---
title: "A tube contains a volume of water and a volume of mercury as shown in the figure above. Both ends of the tube are open. Points \\( A \\) and \\( B \\) are at the same level and points \\( C \\) and \\( D \\) are at the same level. The distance between points \\( A \\) and \\( B \\) and the surface of the liquids are shown. Which of the following correctly relates the gauge pressures at the points shown? The density of the water is \\( 1{,}000 \\) \\( \\text{kg/m}^3 \\) and the density of the mercury is \\( 13{,}600 \\) \\( \\text{kg/m}^3 \\)."
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/108952/"
date_modified: "2026-08-21T15:34:29+00:00"
---

# A tube contains a volume of water and a volume of mercury as shown in the figure above. Both ends of the tube are open. Points \( A \) and \( B \) are at the same level and points \( C \) and \( D \) are at the same level. The distance between points \( A \) and \( B \) and the surface of the liquids are shown. Which of the following correctly relates the gauge pressures at the points shown? The density of the water is \( 1{,}000 \) \( \text{kg/m}^3 \) and the density of the mercury is \( 13{,}600 \) \( \text{kg/m}^3 \).

A tube contains a volume of water and a volume of mercury as shown in the figure above. Both ends of the tube are open. Points \( A \) and \( B \) are at the same level and points \( C \) and \( D \) are at the same level. The distance between points \( A \) and \( B \) and the surface of the liquids are shown. Which of the following correctly relates the gauge pressures at the points shown? The density of the water is \( 1{,}000 \) \( \text{kg/m}^3 \) and the density of the mercury is \( 13{,}600 \) \( \text{kg/m}^3 \).

Figure 1. U-tube manometer with water and mercury showing points A–D.

![A U-shaped glass tube is drawn in vertical orientation with the open ends at the top of the two vertical limbs. The left limb contains a column of clear fluid labeled "water" extending down to a curved interface with a darker shaded fluid labeled "mercury" that fills the bottom of the U and part of both limbs. A solid horizontal dashed line marks the position of points A (in the left limb) and B (in the right limb); both points lie inside the water region, exactly opposite each other horizontally. A vertical double-headed arrow next to the left limb measures the distance from the water surface to point A and is labeled "0.15 m". In the right limb, a shorter vertical double-headed arrow measures the distance from the water surface to point B and is labeled "0.01 m". A second horizontal dashed line lower in the diagram marks points C (left limb) and D (right limb); both of these points are inside the mercury region and lie exactly opposite each other horizontally. The mercury region is shaded uniformly for distinction. All four points A, B, C, and D are indicated by solid black dots with their letters printed beside them. The tube walls are drawn with thin straight lines, and the curvature at the bottom of the U is smooth and semicircular. No other markings are present.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326478-NkjMUT.jpg)

![A U-shaped glass tube (manometer) is shown in cross-section. The left vertical limb is filled with clear fluid labeled "water." The right vertical limb and the curved bottom section are shaded gray to represent "mercury." The open ends of both limbs are exposed to the atmosphere. A horizontal dashed line connects point A on the left limb to point B on the right limb; both points are located inside the fluid at exactly the same vertical height below their respective fluid surfaces. A double-headed vertical bracket on the left indicates the distance from the water surface to point A is 0.15 m. A similar bracket on the right shows the distance from the mercury surface to point B is 0.01 m. A second horizontal dashed line, lower in the tube, connects point C on the left side (inside the mercury below the water–mercury interface) to point D on the right side (also in the mercury). Points C and D are at the same vertical height. All four points A, B, C, and D are marked by solid black dots, each labeled with its respective letter. The left limb is narrower but drawn to the same scale as the right; the mercury surface in the right limb is slightly higher than the water–mercury interface on the left because of the density difference. The background is blank and no other forces or arrows are drawn.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326466-PHOW74.jpg)

![A U-shaped glass tube (manometer) is shown in cross-section. The left vertical limb is filled with clear fluid labeled "water." The right vertical limb and the curved bottom section are shaded gray to represent "mercury." The open ends of both limbs are exposed to the atmosphere. A horizontal dashed line connects point A on the left limb to point B on the right limb; both points are located inside the fluid at exactly the same vertical height below their respective fluid surfaces. A double-headed vertical bracket on the left indicates the distance from the water surface to point A is 0.15 m. A similar bracket on the right shows the distance from the mercury surface to point B is 0.01 m. A second horizontal dashed line, lower in the tube, connects point C on the left side (inside the mercury below the water–mercury interface) to point D on the right side (also in the mercury). Points C and D are at the same vertical height. All four points A, B, C, and D are marked by solid black dots, each labeled with its respective letter. The left limb is narrower but drawn to the same scale as the right; the mercury surface in the right limb is slightly higher than the water–mercury interface on the left because of the density difference. The background is blank and no other forces or arrows are drawn.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326457-xNpI40.jpg)

![A U-shaped glass tube is drawn with two vertical arms of equal inner radius connected by a smoothly curved bottom section. The open tops of both arms are at the same horizontal level and open to the atmosphere. The liquid in the tube is separated into two layers: an upper clear layer labeled "water" that fills the upper portions of each arm and a lower shaded layer labeled "mercury" that occupies the curved bottom and a small portion of each arm. A dashed horizontal line passes through a black filled circle labeled "A" in the left water column and a black filled circle labeled "B" in the right water column, indicating that points A and B are at the same vertical height. Another dashed horizontal line lower in the tube passes through a black filled circle labeled "C" on the left side of the mercury and a black filled circle labeled "D" on the right side of the mercury, indicating C and D are at the same height. A vertical double-headed arrow beside the left arm marks the distance between point A and the water surface as 0.15 m, with the number "0.15 m" directly beside the arrow. A similar vertical double-headed arrow beside the right arm marks the distance between point B and the local water surface as 0.01 m, labeled "0.01 m". The mercury layer is shaded uniformly, while the water layer is unshaded. All labels A, B, C, and D are printed in small bold font next to their respective points.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326448-LaHT9D.jpg)

![A U-shaped glass tube is drawn with two vertical arms of equal inner radius connected by a smoothly curved bottom section. The open tops of both arms are at the same horizontal level and open to the atmosphere. The liquid in the tube is separated into two layers: an upper clear layer labeled "water" that fills the upper portions of each arm and a lower shaded layer labeled "mercury" that occupies the curved bottom and a small portion of each arm. A dashed horizontal line passes through a black filled circle labeled "A" in the left water column and a black filled circle labeled "B" in the right water column, indicating that points A and B are at the same vertical height. Another dashed horizontal line lower in the tube passes through a black filled circle labeled "C" on the left side of the mercury and a black filled circle labeled "D" on the right side of the mercury, indicating C and D are at the same height. A vertical double-headed arrow beside the left arm marks the distance between point A and the water surface as 0.15 m, with the number "0.15 m" directly beside the arrow. A similar vertical double-headed arrow beside the right arm marks the distance between point B and the local water surface as 0.01 m, labeled "0.01 m". The mercury layer is shaded uniformly, while the water layer is unshaded. All labels A, B, C, and D are printed in small bold font next to their respective points.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326432-fjdtmY.jpg)

![A U-shaped glass tube is drawn in cross-section. The open ends of the tube are vertical and extend upward, exposed to the atmosphere. The left vertical arm is filled with water labeled "water." A horizontal dashed line marks the water surface at the very top of this arm. A point labeled "A" (solid black dot) is marked on the water column ( 0.15 ; text{m} ) below the surface; a double-headed vertical arrow beside the column shows the distance and the number ( 0.15 ; text{m} ). The right vertical arm also contains water, but its surface is lower than the left side. A dashed line marks this surface, and a point labeled "B" (solid black dot) is located ( 0.01 ; text{m} ) below that right-side surface; a vertical bracket with the number ( 0.01 ; text{m} ) is shown next to that arm. The bottom curved portion of the U-tube is shaded and labeled "mercury." Two points, "C" on the left side of the mercury and "D" on the right side, are indicated at exactly the same horizontal level in the mercury; a dashed horizontal line passes through both C and D aligning them. All four points A, B, C, and D are shown as filled circles. The relative heights clearly show A and B aligned horizontally, and C and D aligned horizontally but lower than A and B. No other dimensions are given. Arrows indicating atmospheric pressure act downward on both liquid surfaces.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326421-iLjXNI.jpg)

![A U-shaped glass tube is drawn in cross-section. The open ends of the tube are vertical and extend upward, exposed to the atmosphere. The left vertical arm is filled with water labeled "water." A horizontal dashed line marks the water surface at the very top of this arm. A point labeled "A" (solid black dot) is marked on the water column ( 0.15 ; text{m} ) below the surface; a double-headed vertical arrow beside the column shows the distance and the number ( 0.15 ; text{m} ). The right vertical arm also contains water, but its surface is lower than the left side. A dashed line marks this surface, and a point labeled "B" (solid black dot) is located ( 0.01 ; text{m} ) below that right-side surface; a vertical bracket with the number ( 0.01 ; text{m} ) is shown next to that arm. The bottom curved portion of the U-tube is shaded and labeled "mercury." Two points, "C" on the left side of the mercury and "D" on the right side, are indicated at exactly the same horizontal level in the mercury; a dashed horizontal line passes through both C and D aligning them. All four points A, B, C, and D are shown as filled circles. The relative heights clearly show A and B aligned horizontally, and C and D aligned horizontally but lower than A and B. No other dimensions are given. Arrows indicating atmospheric pressure act downward on both liquid surfaces.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326411-Lk6UzI.jpg)

![A U-shaped tube is drawn in cross-section. Both vertical arms are open to the atmosphere at the top. The left arm is filled with clear water nearly to the brim, its free surface indicated by a horizontal dashed line. Measured downward from this water surface to a point labeled A, a vertical double-headed arrow shows a distance of exactly 0.15 m. Point A is marked by a solid black dot on the water column centerline. Directly below A, at the bottom of the curved U-section, another solid dot is labeled C; the water–mercury interface is a smooth curved line that meets the left wall at C. The lower curved portion and all of the right arm up to the mercury–air interface are shaded to indicate mercury. In the right arm, a solid dot labeled D lies on the mercury surface level with point C. Moving upward from D a short vertical double-headed arrow of 0.01 m reaches point B, another solid dot on the water side (the right arm contains only mercury above C so B is in the water region on a small downward extension sketched on the right). Dashed horizontal lines through A and B emphasize they are at the same vertical height; another dashed horizontal through C and D shows those two points share the same level. All four dashed lines terminate at the tube walls. The left column is labeled "water"; the shaded region is labeled "mercury."](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326398-bLH4cp.jpg)

![A U-shaped tube is drawn in cross-section. Both vertical arms are open to the atmosphere at the top. The left arm is filled with clear water nearly to the brim, its free surface indicated by a horizontal dashed line. Measured downward from this water surface to a point labeled A, a vertical double-headed arrow shows a distance of exactly 0.15 m. Point A is marked by a solid black dot on the water column centerline. Directly below A, at the bottom of the curved U-section, another solid dot is labeled C; the water–mercury interface is a smooth curved line that meets the left wall at C. The lower curved portion and all of the right arm up to the mercury–air interface are shaded to indicate mercury. In the right arm, a solid dot labeled D lies on the mercury surface level with point C. Moving upward from D a short vertical double-headed arrow of 0.01 m reaches point B, another solid dot on the water side (the right arm contains only mercury above C so B is in the water region on a small downward extension sketched on the right). Dashed horizontal lines through A and B emphasize they are at the same vertical height; another dashed horizontal through C and D shows those two points share the same level. All four dashed lines terminate at the tube walls. The left column is labeled "water"; the shaded region is labeled "mercury."](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1787326387-98rQ25.jpg)

![Figure 1. U-tube manometer with water and mercury showing points A–D.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108952-1773217622.png)

- **A.** \[ P_A > P_B \text{ and } P_C > P_D \]
- **B.** \[ P_A > P_B \text{ and } P_C = P_D \]
- **C.** \[ P_A = P_B \text{ and } P_C = P_D \]
- **D.** \[ P_A = P_B \text{ and } P_C > P_D \]

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/108952/*