DensityCambridge IGCSE Physics: Revision notes

Density is a measure of how much mass is packed into a given volume. It tells us how tightly the particles in a substance are arranged.

The formula for density is:

ρ = m / V

Where:

• ρ (rho) = density in kg/m³ or g/cm³
• m = mass in kg or g
• V = volume in m³ or cm³

This is a fundamental equation that you must be able to recall and rearrange:

• m = ρ × V (to find mass)
• V = m / ρ (to find volume)

Density is often expressed in two common units:

• kg/m³ (standard SI unit)
• g/cm³ (commonly used in practical work)

Note: 1 g/cm³ = 1000 kg/m³

To determine the density of a liquid, follow this procedure:

1. Measure the mass: Use an electronic balance to find the mass of an empty measuring cylinder (or graduated flask)
2. Add liquid: Pour the liquid into the measuring cylinder to a known volume
3. Measure again: Weigh the cylinder with the liquid inside
4. Calculate mass of liquid: Subtract the empty cylinder's mass from the total
5. Read the volume: Use the scale on the measuring cylinder to note the volume
6. Calculate density: Use ρ = m/V

Key points:

• Use a measuring cylinder (graduated in cm³) to determine volume accurately
• Measure the volume at eye level to avoid parallax error
• An electronic balance gives more precise mass measurements than a mechanical balance
• Always subtract the mass of the empty container

For solids with regular geometric shapes (such as cubes, cylinders, or rectangular blocks), the volume can be calculated mathematically rather than measured directly.

Procedure:

1. Measure dimensions: Use a ruler or caliper to measure all necessary dimensions of the solid

   • For a cube: measure one side length (s); volume = s³
   • For a rectangular block: measure length (l), width (w), and height (h); volume = l × w × h
   • For a cylinder: measure radius (r) and height (h); volume = πr²h

2. Measure mass: Use an electronic balance to find the mass of the object

3. Calculate volume: Apply the appropriate geometric formula

4. Calculate density: Use ρ = m/V

Advantages of this method:

• No need for displacement apparatus
• More precise measurements of dimensions using rulers or calipers
• Suitable for solid objects that do not absorb water

For solids with irregular shapes, volume cannot be calculated mathematically. Instead, we use the water displacement method (also called the displacement method).

Procedure:

1. Prepare apparatus: Fill a measuring cylinder with water to a known volume (e.g. 50 cm³)
2. Record initial volume: Note the water level carefully at eye level
3. Immerse the object: Carefully lower the irregular solid into the water, ensuring it is completely submerged
4. Record final volume: Read the new water level at eye level
5. Calculate volume of solid: Volume = Final volume − Initial volume
6. Measure mass: Use an electronic balance to find the mass of the solid (it must be dry)
7. Calculate density: Use ρ = m/V

Important notes:

• The object must be completely submerged in water
• The object must be impermeable (does not absorb water)
• Use a displacement can or large measuring cylinder for larger objects
• The volume of water displaced equals the volume of the solid
• Always read the meniscus at eye level to minimise parallax error

Whether an object floats or sinks in a fluid depends on how its density compares to the density of the fluid.

Floating and sinking rules:

Examples:

• Wood (ρ ≈ 0.7 g/cm³) floats in water (ρ = 1.0 g/cm³) because wood is less dense
• Iron (ρ ≈ 7.9 g/cm³) sinks in water because iron is more dense
• Ice (ρ ≈ 0.92 g/cm³) floats in water (ρ = 1.0 g/cm³)

Key point: The absolute density values matter only in comparison. You must compare the density of the object to the density of the fluid it is placed in.

Exam tip: If asked whether an object will float, always state the comparison of densities. Simply saying "the object is less dense" is better than guessing.

When two immiscible liquids (liquids that do not mix) are placed together, they separate into layers based on their densities. The less dense liquid floats on top of the denser liquid.

Layering rule:

• The liquid with the lower density occupies the top layer
• The liquid with the higher density occupies the bottom layer

Common examples:

• Oil (ρ ≈ 0.9 g/cm³) floats on water (ρ = 1.0 g/cm³)
• Petrol (ρ ≈ 0.7 g/cm³) floats on oil
• Alcohol (ρ ≈ 0.8 g/cm³) floats on water
• Mercury (ρ ≈ 13.6 g/cm³) sinks below water

Predicting liquid layers:

1. List the liquids with their density values
2. Arrange from highest to lowest density (or lowest to highest)
3. The densest liquid is at the bottom, the least dense is at the top
4. Intermediate liquids arrange in order between them

Important condition: This prediction only works if the liquids do not mix. The exam specification will confirm that liquids do not mix if required.