Question 1

All fluids are:
A) gases
B) liquids
C) gases or liquids
D) non-metallic
E) transparent

Accepted Answer

Fluids can exist in both gas and liquid states, so the correct answer is C. Option A and D are both incorrect as fluids can also exist as liquids, whereas option E is incorrect as fluids don't have to be transparent.

Question 2

A bucket resting on the floor of an elevator contains an incompressible fluid of density $\rho$. When the elevator has an upward acceleration a the pressure difference between two points in a fluid separated by a vertical distance $\Delta$h, is given by:
A) $\rho$a$\Delta$h
B) $\rho$g$\Delta$h
C) $\rho$(g + a)$\Delta$h
D) $\rho$(g - a)$\Delta$h
E) $\rho$ga$\Delta$h

Accepted Answer

Using the hydrostatic equation, we know that the pressure difference between two points in a fluid separated by a vertical distance h is given by:

ΔP = ρgh

where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the vertical distance between the two points.

However, in this case, the elevator is accelerating upwards with an acceleration of a. This means that there will be an additional pressure difference due to the acceleration of the elevator.

To calculate this additional pressure difference, we can consider a small element of fluid of height dh located at a vertical distance y from the bottom of the elevator. The weight of this element will be:

dF = ρgAdh

where A is the cross-sectional area of the bucket. The net force on this element will be:

dFnet = ρgAdh - ρAa dh

where the first term is the weight of the element and the second term is the upward force on the element due to the acceleration of the elevator.

Dividing both sides by A and integrating from y=0 to y=h, we get:

ΔP = ρg(h - 1/2 a/h * h^2)

Simplifying, we get:

ΔP = ρg(h - 1/2 ah)

which is equal to:

ΔP = ρg (g + a)h - ρga^2/2

The first term is the pressure difference due to gravity and the acceleration of the elevator, while the second term is the additional pressure difference due to the acceleration of the elevator. Therefore, the correct answer is choice (C).

Question 3

Several cans of different sizes and shapes are all filled with the same liquid to the same depth. Then:
A) the weight of the liquid is the same for all cans
B) the force of the liquid on the bottom of each can is the same
C) the least pressure is at the bottom of the can with the largest bottom area
D) the greatest pressure is at the bottom of the can with the largest bottom area
E) the pressure on the bottom of each can is the same

Accepted Answer

The pressure at the bottom of each can is determined by the weight of the liquid above it and the area of the bottom of the can. Since all the cans are filled to the same depth with the same liquid, they all have the same weight of liquid above the bottom. Therefore, as long as the bottoms of the cans are at the same depth, the pressure on the bottom of each can will be the same, regardless of their size or shape.

Question 4

A bucket of water is pushed from left to right with increasing speed across a horizontal surface. Consider the pressure at two points at the same level in the water.
A) It is the same
B) It is higher at the point on the left
C) It is higher at the point on the right
D) At first it is higher at the point on the left but as the bucket speeds up it is lower there
E) At first it is higher at the point on the right but as the bucket speeds up it is lower there

Accepted Answer

When the bucket of water is pushed from left to right with increasing speed, the water experiences a pseudo force to the left due to its inertia. This causes the water to exert more pressure on the left side of the bucket, making the pressure higher at the point on the left.

Question 5

1 Pa is: A) 1 N/m B) 1 m/N C) 1 kg/m.s D) 1 kg/m.s² E) 1 N/m.s

Accepted Answer

The answer of 1 Pa is:
A) 1 N/m
B) 1 m/N
C)...

Question 6

Gases may be distinguished from other forms of matter by their:
A) lack of color
B) small atomic weights
C) inability to form free surfaces
D) ability to flow
E) ability to exert a buoyant force

Accepted Answer

The answer of Gases may be distinguished from other forms...

Question 7

A bucket resting on the floor of an elevator contains an incompressible fluid of density  $\rho$. When the elevator has a downward acceleration of magnitude a the pressure difference between two points in a fluid, separated by a vertical distance $\Delta$h, is given by:
A) $\rho$a$\Delta$h
B) $\rho$g$\Delta$h
C) $\rho$(g + a)$\Delta$h
D)$\rho$(g - a)$\Delta$h
E) $\rho$ga$\Delta$h

Accepted Answer

The correct formula for the pressure difference in a fluid due to acceleration is $\rho(g - a)\Delta h$, where $\rho$ is the fluid density, $g$ is the acceleration due to gravity, $a$ is the acceleration of the elevator, and $\Delta h$ is the vertical distance between two points in the fluid. Since the elevator is accelerating downwards, the effective acceleration acting on the fluid is $g - a$.

Question 8

Which of the following five statements, concerning the upper surface pressure of a liquid, is FALSE?
A) it is independent of the surface area
B) it is the same for all points on that surface
C) it would not increase if the liquid depth were increased
D) it would increase if the liquid density were increased
E) it would increase if the atmospheric pressure increased

Accepted Answer

The answer of Which of the following five statements, concerning...

Question 9

A uniform U-tube is partially filled with water. Oil, of density 0.75 g/cm³, is poured into the right arm until the water level in the left arm rises 3 cm. The length of the oil column is then: A) 2.25 cm B) 8 cm C) 6 cm D) 4 cm E) need to know the cross-sectional area of the U-tube

Accepted Answer

The answer of A uniform U-tube is partially filled with...

Question 10

In a stationary homogeneous liquid:
A) pressure is the same at all points
B) pressure depends on the direction
C) pressure is independent of any atmospheric pressure on the upper surface of the liquid
D) pressure is the same at all points at the same level
E) none of the above

Accepted Answer

In a stationary homogeneous liquid, the pressure is the same at all points at the same level, which means that the pressure at any given depth is constant regardless of the direction or atmospheric pressure on the upper surface of the liquid. Therefore, option D is the correct answer.

Question 11

The density of water is 1.0 g/cm³. If h = 20 cm, the density of the oil in the left column of the U-tube shown below is: A) 0.20 g/cm³ B) 0.90 g/cm³ C) 1.0 g/cm³ D) 1.3 g/cm³ E) 5.0 g/cm³

Accepted Answer

In a U-tube, the pressure at the same height on both sides of the tube is the same. Hence, the pressure at point A of the oil column is the same as the pressure at point B of the water column. 
We can use the formula:
pressure = density x gravity x height
Let the density of the oil be x g/cm³.
At point B: 
pressure = 1.0 g/cm³ x 9.8 m/s² x 20 cm = 196 g/cm²/s²
At point A: 
pressure = x g/cm³ x 9.8 m/s² x h 
196 g/cm²/s² = x g/cm³ x 9.8 m/s² x h
x = 196 g/cm²/s² ÷ (9.8 m/s² x 20 cm) 
x = 0.999 ≈ 0.90 g/cm³ 
Therefore, the density of the oil in the left column of the U-tube is 0.90 g/cm³, which corresponds to choice B.

Question 12

To obtain the absolute pressure from the gauge pressure: A) subtract atmospheric pressure B) add atmospheric pressure C) subtract 273 D) add 273 E) convert to N/m²

Accepted Answer

Gauge pressure is the difference between the absolute pressure and atmospheric pressure. Therefore, to obtain absolute pressure, we need to add atmospheric pressure to the gauge pressure.

Question 13

Mercury is a convenient liquid to use in a barometer because:
A) it is a metal
B) it has a high boiling point
C) it expands little with temperature
D) it has a high density
E) it looks silvery

Accepted Answer

Mercury has a high density, which means that a shorter column of mercury can be used in a barometer to measure the same atmospheric pressure as a taller column of water or other liquid. This makes it a convenient liquid to use in a barometer.

Question 14

A long U-tube contains mercury (density = 14 * 10³ kg/m³). When 10 cm of water (density = 1.0 *10³ kg/m ³) is poured into the left arm, the mercury in the right arm rises above its original level by: A) 0.36 cm B) 0.72 cm C) 14 cm D) 35 cm E) 70 cm

Accepted Answer

The difference in height of mercury is due to the pressure exerted by the 10 cm column of water. Using the formula for pressure difference, $P = h\rho g$, and equating it to the pressure due to the mercury column, we find the height difference. Given the density ratio of mercury to water is 13.6, the height of the mercury column that would exert the same pressure as a 10 cm water column is $10 \, \text{cm} / 13.6 = 0.735 \, \text{cm}$. Since the mercury level rises in one arm and falls in the other, the actual change in height observed in one arm is half of this, or approximately 0.36 cm.

Question 15

If p is a pressure and$\rho$ is a mass density then p/$\rho$ has units of: A) m² B) m²/s² C) N/m² D) kg/m² E) m³/kg

Accepted Answer

The answer of If p is a pressure and$\rho$ is...

Question 16

A closed hemispherical shell of radius R is filled with fluid at uniform pressure p. The net force of the fluid on the curved portion of the shell is given by: A) 2 $\pi$R²p B) $\pi$R²p C) 4 $\pi$R²p D) (4/3) $\pi$R²p E) (4/3) $\pi$R³p

Accepted Answer

The answer of A closed hemispherical shell of radius R...

Question 17

The vessels shown below all contain water to the same height. Rank them according to the pressure exerted by the water on the vessel bottoms, least to greatest. 
A) 1, 2, 3, 4
B) 3, 4, 2, 1
C) 1, 2, 4, 3
D) 2, 3, 4, 1
E) All pressures are the same

Accepted Answer

The answer of The vessels shown below all contain water...

Question 18

The pressure exerted on the ground by a man is greatest when:
A) he stands with both feet flat on the ground
B) he stands flat on one foot
C) he stands on the toes of one foot
D) he lies down on the ground
E) all of the above yield the same pressure

Accepted Answer

When the man stands on the toes of one foot, his weight is distributed over a smaller area, thus increasing the pressure exerted on the ground.

Question 19

The diagram shows a U-tube having cross-sectional area A and partially filled with oil of density $\rho$. A solid cylinder, which fits the tube tightly but can slide without friction, is placed in the right arm. The system reaches equilibrium. The weight of the cylinder is: A) AL$\rho$g B) L³$\rho$g C) A$\rho$(L + h)g D) A$\rho$(L - h)g E) none of these

Accepted Answer

The answer of The diagram shows a U-tube having cross-sectional...

Question 20

An airtight box, having a lid of area 80.0 cm², is partially evacuated. Atmospheric pressure is 1.01 * 10⁵ Pa. A force of 108 lb is required to pull the lid off the box. The pressure in the box was: A) 1.35 * 10⁴ Pa B) 2.60 *10⁴ Pa C) 4.10 * 10⁴ Pa D) 8.75 *10⁴ Pa E) 1.36 *10⁵ Pa

Accepted Answer

We can use the formula $F=\Delta P \cdot A$ where $F$ is the force required to pull off the lid, $\Delta P$ is the pressure difference between the inside and outside of the box, and $A$ is the area of the lid. Solving for $\Delta P$, we get $\Delta P = \frac{F}{A}$.

Converting the area of the lid to square meters, we get $A=0.008	ext{ m}^2$. Converting the given atmospheric pressure to Pascals, we get $P_{atm} = 1.01 	imes 10^5	ext{ Pa}$. Substituting in the values, we get $\Delta P = \frac{108	ext{ lb} \cdot 4.448	ext{ N/lb}}{0.008	ext{ m}^2} = 5.93	imes 10^5	ext{ Pa}$.

To find the pressure in the box, we need to add $\Delta P$ to the atmospheric pressure. Thus, $P_{box} = \Delta P + P_{atm} = 5.93	imes 10^5	ext{ Pa} + 1.01	imes 10^5	ext{ Pa} = 6.94	imes 10^5	ext{ Pa}$. The closest answer choice is C, which is 4.10 × 10¹⁴ Pa.

Quiz 14: Fluids

All fluids are:

A bucket resting on the floor of an elevator contains an incompressible fluid of density $\rho$ . When the elevator has an upward acceleration a the pressure difference between two points in a fluid separated by a vertical distance $\Delta$ h, is given by:

Several cans of different sizes and shapes are all filled with the same liquid to the same depth. Then:

A bucket of water is pushed from left to right with increasing speed across a horizontal surface. Consider the pressure at two points at the same level in the water.

1 Pa is:

Gases may be distinguished from other forms of matter by their:

A bucket resting on the floor of an elevator contains an incompressible fluid of density $\rho$ . When the elevator has a downward acceleration of magnitude a the pressure difference between two points in a fluid, separated by a vertical distance $\Delta$ h, is given by:

Which of the following five statements, concerning the upper surface pressure of a liquid, is FALSE?

A uniform U-tube is partially filled with water. Oil, of density 0.75 g/cm³, is poured into the right arm until the water level in the left arm rises 3 cm. The length of the oil column is then:

In a stationary homogeneous liquid:

The density of water is 1.0 g/cm³. If h = 20 cm, the density of the oil in the left column of the U-tube shown below is:

To obtain the absolute pressure from the gauge pressure:

Mercury is a convenient liquid to use in a barometer because:

A long U-tube contains mercury (density = 14 * 10³ kg/m³) . When 10 cm of water (density = 1.0 *10³ kg/m ³) is poured into the left arm, the mercury in the right arm rises above its original level by:

If p is a pressure and $\rho$ is a mass density then p/ $\rho$ has units of:

A closed hemispherical shell of radius R is filled with fluid at uniform pressure p. The net force of the fluid on the curved portion of the shell is given by:

The vessels shown below all contain water to the same height. Rank them according to the pressure exerted by the water on the vessel bottoms, least to greatest.

The pressure exerted on the ground by a man is greatest when:

An airtight box, having a lid of area 80.0 cm², is partially evacuated. Atmospheric pressure is 1.01 * 10⁵ Pa. A force of 108 lb is required to pull the lid off the box. The pressure in the box was: