Density – problems and solutions

1. The volume of an object is 8 cm^{3} and mass of an object is 84 gram. What is the density of the object?

__Known :__

Volume (V) = 8 cm^{3}

Mass (m) = 84 gram

__Wanted :__ density (ρ)

__Solution :__

ρ = m / V = 84 gram / 8 cm^{3 }= 10.5 gram/cm^{3}

2. Volume of an block is 5 cm^{3}. If the density of the block is 250 g/cm^{3}, what is the mass of the block ?

__Known :__

Volume (V) = 5 cm^{3}

Density (ρ) = 250 g/cm^{3}

__Wanted :__ Mass of the block

__Solution :__

ρ = m / V

*ρ = density, V = volume, m = mass*

Mass of block :

m = ρ V = (250 g/cm^{3})(5 cm^{3}) = 1250 gram

3. Volume of water is 35 cm^{3} and mass of water is 60 gram, what is the density of the water.

__Known :__

Volume of water (V) = 35 cm^{3}

Mass of water (m) = 60 gram

__Wanted:__ density (ρ)

__Solution :__

density :

ρ = m / V = 60/35 = 1.71 gram/cm^{3}

4. Mass of an metal is 120 gram and volume of an metal is 60 cm^{3}. What is the density of the metal?

__Known :__

Mass (m) = 120 gram

Volume (V) = 60 cm^{3}

__Wanted :__ density

__Solution :__

ρ = m / V

ρ = 120 gram / 60 cm^{3}

ρ = 2 gram/cm^{3}

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 cm^{3}

__Wanted :__ density

__Solution :__

ρ = m / V = 300 gram / 20 cm^{3 }= 15 gram/cm^{3 }

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 dm^{3} = 1/1000 m^{3 }= 0.001 m^{3}

0.04 liters = (0.04)(0.001) m^{3} = 0.00004 m^{3}

Density :

ρ = m / V = 0.316 kg / 0.00004 m^{3 }= 316 kg / 0.04 m^{3} = 7900 kg/m^{3 }

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 dm^{3 }= 1/1000 m^{3 }= 0.001 m^{3}

0.02 liters = 0.02 x 0.001 m^{3} = 0.00002 m^{3}

__Wanted :__ density

__Solution :__

Density :

ρ = m / V = 0.120 kg / 0.00002 m^{3 }= 120 kg / 0.02 m^{3} = 6000 kg/m^{3}

**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=VolumeMass $.

**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 $1g/cm$?****Answer**: The density value of $1g/cm$ 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.

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