arm. Which of the following expressions correctly represents the density of the oil?"
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url: "https://nerd-notes.com/ubq/107125/"
date_modified: "2026-08-18T02:38:25+00:00"
---

# A U-tube open to the atmosphere at both ends is partially filled with water of density \( \rho_w \). Oil of density \( \rho_o \) (where \( \rho_o < \rho_w \)) is poured into the left arm until it forms a column of height \( L \). The interface between the oil and water in the left arm is found to be a vertical distance \( d \) below the water surface in the right arm. Which of the following expressions correctly represents the density of the oil?

A U-tube open to the atmosphere at both ends is partially filled with water of density \( \rho_w \). Oil of density \( \rho_o \) (where \( \rho_o < \rho_w \)) is poured into the left arm until it forms a column of height \( L \). The interface between the oil and water in the left arm is found to be a vertical distance \( d \) below the water surface in the right arm. Which of the following expressions correctly represents the density of the oil?

- **A.** \[ \rho_o = \rho_w \left( \frac{d}{L + d} \right) \]
- **B.** \[ \rho_o = \rho_w \left( \frac{L – d}{L} \right) \]
- **C.** \[ \rho_o = \rho_w \left( \frac{L}{d} \right) \]
- **D.** \[ \rho_o = \rho_w \left( \frac{d}{L} \right) \]

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/107125/*