Density

IGCSE Edexcel Physics
5.3–5.4 Density, mass and volume
Key Concepts: Density = mass ÷ volume: $\rho = m/V$. Units: kg/m³. Solids and liquids have higher densities than gases because particles are more closely packed. An object floats if its density is less than that of the fluid.

Section A — Density Concepts

1. Define density and write its equation, defining all symbols and units. [3]
2. Explain in terms of particle spacing why a solid has a higher density than a gas. [2]
3. A piece of wood floats on water. State what this tells you about the density of the wood compared to water. [1]

Section B — Density Calculations

4. A block has mass 3.6 kg and volume $0.004\,\text{m}^3$. Calculate its density. [2]
5. A liquid has density $800\,\text{kg/m}^3$ and volume $0.002\,\text{m}^3$. Calculate its mass. [2]
6. A metal has density $7800\,\text{kg/m}^3$ and mass 195 kg. Calculate its volume. [2]
7. A rectangular block measures 0.1 m × 0.2 m × 0.05 m and has mass 0.9 kg. Calculate the density. [3]

Section C — Measuring Density (Practical)

8. Describe how you would measure the density of a regular solid (e.g. a cuboid) using a ruler and a balance. [3]
9. Describe how you would find the volume of an irregularly shaped stone and then calculate its density. [4]

Total marks: 22

Mark Scheme

1. Density is the mass per unit volume [1]; $\rho = m/V$ [1]; $\rho$ in kg/m³, $m$ in kg, $V$ in m³ [1] [3]
2. In a solid, particles are closely and regularly packed [1]; in a gas, particles are far apart [1]; so the same mass occupies a much larger volume in a gas [1] (award any 2) [2]
3. The density of the wood is less than the density of water (less than 1000 kg/m³) [1]
4. $\rho = m/V = 3.6/0.004 = 900\,\text{kg/m}^3$ [2]
5. $m = \rho V = 800 \times 0.002 = 1.6\,\text{kg}$ [2]
6. $V = m/\rho = 195/7800 = 0.025\,\text{m}^3$ [2]
7. $V = 0.1 \times 0.2 \times 0.05 = 0.001\,\text{m}^3$ [1]; $\rho = 0.9/0.001 = 900\,\text{kg/m}^3$ [2] [3]
8. Measure length, width and height with a ruler [1]; calculate volume $V = l \times w \times h$ [1]; measure mass with a balance; $\rho = m/V$ [1] [3]
9. Partially fill a measuring cylinder with water, record initial volume [1]; submerge stone fully and record new volume [1]; volume of stone = difference in readings [1]; measure mass with a balance; calculate $\rho = m/V$ [1] [4]