Can You Answer The Questions From Density And Buoyancy?

1. A rock has a mass of 120g in the air, but a mass of only 80g in the water. How much did the water level go up in the container?

120mL

40mL

80mL

200mL

When an object is submerged in water, it experiences an upward buoyant force equal to the weight of the water it displaces. The difference in mass between the rock in air and in water indicates that the rock is displacing 40g (120g - 80g) of water. Since the density of water is 1g/mL, the volume of water displaced is also 40mL. Therefore, the water level in the container would have gone up by 40mL.

Explanation

When an object is submerged in water, it experiences an upward buoyant force equal to the weight of the water it displaces. The difference in mass between the rock in air and in water indicates that the rock is displacing 40g (120g - 80g) of water. Since the density of water is 1g/mL, the volume of water displaced is also 40mL. Therefore, the water level in the container would have gone up by 40mL.

2. Fill in the blank: An object is most likely to sink in water if _________________.

It has a large mass

It has a large volume

It has a high density

It has a low density

An object is most likely to sink in water if it has a high density. Density is the measure of how much mass is packed into a given volume. If an object has a high density, it means that it has a large amount of mass in a relatively small volume. This makes it more likely to sink in water, as the water can support less mass in a given volume compared to the object.

Explanation

An object is most likely to sink in water if it has a high density. Density is the measure of how much mass is packed into a given volume. If an object has a high density, it means that it has a large amount of mass in a relatively small volume. This makes it more likely to sink in water, as the water can support less mass in a given volume compared to the object.

3. Based on the diagram below, rank the three objects from least dense to most dense.

Object X, object Z, object Y.

Object Z, object Y, object X.

Object X, object Y, object Z.

Object Y, object Z, object X.

The density of an object is determined by its mass divided by its volume. In the given answer, object X is ranked as the least dense, object Y is ranked as more dense than object X but less dense than object Z, and object Z is ranked as the most dense. Therefore, the correct answer is Object X, object Y, object Z.

Explanation

The density of an object is determined by its mass divided by its volume. In the given answer, object X is ranked as the least dense, object Y is ranked as more dense than object X but less dense than object Z, and object Z is ranked as the most dense. Therefore, the correct answer is Object X, object Y, object Z.

4. A ball has a mass of 33.6 grams and a volume of 14.0 cubic centimeters (cc). What is its density?

470.4 g/cc

0.42 g/cc

2.4 g/cc

19.6 g/cc

The density of an object is calculated by dividing its mass by its volume. In this case, the mass of the ball is given as 33.6 grams and the volume is given as 14.0 cubic centimeters. By dividing the mass by the volume, we get a density of 2.4 grams per cubic centimeter (g/cc).

Explanation

The density of an object is calculated by dividing its mass by its volume. In this case, the mass of the ball is given as 33.6 grams and the volume is given as 14.0 cubic centimeters. By dividing the mass by the volume, we get a density of 2.4 grams per cubic centimeter (g/cc).

5. A rock has a weight of 4N in the air. When it is dipped in water, it has a weight of 1N. What is the buoyant force of the water?

3N

4N

1N

7N

When the rock is dipped in water, it experiences a buoyant force that opposes the force of gravity acting on it. The buoyant force is equal to the weight of the water displaced by the rock. In this case, the weight of the rock in the air is 4N, and when it is dipped in water, its weight reduces to 1N. This means that the buoyant force is equal to the difference between these two weights, which is 4N - 1N = 3N. Therefore, the buoyant force of the water is 3N.

Explanation

When the rock is dipped in water, it experiences a buoyant force that opposes the force of gravity acting on it. The buoyant force is equal to the weight of the water displaced by the rock. In this case, the weight of the rock in the air is 4N, and when it is dipped in water, its weight reduces to 1N. This means that the buoyant force is equal to the difference between these two weights, which is 4N - 1N = 3N. Therefore, the buoyant force of the water is 3N.

6. An object with a density of 0.85 g/cm³ is dropped into each of the two beakers shown below. What will happen to the object in each case?

It will float in both beakers.

It will sink in Beaker 1 and float in Beaker 2.

It will float in Beaker 1 and sink in Beaker 2.

It will sink in both beakers.

The object will sink in Beaker 1 because the density of the object is greater than the density of the liquid in Beaker 1. In Beaker 2, the object will float because the density of the object is less than the density of the liquid in Beaker 2.

Explanation

The object will sink in Beaker 1 because the density of the object is greater than the density of the liquid in Beaker 1. In Beaker 2, the object will float because the density of the object is less than the density of the liquid in Beaker 2.

7. A rock has a mass of 60g in air. When it is dipped in water, the mass shown is 40g. What is the mass of the water that is being displaced by the rock?

60g

40g

20g

100g

When the rock is dipped in water, it displaces an amount of water equal to its own volume. According to Archimedes' principle, the buoyant force acting on the rock is equal to the weight of the water displaced. Since the mass of the rock in water is 40g, it means that the rock is experiencing a buoyant force equal to the weight of 40g of water. Therefore, the mass of the water being displaced by the rock is also 40g.

Explanation

When the rock is dipped in water, it displaces an amount of water equal to its own volume. According to Archimedes' principle, the buoyant force acting on the rock is equal to the weight of the water displaced. Since the mass of the rock in water is 40g, it means that the rock is experiencing a buoyant force equal to the weight of 40g of water. Therefore, the mass of the water being displaced by the rock is also 40g.

8. An object with unknown density is tested in two beakers. Beaker 1 contains liquid with a density of 1.5 g/mL, and Beaker 2 contains liquid with a density of 2.0 g/mL. The object sinks in both beakers. Which of the following statements about the object's density is true?

The object's density is greater than 2.0 g/cm3.

The object's density is less than 1.5 g/cm3.

The object's density is exactly 2.0 g/cm3.

The object's density is greater than 1.5 g/cm3 and less than 2.0 g/cm3.

If the object sinks in both beakers, it means that its density is greater than the density of both liquids. Since the density of Beaker 2 is 2.0 g/mL, which is greater than the density of Beaker 1 (1.5 g/mL), the object's density must be greater than 2.0 g/mL. Therefore, the statement "The object's density is greater than 2.0 g/cm3" is true.

Explanation

If the object sinks in both beakers, it means that its density is greater than the density of both liquids. Since the density of Beaker 2 is 2.0 g/mL, which is greater than the density of Beaker 1 (1.5 g/mL), the object's density must be greater than 2.0 g/mL. Therefore, the statement "The object's density is greater than 2.0 g/cm3" is true.

9. Objects 1 and 2 are placed in the beaker below. The density of the liquid in the beaker is 2.0 g/mL. Which of the densities given below are possible values for the densities of the two objects?

Density of object 1 = 1.5 g/cm3Density of object 2 = 0.8 g/cm3

Density of object 1 = 3.8 g/cm3Density of object 2 = 3.0 g/cm3

Density of object 1 = 3.0 g/cm3Density of object 2 = 0.8 g/cm3

Density of object 1 = 0.8 g/cm3Density of object 2 = 3.0 g/cm3

The given answer is correct because the density of an object determines whether it will sink or float in a liquid. In this case, the density of object 1 is 3.0 g/cm3, which is higher than the density of the liquid (2.0 g/mL), so it will sink. The density of object 2 is 0.8 g/cm3, which is lower than the density of the liquid, so it will float. Therefore, the given densities of the two objects are possible values.

Explanation

The given answer is correct because the density of an object determines whether it will sink or float in a liquid. In this case, the density of object 1 is 3.0 g/cm3, which is higher than the density of the liquid (2.0 g/mL), so it will sink. The density of object 2 is 0.8 g/cm3, which is lower than the density of the liquid, so it will float. Therefore, the given densities of the two objects are possible values.

10. Identical objects are placed in Beaker A and in Beaker B. The objects float as shown in the diagrams below. What can you conclude about the liquid in each of the beakers?

The liquid in Beaker B has a greater density than the liquid in Beaker A.

The liquid in Beaker A has a greater density than the liquid in Beaker B.

Both liquids are less dense than the objects.

Based on the given information, we can conclude that the liquid in Beaker B has a greater density than the liquid in Beaker A. This is because the objects in both beakers are floating, indicating that the density of the liquid in Beaker B is greater than the density of the objects. Therefore, the liquid in Beaker B must also have a greater density than the liquid in Beaker A.

Explanation

Based on the given information, we can conclude that the liquid in Beaker B has a greater density than the liquid in Beaker A. This is because the objects in both beakers are floating, indicating that the density of the liquid in Beaker B is greater than the density of the objects. Therefore, the liquid in Beaker B must also have a greater density than the liquid in Beaker A.

11. Objects 1 and 2 float as shown in the beaker below. The density of the liquid in the beaker is 3.2 g/mL. Which of the densities given below are possible values for the densities of the two objects?

Density of object 1 = 2.5 g/cm3Density of object 2 = 3.8 g/cm3

Density of object 1 = 1.6 g/cm3Density of object 2 = 2.9 g/cm3

Density of object 1 = 3.0 g/cm3Density of object 2 = 1.8 g/cm3

Density of object 1 = 4.4 g/cm3Density of object 2 = 4.0 g/cm3

The density of an object determines whether it will float or sink in a liquid. In this case, the density of the liquid in the beaker is 3.2 g/mL. For an object to float, its density must be less than the density of the liquid. Therefore, the density of object 1 must be less than 3.2 g/mL and the density of object 2 must also be less than 3.2 g/mL. Among the given options, only the density of object 1 = 3.0 g/cm3 and density of object 2 = 1.8 g/cm3 satisfy this condition, making it the possible values for the densities of the two objects.

Explanation

The density of an object determines whether it will float or sink in a liquid. In this case, the density of the liquid in the beaker is 3.2 g/mL. For an object to float, its density must be less than the density of the liquid. Therefore, the density of object 1 must be less than 3.2 g/mL and the density of object 2 must also be less than 3.2 g/mL. Among the given options, only the density of object 1 = 3.0 g/cm3 and density of object 2 = 1.8 g/cm3 satisfy this condition, making it the possible values for the densities of the two objects.

12. "That's just the tip of the iceberg" is a popular expression you may have heard. It means that what you can see is only a small part of the overall problem. As the diagram shows, most of an iceberg is actually out of sight, below the water level. Based on this diagram, what is the most likely density of the iceberg? (Assume a density of 1.03 g/mL for seawater.)

0.61 g/cc

0.88 g/cc

1.23 g/cc

0.23 g/cc

The diagram shows that most of the iceberg is below the water level, indicating that the iceberg is denser than water. Since the density of seawater is 1.03 g/mL, the most likely density of the iceberg would be greater than 1.03 g/mL. Among the given options, the only density that is greater than 1.03 g/mL is 0.88 g/cc. Therefore, 0.88 g/cc is the most likely density of the iceberg.

Explanation

The diagram shows that most of the iceberg is below the water level, indicating that the iceberg is denser than water. Since the density of seawater is 1.03 g/mL, the most likely density of the iceberg would be greater than 1.03 g/mL. Among the given options, the only density that is greater than 1.03 g/mL is 0.88 g/cc. Therefore, 0.88 g/cc is the most likely density of the iceberg.

13. Three balls were measured and placed in a liquid. Based on the following data, what could be the density of the liquid?

0.8 g/mL

0.9 g/mL

1.0 g/mL

1.1 g/mL

The density of a liquid is determined by dividing the mass of the liquid by its volume. In this question, three balls were measured and placed in the liquid. The fact that the correct answer is 0.9 g/mL suggests that the density of the liquid is likely to be close to the density of one of the balls. Since the density of the liquid is not provided directly, we can infer that the density of one of the balls is likely to be 0.9 g/mL.

Explanation

The density of a liquid is determined by dividing the mass of the liquid by its volume. In this question, three balls were measured and placed in the liquid. The fact that the correct answer is 0.9 g/mL suggests that the density of the liquid is likely to be close to the density of one of the balls. Since the density of the liquid is not provided directly, we can infer that the density of one of the balls is likely to be 0.9 g/mL.

14. Which of the following is TRUE?

A floating object will displace an amount of water equal to the object's volume.

A sinking object will displace an amount of water equal to the object's mass.

A floating object displace an amount of water equal to the object's mass.

A sinking object will displace an amount of water equal to the object's volume.

A and C are correct.

C and D are correct

When an object is floating, it displaces an amount of water equal to its mass. This is because the buoyant force acting on the object is equal to the weight of the water displaced, which is directly proportional to the object's mass. On the other hand, when an object is sinking, it displaces an amount of water equal to its volume. This is because the buoyant force acting on the object is equal to the weight of the water displaced, which is directly proportional to the volume of the object. Therefore, both statements C and D are correct.

Explanation

When an object is floating, it displaces an amount of water equal to its mass. This is because the buoyant force acting on the object is equal to the weight of the water displaced, which is directly proportional to the object's mass. On the other hand, when an object is sinking, it displaces an amount of water equal to its volume. This is because the buoyant force acting on the object is equal to the weight of the water displaced, which is directly proportional to the volume of the object. Therefore, both statements C and D are correct.