Density – problems and solutions

Density – problems and solutions

1. The volume of an object is 8 cm³ and mass of an object is 84 gram. What is the density of the object?

Known :

Volume (V) = 8 cm³

Mass (m) = 84 gram

Wanted : density (ρ)

Solution :

ρ = m / V = 84 gram / 8 cm³ = 10.5 gram/cm³

2. Volume of an block is 5 cm³. If the density of the block is 250 g/cm³, what is the mass of the block ?

Known :

Volume (V) = 5 cm³

Density (ρ) = 250 g/cm³

Wanted : Mass of the block

Solution :

ρ = m / V

ρ = density, V = volume, m = mass

Mass of block :

m = ρ V = (250 g/cm³)(5 cm³) = 1250 gram

3. Volume of water is 35 cm³ and mass of water is 60 gram, what is the density of the water.

Known :

Volume of water (V) = 35 cm³

Mass of water (m) = 60 gram

Wanted: density (ρ)

Solution :

density :

ρ = m / V = 60/35 = 1.71 gram/cm³

4. Mass of an metal is 120 gram and volume of an metal is 60 cm³. What is the density of the metal?

Known :

Mass (m) = 120 gram

Volume (V) = 60 cm³

Wanted : density

Solution :

ρ = m / V

ρ = 120 gram / 60 cm³

ρ = 2 gram/cm³

5.

Based on the table, an object with the same density is…

Solution :

Formula of density :

ρ = m / V

ρ = density, m = mass, V = volume

6. Based on the figure below, if the mass of an object is 300 gram, what is the density of the object.

Known :

Mass (m) = 300 gram

Volume (V) = volume of spilled water = 20 cm³

Wanted : density

Solution :

ρ = m / V = 300 gram / 20 cm³ = 15 gram/cm³

7. Mass of object is 316 gram, placed in a container as shown in figure. What is the density of the object.

Known :

Mass (m) = 316 gram

Volume (V) = volume of spilled water = 40 ml

Wanted : density

Solution :

Mass = 316 gram = 316/1000 kg = 0.316 kg

Volume = 40 ml = 40/1000 liters = 4/100 liters = 0.04 liters

1 liter = 1 dm³ = 1/1000 m³ = 0.001 m³

0.04 liters = (0.04)(0.001) m³ = 0.00004 m³

Density :

ρ = m / V = 0.316 kg / 0.00004 m³ = 316 kg / 0.04 m³ = 7900 kg/m³

8.

The density of stone based on the image is…

Known :

Mass (m) = 100 gram + 20 gram = 120 gram = 120 / 1000 kilogram = 0.120 kilogram

Volume (V) = 80 ml – 60 ml = 20 ml = 20 / 1000 liters = 2/100 liters = 0.02 liters

1 liter = 1 dm³ = 1/1000 m³ = 0.001 m³

0.02 liters = 0.02 x 0.001 m³ = 0.00002 m³

Wanted : density

Solution :

Density :

ρ = m / V = 0.120 kg / 0.00002 m³ = 120 kg / 0.02 m³ = 6000 kg/m³

1. What is density?
   • Answer: Density is a measure of how much mass is contained in a given volume. It is calculated by dividing the mass of an object by its volume: Density=MassVolumeDensity=VolumeMass​.
2. How does the density of an object relate to its ability to float or sink in a fluid?
   • Answer: Objects with a density greater than the fluid will sink, while objects with a density less than the fluid will float.
3. Why do some seemingly large objects, like a massive ship, float in water?
   • Answer: It’s all about displaced volume. A ship, while heavy, has a shape that displaces a large volume of water. If the weight of the water displaced is greater than or equal to the weight of the ship, the ship will float.
4. How does temperature typically affect the density of a substance?
   • Answer: Generally, as temperature increases, the density of a substance decreases because the molecules move more and tend to occupy a larger volume. There are exceptions, such as the anomalous expansion of water below 4°C.
5. What is the significance of the density of water being 1 g/cm³?
   • Answer: The density value of 1g/cm³ for water is a convenient benchmark. Substances with densities greater than this will sink in water, while those with densities less will float.
6. Why might two objects have the same mass but different densities?
   • Answer: The two objects could be made of different materials (and thus have different atomic or molecular structures) or they could have different volumes. An object with a larger volume and the same mass as a smaller object will have a lower density.
7. How does compressing a gas affect its density?
   • Answer: Compressing a gas decreases its volume. Since the mass remains constant, reducing the volume will increase the density of the gas.
8. Why do some heavy metals, like lead, feel “heavier” than others of the same size?
   • Answer: The “heaviness” you feel is actually the density. Lead has a higher density than many other metals, so a piece of lead feels heavier than another metal of the same volume.
9. How can an object be denser than a fluid but not sink immediately when placed on the fluid’s surface?
   • Answer: Surface tension can sometimes support objects denser than the fluid, especially if the object is small or has a shape that can be “cradled” by the fluid’s surface. Over time, however, if the object’s density is greater, it will likely sink.
10. Can the density of a homogeneous object be different at different points inside the object?

• Answer: No. For a homogeneous object, the density is uniform throughout, meaning it has the same value at every point inside the object.