The amount of matter in an object — scalar, measured in kg. Mass does not change with location.
Weight
The gravitational force on an object — vector, measured in N. Weight changes with location (different g).
W = mgW = weight (N) · m = mass (kg) · g = gravitational field strength (N/kg)
On Earth, g = 10 N/kg. On the Moon, g ≈ 1.6 N/kg. A 60 kg person weighs 600 N on Earth but only 96 N on the Moon — their mass is still 60 kg in both places.
Classic exam trap
"An astronaut has less weight on the Moon — their mass is also less." WRONG. Mass is constant. Only weight changes. A 70 kg astronaut is still 70 kg on the Moon.
2. Density
Density
Mass per unit volume — how much matter is packed into a given space.
ρ = m ÷ Vρ = density (kg/m³ or g/cm³) · m = mass (kg or g) · V = volume (m³ or cm³)
Worked example
A block has mass 240 g and volume 80 cm³. Find its density.
ρ = m ÷ V = 240 ÷ 80 = 3 g/cm³
To convert: 3 g/cm³ = 3000 kg/m³.
Measuring density of irregular objects
Measure mass using a balance.
Partially fill a measuring cylinder with water. Record volume V₁.
Submerge the object. Record new volume V₂.
Volume of object = V₂ − V₁ (displacement method).
Calculate ρ = m ÷ (V₂ − V₁).
3. Floating and Sinking
An object floats if its average density is less than the fluid it is placed in. It sinks if its average density is greater.
Condition
Result
Object density < fluid density
Object floats
Object density = fluid density
Object is neutrally buoyant (suspended)
Object density > fluid density
Object sinks
A steel ship floats because its hull is hollow — the average density of (steel + air inside) is less than water. A solid block of steel sinks because steel density (≈7800 kg/m³) > water density (1000 kg/m³).
Upthrust
Any object submerged in a fluid experiences an upward force called upthrust (buoyancy). Upthrust = weight of fluid displaced. When upthrust = weight, the object floats.
Density Formula
ρ = m / V
density (kg/m3) = mass (kg) / volume (m3). Rearrange: m = ρV or V = m/ρ
Weight Formula
W = mg
weight (N) = mass (kg) x gravitational field strength (N/kg). g = 10 N/kg on Earth.
Must-Know for Exam
Mass (kg): constant everywhere. Weight (N): depends on gravitational field strength.
g = 10 N/kg on Earth; g = 1.6 N/kg on Moon. An astronaut on Moon has same mass but less weight.
Density: rho = m/V. Water = 1000 kg/m3. Object floats if its density < fluid density.
Upthrust = weight of fluid displaced (Archimedes' principle). Object floats when upthrust = weight.
Units check: kg/m3 for density. If volume in cm3 and mass in g, density in g/cm3.
4. Common Exam Traps
Trap 1 — Units for density
Always state units: g/cm³ or kg/m³. Mixing units (g/m³) gives a nonsense answer. Water density = 1 g/cm³ = 1000 kg/m³.
Trap 2 — Weight is a force
Weight is measured in newtons (N), not kilograms. "The weight is 5 kg" is wrong. "The weight is 50 N" is correct (for a 5 kg object on Earth).
Key Terms — Flashcard Review
Tap each card to reveal the definition.
Mass
Amount of matter in an object. Unit: kg. Scalar. Constant everywhere - does not change with gravity.
Weight
Gravitational force on an object. W = mg. Unit: newton (N). Vector. Changes with gravitational field strength.
Gravitational field strength
Force per unit mass. g = 10 N/kg on Earth. g = 1.6 N/kg on Moon. Used in W = mg.
Density
Mass per unit volume. rho = m/V. Unit: kg/m3. Intrinsic property - does not depend on amount.
Upthrust
Upward buoyancy force on object submerged in fluid. Equal to weight of fluid displaced (Archimedes).
Floating condition
Object floats when upthrust = weight. Density of object <= density of fluid.
🎯 Practice Quiz — Test Yourself
8 O Level-style questions on this topic. Select an answer to see instant feedback.
Question 1 of 8
What is the weight of a 4 kg object? (g = 10 N/kg)
Explanation: Weight = mg = 4 × 10 = 40 N. Weight is a force (Newtons). Mass is matter (kg).
Question 2 of 8
An object has mass 500 g and volume 250 cm³. Its density is:
Explanation: Density = mass / volume = 500 / 250 = 2 g/cm³.
Question 3 of 8
Which quantity stays the same on the Moon as on Earth?
Explanation: Mass = amount of matter — constant everywhere. Weight = mg; g differs on Moon, so weight changes.
Question 4 of 8
An object floats in water. Its average density is:
Explanation: Objects float when their average density < density of the fluid they displace.
Question 5 of 8
The SI unit of pressure is:
Explanation: Pressure = Force / Area. SI unit = N/m² = Pascal (Pa).
Question 6 of 8
An object has mass 3 kg and volume 0.002 m3. Its density is:
Explanation: density = mass / volume = 3 / 0.002 = 1500 kg/m3. Since 1500 > 1000 (density of water), this object would sink in water.
Question 7 of 8
An astronaut has a mass of 70 kg on Earth. On the Moon (g = 1.6 N/kg), their weight is:
Explanation: W = mg = 70 x 1.6 = 112 N. Mass remains 70 kg everywhere. Weight changes with gravitational field strength.
Question 8 of 8
A wooden block floats in water. This tells us the block's density is:
Explanation: An object floats when its average density is less than the density of the fluid. The upthrust (weight of water displaced) equals the weight of the block. If density = fluid, it is fully submerged but just floating. If greater, it sinks.