The Physics Question Bank

Course: Combined Science + Separate Physics  |  Tier: Foundation + Higher  |  Equation sheet: given in the exam

The equation

density = mass ÷ volume    ρ = m / V

Quantity	Symbol	Unit
density	ρ	kilograms per cubic metre (kg/m³)
mass	m	kilograms (kg)
volume	V	cubic metres (m³)

Rearranged: m = ρ × V  |  V = m ÷ ρ  |  1 cm³ = 1 × 10⁻⁶ m³; 1 litre = 0.001 m³; 1 g/cm³ = 1000 kg/m³

Use FIFA for every answer

• F – Formula: write the equation as it appears on the sheet.
• I – Insert: put in the numbers (convert to standard units first).
• F – Fix: rearrange to make the unknown the subject.
• A – Answer: calculate and always give the unit.

Foundation: aim for Q1–8.   Higher: aim for Q4–10. Most questions need rearranging.

---

Questions

Q1 (F) A block of plastic has a mass of 2 kg and a volume of 0.001 m³. Calculate its density.

Show solution

F: ρ = m / V
I: ρ = 2 ÷ 0.001
F: ρ is already the subject
A: 2000 kg/m³

Q2 (F) A bath holds 0.2 m³ of water (ρ = 1000 kg/m³). Calculate the mass of the water.

Show solution

F: ρ = m / V
I: 1000 = m ÷ 0.2
F: m = 1000 × 0.2
A: 200 kg

Q3 (F) A 540 kg batch of aluminium (ρ = 2700 kg/m³) arrives at a factory. Calculate its volume.

Show solution

F: ρ = m / V
I: 2700 = 540 ÷ V
F: V = 540 ÷ 2700
A: 0.2 m³

Q4 (F) A gold ring has a mass of 19.3 g and a volume of 1.0 cm³. Calculate its density in kg/m³.

Show solution

Convert first: 19.3 g = 0.0193 kg; 1.0 cm³ = 1.0 × 10⁻⁶ m³
F: ρ = m / V
I: ρ = 0.0193 ÷ 1.0 × 10⁻⁶
F: ρ is already the subject
A: 19 300 kg/m³

Q5 (F) Olive oil has a density of 920 kg/m³. Calculate the mass of a 1.5 litre bottle of oil.

Show solution

Convert first: 1.5 litres = 0.0015 m³
F: ρ = m / V
I: 920 = m ÷ 0.0015
F: m = 920 × 0.0015
A: 1.38 kg

Q6 (F/H) A 260 g stone is lowered into a measuring cylinder. The water level rises from 50 cm³ to 150 cm³. Calculate the density of the stone in kg/m³.

Show solution

Volume of stone: 150 − 50 = 100 cm³ = 1.0 × 10⁻⁴ m³; mass = 0.26 kg
F: ρ = m / V
I: ρ = 0.26 ÷ 1.0 × 10⁻⁴
F: ρ is already the subject
A: 2600 kg/m³

Q7 (F/H) A bedroom is 5 m long, 4 m wide and 2.5 m high. Air has a density of 1.2 kg/m³. Calculate the mass of air in the room.

Show solution

Volume: 5 × 4 × 2.5 = 50 m³
F: ρ = m / V
I: 1.2 = m ÷ 50
F: m = 1.2 × 50
A: 60 kg

Q8 (F/H) The Earth has an average density of 5.5 × 10³ kg/m³ and a volume of 1.1 × 10²¹ m³. Calculate its mass, to 2 significant figures.

Show solution

F: ρ = m / V
I: 5.5 × 10³ = m ÷ 1.1 × 10²¹
F: m = 5.5 × 10³ × 1.1 × 10²¹ = 6.05 × 10²⁴ kg
A: 6.1 × 10²⁴ kg (2 s.f.)

Q9 (H) A block of ice has a volume of 0.50 m³. Ice has a density of 920 kg/m³. Calculate the weight of the block. (g = 9.8 N/kg)

Show solution

Step 1 – mass
F: ρ = m / V
I: 920 = m ÷ 0.50
F: m = 920 × 0.50 = 460 kg
Step 2 – weight
W = m g = 460 × 9.8
A: 4508 N

Q10 (H) A metal cube has sides of 4.0 cm and a mass of 170 g. Calculate its density in kg/m³, to 2 significant figures.

Show solution

Volume: 4.0 × 4.0 × 4.0 = 64 cm³ = 6.4 × 10⁻⁵ m³; mass = 0.170 kg
F: ρ = m / V
I: ρ = 0.170 ÷ 6.4 × 10⁻⁵
F: ρ = 2656 kg/m³
A: 2700 kg/m³ (2 s.f.)