This topic covers how much matter an object contains (mass), the force gravity exerts on it (weight), and how tightly that matter is packed (density). It appears in Physics 0625 as calculations, as data-handling questions and as short explanations about floating and sinking. Check the current syllabus on the Cambridge page for the exact wording of each learning objective.
The ideas are simple. The marks are lost on units, on mixing up mass with weight, and on answers that are wrong by a factor of 1000.
What should you know before starting?
You should be comfortable with rearranging a formula such as m = ρV, with standard units (kg, m, s, N) and with volume in cm³ and m³. If those feel uncertain, revisit measurement and quantities first. Forces are introduced properly in forces and momentum.
An orienting example
A solid block has a mass of 0.80 kg and a volume of 100 cm³. Find its weight and its density. Take g = 10 N/kg. (This data is invented for practice.)
Weight: W = mg = 0.80 × 10 = 8.0 N.
Density: convert the volume first, because 100 cm³ = 100 ÷ 1 000 000 = 1.0 × 10⁻⁴ m³. Then ρ = m/V = 0.80 ÷ (1.0 × 10⁻⁴) = 8000 kg/m³.
Check: 0.80 kg is 800 g, and 800 ÷ 100 = 8.0 g/cm³. Multiplying by 1000 gives 8000 kg/m³ again. Two routes give one answer, and the value is close to steel, so the result is reasonable.
In what order should you study the lessons?
- Separate mass from gravitational force: fix the meaning of mass and weight before using either in a formula.
- Convert density units: the g/cm³ and kg/m³ conversion is behind most answers that are wrong by 1000.
- Calculate an unknown volume from mass and density: rearranging the density formula and keeping units consistent.
- Explain floating using an appropriate force model: compare densities, then balance weight and upthrust.
- Identify an unreasonable material-density answer: a habit of checking whether a result could be real.
Finish with the mixed practice set. A mistake log is useful here, because the same unit slip tends to return.
What are the common traps?
- Writing weight in kilograms, or mass in newtons.
- Saying an object’s mass changes on the Moon. Its weight changes; its mass does not.
- Using cm³ with kg, or m³ with g, in the same calculation.
- Converting 1 cm to 0.01 m but forgetting that volume needs the factor cubed.
- Thinking heavy objects always sink. Floating depends on average density, not on weight alone.
How should you use the practice set?
Work each question on paper first, write the unit on every line and only then open the answer. When you are wrong, name the error type (mass/weight, units, rearranging, reasoning) before you read the correction. The practice page routes each error back to the lesson that fixes it.
If you want a teacher to watch this reasoning live, see online one-to-one Physics tuition.