UNIT 1.4: DENSITY

1. Definition

Density is a measure of how much mass is contained in a given volume.

Density (ρ)= Mass (m) / Volume (V) 

Where:

• ρ = density (kg/m³ or g/cm³)

• m = mass (kg or g)

• V = volume (m³ or cm³)

Units:

• SI unit: kg/m³

• Conversion: 1 g/cm³ = 1000 kg/m³

2. Density of Materials

• Solids: usually have high density (e.g., iron, lead)

• Liquids: have medium density (e.g., water = 1 g/cm³)

• Gases: have very low density (e.g., air ≈ 0.0012 g/cm³)

Effect of Temperature: As temperature increases, the volume expands, so density decreases.

3. Measuring Density

A. Regular-Shaped Solids

1. Measure dimensions — length, width, height, or radius.

2. Calculate volume:

   • Cube: V = a³

   • Rectangular prism: V = length × width × height

   • Sphere: V = (4/3)πr³

3. Measure mass using a balance.

4. Calculate density :mass / volume

B. Irregular-Shaped Solids (Water Displacement Method)

1. Record initial water volume (V₁).

2. Submerge the object and record a new volume (V₂).

3. Object volume: V = V₂ – V₁.

4. Measure mass using a balance.

5. Calculate density: ρ = m / V.

C. Liquids

1. Measure volume using a measuring cylinder (read at the bottom of the meniscus).

2. Measure mass of cylinder + liquid, then subtract the mass of the empty cylinder.

3. Calculate density: ρ = m / V.

4. Floating and Sinking

• An object floats if its density is less than the density of the fluid.

• An object sinks if its density is greater than the density of the fluid.

Density of Water: 1 g/cm³ or 1000 kg/m³

Sample Questions

Q1. A metal block has a mass of 540 g and a volume of 60 cm³. Find its density.

Q2. An irregular solid is submerged in water. The water level rises from 50 cm³ to 85 cm³. If the solid’s mass is 70 g, calculate its density.

Q3. A measuring cylinder contains 200 cm³ of a liquid. The cylinder’s mass is 50 g, and the total mass (cylinder + liquid) is 250 g. Find the density of the liquid.

Q4. Two blocks, A and B, have the same volume.

• Mass of A = 200 g

• Mass of B = 300 g a) Which block is denser? b) If placed in water, which block will float?

Written by: Hiba Shakeel — Subject Head of IGCSE Physics 

Curated by: Yassein Abdoun