Question 1

A wooden log floats in a river (density 1000 kg/m³), with one-quarter above the water, carried toward the sea (density 1025 kg/m³) by the river current. What will be the change in the percentage of the volume of log above water when it comes to the sea? A)The log will go up 2%. B)The log will go down 2%. C)The log will go up 27%. D)The log will go down 27%.

Accepted Answer

The log will go up 2% because the sea water is denser than river water, causing the log to float slightly higher. The increase in density from 1000 kg/m^3 to 1025 kg/m^3 results in a decrease in the submerged volume of the log, making a small percentage of the log's volume to be above water compared to when it was in the river.

Question 2

What is the transmural ratio between a soap bubble of diameter D and another one with double the diameter, 2D?
A)The pressure in a bubble with diameter D is 2 times larger than in the 2D bubble.
B)The pressure in a bubble with diameter D is 2 times smaller than in the 2D bubble.
C)The pressure in a bubble with diameter D is 2ð times larger than in the 2D bubble.
D)The pressure in a bubble with diameter D is 2ð times smaller than in the 2D bubble.

Accepted Answer

The pressure difference across the surface of a soap bubble is given by the formula ΔP = 4T/r, where ΔP is the pressure difference, T is the surface tension of the liquid, and r is the radius of the bubble. When the diameter of the bubble is doubled (from D to 2D), the radius is also doubled, leading to a halving of the pressure difference. Therefore, the pressure in the smaller bubble (diameter D) is 2 times larger than in the larger bubble (diameter 2D).

Question 3

If, in an unknown liquid, we measure pressure of 1.2 atm at 0.15 m depth, at what depth will the pressure measure 2.4 atm?
A)0.08 m
B)0.30 m
C)1.05 m
D)2.10 m

Accepted Answer

C

Question 4

A rock is sinking in the water. Which one of these statements correctly describes the buoyant force?
A)It is zero.
B)It is equal to the weight of the wood.
C)It is equal to all the other forces acting on the wood, but opposite in direction.
D)It is equal in magnitude but opposite in direction of the weight of the wood.

Accepted Answer

The buoyant force is equal to the weight of the fluid displaced by the rock, and when an object is sinking, the buoyant force is less than the weight of the object but is still present and acts in the opposite direction to the weight.

Question 5

If P is a pressure, ñ density, g gravitational acceleration, and h height (or depth) of a fluid, where is the relationship P = ñgh applicable?
A)only in liquids
B)only in gases
C)only in gases of uniform density (ideal gases)
D)in any type of fluid with uniform density (ideal fluid)

Accepted Answer

The equation P = ñgh is applicable in any type of fluid (liquids or gases) as long as the fluid has a uniform density, which is often referred to as an ideal fluid condition. This equation is derived from the basic principles of fluid statics and is used to calculate the pressure at a given depth (or height) in a fluid.

Question 6

An iceberg has a density 917 kg/m³, and seawater has a density 1025 kg/m³. What fraction of the iceberg is under the surface of the water? A)9.3% B)10.5% C)89.5% D)90.7%

Accepted Answer

The answer of An iceberg has a density 917 kg/m³,...

Question 7

An air bubble is 50 cm below the surface of a lake. In that case, we assume that the bubble has only one surface to generate surface tension. The gauge pressure inside the bubble is 6.0 × 10³ Pa. What is radius of the bubble? (The density of the water is ñ_H2O = 1000 kg/m³, and the surface tension is ó = 0.073 N/m.) A)2.6 × 10^-4 m B)1.3 × 10^-4 m C)6.0 × 10^-7 m D)3.0 × 10^-7 m

Accepted Answer

The gauge pressure inside the bubble can be expressed as the sum of the hydrostatic pressure due to the depth of the water and the pressure due to surface tension. The hydrostatic pressure is given by $P_h = \rho gh$, where $\rho = 1000 \, \text{kg/m}^3$ is the density of water, $g = 9.8 \, \text{m/s}^2$ is the acceleration due to gravity, and $h = 0.5 \, \text{m}$ is the depth of the bubble. The pressure due to surface tension is given by $P_s = \frac{2\sigma}{r}$, where $\sigma = 0.073 \, \text{N/m}$ is the surface tension and $r$ is the radius of the bubble. The total gauge pressure is the sum of these two pressures: $P = P_h + P_s$.Given $P = 6.0 \times 10^3 \, \text{Pa}$, we can solve for $r$ by first calculating $P_h$ and then rearranging the equation for $P_s$ to solve for $r$.Calculating $P_h = \rho gh = 1000 \times 9.8 \times 0.5 = 4900 \, \text{Pa}$.Since $P = P_h + P_s$, we have $6000 = 4900 + \frac{2\sigma}{r}$.Rearranging for $r$, we get $r = \frac{2\sigma}{P - P_h}$.Substituting the given values, $r = \frac{2 \times 0.073}{6000 - 4900} = \frac{0.146}{1100} = 1.3 \times 10^{-4} \, \text{m}$.

Question 8

How far below the surface of water do you need to dive to double the atmospheric pressure? (Note: Atmospheric pressure is P_atm = 1.01 × 10⁵ Pa, and density of water is ñ = 1000 kg/m³.) A)1 m B)2 m C)10 m D)20 m

Accepted Answer

To double the atmospheric pressure, the pressure from the water column must equal 1 atm. Using the formula P = ρgh, where ρ = 1000 kg/m³, g = 9.81 m/s², and P = 1.01 × 10⁵ Pa, solving for h gives approximately 10 m.

Question 9

A metal cube fully submerged in water shows an apparent weight of 1.9 N. When completely submerged in acetone, its apparent weight is 2.2 N. What is the length of the side of the cube? (Note: The density of water is ñ_water = 1000 kg/m³ and of acetone ñ_acetone = 784 kg/m³.) A)5.0 × 10^-2 m B)2.5 × 10^-3 m C)1.4 × 10^-4 m D)We need to know the mass of the cube to calculate the length.

Accepted Answer

The apparent weight of an object submerged in a fluid is given by the weight of the object in air minus the buoyant force acting on it. The buoyant force is equal to the weight of the fluid displaced by the object, which depends on the volume of the object and the density of the fluid. Since the volume of the cube remains constant, the difference in apparent weights in water and acetone is due to the difference in the buoyant forces, which in turn depends on the densities of the fluids.Given:- Apparent weight in water = 1.9 N- Apparent weight in acetone = 2.2 N- Density of water = 1000 kg/m³- Density of acetone = 784 kg/m³The actual weight of the cube (W) can be found by adding the buoyant force in water to its apparent weight in water, which is the same as adding the buoyant force in acetone to its apparent weight in acetone. The buoyant force is the product of the volume of the cube, the density of the fluid, and the acceleration due to gravity (g = 9.8 m/s²). Since we are not given the mass of the cube directly, we can use the relationship between the buoyant forces and the apparent weights to find the volume of the cube, and from the volume, we can calculate the length of the side of the cube.Let's denote:- V as the volume of the cube,- ρ_water as the density of water,- ρ_acetone as the density of acetone,- g as the acceleration due to gravity.The buoyant force in water is V * ρ_water * g, and in acetone, it's V * ρ_acetone * g. The difference in apparent weights is due to the difference in buoyant forces, so we can set up the equation based on the difference in buoyant forces and solve for V. Once we have V, we can find the length of a side of the cube (L) since V = L³.By solving the equations with the given densities and the difference in apparent weights, we find that the volume of the cube corresponds to a side length that matches choice A, 5.0 × 10^-2 m, without needing the mass of the cube directly. This calculation involves algebraic manipulation and substitution of the given values into the formula for buoyant force and subsequently into the formula for the volume of a cube.

Question 10

What unit is used to measure surface tension? A)N m B)Pa C)kg/s² D)kg m/s²

Accepted Answer

The answer of What unit is used to measure surface...

Question 11

A bucket of water has some ice floating in it. When water freezes into ice, the ice becomes less dense than water, and about 9% of ice volume is above the water. When the ice melts, what happens to the level of water in the bucket?
A)The level will go up 9%.
B)The level will go down 9%.
C)The level will go down more than 9%.
D)The level will remain the same.

Accepted Answer

When ice melts in water, it converts into water having the same volume as the part of the ice that was submerged. Since ice floats due to being less dense, with about 9% of its volume above water, this portion exactly compensates for the volume it displaces underwater. Therefore, the water level remains unchanged.

Question 12

Figure 11.1 
-Dolphins are sleeping at the bottom of a cove, floating low above the ocean floor. Which diagram in Fig. 11.1 shows the correct forces acting on the dolphins?
A)diagram (a)
B)diagram (b)
C)diagram (c)
D)diagram (d)

Accepted Answer

The dolphins are floating low above the ocean floor, so the buoyant force is greater than the weight of the dolphins. The dolphins are not moving, so the net force on the dolphins is zero. The only forces acting on the dolphins are the buoyant force and the weight of the dolphins.

Question 13

A 0.25 kg balloon is filled with helium. If the balloon is a sphere with a radius of 4 m, what is the maximum number of standard men it can lift? (Note: The density of air is ñ_air = 1.20 kg/m³ and of helium ñ_helium = 0.179 kg/m³; standard man has a mass of 70 kg.) A)3 standard men B)4 standard men C)6 standard men D)38 standard men

Accepted Answer

The answer of A 0.25 kg balloon is filled with...

Question 14

In a glass of water, an olive sits atop a cube of ice. When the olive falls and sinks in the water, what happens to the level of water in the glass?
A)The level will go up.
B)The level will go down.
C)The level will remain the same.
D)We need to know the mass of the olive to answer.

Accepted Answer

The answer of In a glass of water, an olive...

Question 15

What would the perimeter of each foot have to be to enable a standard man (70 kg) to stand on the water on both feet, held up by surface tension? (Note: Surface tension for water ó = 0.073 N/m.) A)9.3 × 10³ m B)4.7 × 10³ m C)9.6 × 10² m D)4.8 × 10² m

Accepted Answer

The force due to surface tension is given by F = 2 * perimeter * surface tension. To support the man's weight (mg), set F = mg. Solving for the perimeter gives perimeter = mg / (2 * surface tension). Substituting the given values, perimeter = (70 * 9.8) / (2 * 0.073) = 4.7 × 10^3 m.

Question 16

A piece of wood is floating on the water. Which one of these statements correctly describes buoyant force?
A)It is zero.
B)It is equal to the weight of the wood.
C)It is equal to all the other forces acting on the wood, but is opposite in direction.
D)It is equal in magnitude but opposite in direction to the weight of the wood.

Accepted Answer

The answer of A piece of wood is floating on...

Question 17

Which of these statements best describes the reason that fish can float in water?
A)The density of fish is higher than the density of water.
B)The weight of fish is higher than the weight of the same volume of water.
C)The density of fish is equal to the density of water.
D)The density of fish is lower than the density of water.

Accepted Answer

Fish can float in water because their density is approximately equal to the density of water, allowing them to achieve neutral buoyancy.

Question 18

A body is immersed in a fluid. Which of these statements correctly describes buoyant force?
A)It is equal to the weight of the object.
B)It is equal to the weight of the fluid displaced by the object.
C)It is equal to the pressure of water below the object.
D)It is equal to the mass of the fluid displaced by the object.

Accepted Answer

The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object, as stated by Archimedes' principle. This principle explains why objects float or sink in fluids based on the relationship between the weight of the object and the weight of the displaced fluid.

Question 19

What is the diameter of a capillary tube holding methanol, if the methanol rises to the same height as water in a 1 mm diameter tube? (Take 0° for contact angles, surface tension for water ó_H2O= 0.073 N/m, and of methanol ó_methanol = 0.023 N/m. Density of water is ñ_H2O = 1000 kg/m³, and of methanol ñ_methanol = 792 kg/m³.) A)0.2 mm B)0.4 mm C)2.0 mm D)4.0 mm

Accepted Answer

The capillary rise is inversely proportional to the diameter and directly proportional to the surface tension. Since methanol has a lower surface tension than water, the diameter of the tube for methanol must be smaller to achieve the same capillary rise. Calculating using the formula for capillary rise, the diameter for methanol is approximately 0.4 mm.

Question 20

You have a fluid in a beaker, but you need to increase the density of the contents of the beaker. How can you obtain higher density?
A)increase the fluid volume per unit mass
B)double the mass and volume of a fluid
C)halve the volume and mass of a fluid
D)increase the mass per unit volume

Accepted Answer

Density is defined as mass per unit volume. Increasing the mass while keeping the volume constant, or reducing the volume while keeping the mass constant, will increase the density. Option D directly states increasing mass per unit volume, which is the definition of increasing density.

Quiz 11: Static Fluids

A wooden log floats in a river (density 1000 kg/m³) , with one-quarter above the water, carried toward the sea (density 1025 kg/m³) by the river current. What will be the change in the percentage of the volume of log above water when it comes to the sea?

What is the transmural ratio between a soap bubble of diameter D and another one with double the diameter, 2D?

If, in an unknown liquid, we measure pressure of 1.2 atm at 0.15 m depth, at what depth will the pressure measure 2.4 atm?

A rock is sinking in the water. Which one of these statements correctly describes the buoyant force?

If P is a pressure, ñ density, g gravitational acceleration, and h height (or depth) of a fluid, where is the relationship P = ñgh applicable?

An iceberg has a density 917 kg/m³, and seawater has a density 1025 kg/m³. What fraction of the iceberg is under the surface of the water?

How far below the surface of water do you need to dive to double the atmospheric pressure? (Note: Atmospheric pressure is P_atm = 1.01 × 10⁵ Pa, and density of water is ñ = 1000 kg/m³.)

A metal cube fully submerged in water shows an apparent weight of 1.9 N. When completely submerged in acetone, its apparent weight is 2.2 N. What is the length of the side of the cube? (Note: The density of water is ñ_water = 1000 kg/m³ and of acetone ñ_acetone = 784 kg/m³.)

What unit is used to measure surface tension?

A bucket of water has some ice floating in it. When water freezes into ice, the ice becomes less dense than water, and about 9% of ice volume is above the water. When the ice melts, what happens to the level of water in the bucket?

Figure 11.1 -Dolphins are sleeping at the bottom of a cove, floating low above the ocean floor. Which diagram in Fig. 11.1 shows the correct forces acting on the dolphins?

A 0.25 kg balloon is filled with helium. If the balloon is a sphere with a radius of 4 m, what is the maximum number of standard men it can lift? (Note: The density of air is ñ_air = 1.20 kg/m³ and of helium ñ_helium = 0.179 kg/m³; standard man has a mass of 70 kg.)

In a glass of water, an olive sits atop a cube of ice. When the olive falls and sinks in the water, what happens to the level of water in the glass?

What would the perimeter of each foot have to be to enable a standard man (70 kg) to stand on the water on both feet, held up by surface tension? (Note: Surface tension for water ó = 0.073 N/m.)

A piece of wood is floating on the water. Which one of these statements correctly describes buoyant force?

Which of these statements best describes the reason that fish can float in water?

A body is immersed in a fluid. Which of these statements correctly describes buoyant force?

You have a fluid in a beaker, but you need to increase the density of the contents of the beaker. How can you obtain higher density?