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
- 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=MassVolume.
- 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.
- 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.
- 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.
- What is the significance of the density of water being ?
- Answer: The density value of for water is a convenient benchmark. Substances with densities greater than this will sink in water, while those with densities less will float.
- 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.
- 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.
- 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.
- 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.
- 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.
