Unit 5 Concepts Quiz

1. Density is...

Proportional to both mass and volume

Proportional to mass and inversely proportional to volume.

Inversely proportional to mass and proportional to volume

Inversely proportional to both mass and volume

The density of a substance is defined as its mass per unit volume. This means that as the mass of an object increases, its density also increases. On the other hand, as the volume of an object increases, its density decreases. Therefore, density is proportional to mass and inversely proportional to volume.

Explanation

The density of a substance is defined as its mass per unit volume. This means that as the mass of an object increases, its density also increases. On the other hand, as the volume of an object increases, its density decreases. Therefore, density is proportional to mass and inversely proportional to volume.

2. Substance A has a density of 3.0 g/cm3 and substance B has a density of 4.0 g/cm3. In order to obtain equal masses of these two substances, the ratio of the volume of A to the volume of B will be equal to

1:3

4:3

3:4

1:4

The ratio of the volume of substance A to the volume of substance B will be 4:3. This is because density is defined as mass divided by volume, and since we want to obtain equal masses of the two substances, we need to have the same ratio of volumes. Since substance A has a lower density than substance B, it will have a larger volume for the same mass. Therefore, the ratio of the volume of substance A to the volume of substance B will be 4:3.

Explanation

The ratio of the volume of substance A to the volume of substance B will be 4:3. This is because density is defined as mass divided by volume, and since we want to obtain equal masses of the two substances, we need to have the same ratio of volumes. Since substance A has a lower density than substance B, it will have a larger volume for the same mass. Therefore, the ratio of the volume of substance A to the volume of substance B will be 4:3.

3. Consider three drinking glasses. All three have the same area base, and all three are filled to the same depth with water. Glass A is cylindrical. Glass B is wider at the top than at the bottom, and so holds more water than A. Glass C is narrower at the top than at the bottom, and so holds less water than A. Which glass has the greatest liquid pressure at the bottom?

Glass A

Glass B

Glass C

All Equal

The liquid pressure at the bottom of each glass is determined by the weight of the water above it. Since all three glasses are filled to the same depth with water, they all have the same amount of water above the bottom. Therefore, the liquid pressure at the bottom of each glass is equal.

Explanation

The liquid pressure at the bottom of each glass is determined by the weight of the water above it. Since all three glasses are filled to the same depth with water, they all have the same amount of water above the bottom. Therefore, the liquid pressure at the bottom of each glass is equal.

4. A person’s blood pressure is generally measured on the arm, at approximately the same level as the heart. How would the results differ if the measurement were made on the person’s leg instead?

The blood pressure would be lower

The blood pressure would be higher

The blood pressure would stay the same

Assuming that the flow speed of the blood does not change, then Bernoulli’s equation indicates that at a lower height, the pressure will be greater.

Explanation

Assuming that the flow speed of the blood does not change, then Bernoulli’s equation indicates that at a lower height, the pressure will be greater.

5. 50 cm3 of wood is floating on water, and 50 cm3 of iron is totally submerged. Which has the greater buoyant force on it?

The wood

The iron

Both have the same buoyant force

Cannot be determined without knowing their densities

Buoyant force is calculated using the volume of displaced fluid, the submerged iron will displace more fluid, therefore there will be a larger buoyant force.

Explanation

Buoyant force is calculated using the volume of displaced fluid, the submerged iron will displace more fluid, therefore there will be a larger buoyant force.

6. Imagine holding two identical bricks in place under water. Brick 1 is just beneath the surface of the water, while brick 2 is held about 2 feet down. The force needed to hold brick 2 in place is:

Greater

The same

Smaller

The force needed to hold the brick in place underwater is: W – FB. According to Archimedes’ Principle, FB is equal to the weight of the fluid displaced. Since each brick displaces the same amount of fluid, then FB is the same in both cases.

Explanation

The force needed to hold the brick in place underwater is: W – FB. According to Archimedes’ Principle, FB is equal to the weight of the fluid displaced. Since each brick displaces the same amount of fluid, then FB is the same in both cases.

7. While swimming near the bottom of a pool, you let out a small bubble of air. As the bubble rises toward the surface, what happens to its diameter?

Bubble diameter decreases

Bubble diameter stays the same

Bubble diameter increases

As the bubble rises, its depth decreases, so the water pressure surrounding the bubble also decreases. This allows the air in the bubble to expand (due to the decreased pressure outside) and so the bubble diameter will increase.

Explanation

As the bubble rises, its depth decreases, so the water pressure surrounding the bubble also decreases. This allows the air in the bubble to expand (due to the decreased pressure outside) and so the bubble diameter will increase.

8. A 10-kg piece of aluminum sits at the bottom of a lake, right next to a 10-kg piece of lead. Which has the greater buoyant force on it?

The aluminum

The lead

Both have the same buoyant force

Cannot be determined without knowing their volumes

Aluminum is less dense than lead, therefore a 10kg piece of it must have a larger volume and displace more water. So the buoyant force on the aluminum is larger.

Explanation

Aluminum is less dense than lead, therefore a 10kg piece of it must have a larger volume and displace more water. So the buoyant force on the aluminum is larger.

9. An object floats in water with 3/4 of its volume submerged. What is the ratio of the density of the object to that of water?

1/4

3/4

4/3

1/2

When an object floats in water, it displaces a volume of water equal to its own volume. In this case, since 3/4 of the object's volume is submerged, it displaces 3/4 of its own volume in water. This means that the density of the object is 3/4 times the density of water. Therefore, the ratio of the density of the object to that of water is 3/4.

Explanation

When an object floats in water, it displaces a volume of water equal to its own volume. In this case, since 3/4 of the object's volume is submerged, it displaces 3/4 of its own volume in water. This means that the density of the object is 3/4 times the density of water. Therefore, the ratio of the density of the object to that of water is 3/4.

10. Water flows through a 1-cm diameter pipe connected to a 1/2-cm diameter pipe. Compared to the speed of the water in the 1-cm pipe, the speed in the 1/2-cm pipe is:

One quarter

One half

The same

Double

Four times

The area of the small pipe is less, so we know that the water will flow faster there. Since A ∝ r2, when the radius is reduced by 1/2, the area is reduced by 1/4, so the speed must increase by 4 times to keep the flow rate (A × v) constant.

Explanation

The area of the small pipe is less, so we know that the water will flow faster there. Since A ∝ r2, when the radius is reduced by 1/2, the area is reduced by 1/4, so the speed must increase by 4 times to keep the flow rate (A × v) constant.