Mass, Weight and Density: Complete O Level Physics Cheatsheet
O Level Physics, Chapter 4 · Read time: ~7 minutes
Key Formulas
Mass vs weight
Mass is the amount of matter in an object, measured in kilograms (kg). It's a scalar, and it does not change no matter where the object is, on Earth, on the Moon, or in space.
Weight is the gravitational force acting on an object's mass: W = mg. It's a vector (it acts downward, toward the centre of the gravitational body), and it does change depending on the gravitational field strength at that location.
Gravitational field strength (g) is the weight per unit mass at a location, measured in newtons per kilogram (N/kg). On the Moon, g is about a sixth of its value on Earth, so the same object weighs about six times less there, even though its mass is unchanged.
Trap: Never say an object's mass changes because it moved to the Moon or into space. Its mass stays exactly the same, only its weight changes, because g is different. Also, mass is measured with a beam/lever balance, while weight is measured with a spring balance or newton meter, don't mix up which instrument measures which quantity.
Density
Density is mass per unit volume: ρ = m / V. It tells you how 'tightly packed' the matter in an object is, an object with a higher density has more mass squeezed into the same volume.
Units: kg/m³ is the SI unit, but g/cm³ is also very common in questions. To convert, 1 g/cm³ = 1000 kg/m³.
Regular objects (cubes, cylinders, spheres): find the volume using the relevant geometry formula, then measure the mass on a balance.
Irregular objects (a stone, a small irregular metal piece): find the volume using the displacement method, lower the object into a partially-filled measuring cylinder (or an overflow/eureka can) and measure the volume of water displaced, this equals the object's volume.
Trick: Whether an object floats or sinks in a liquid depends on comparing its density to the liquid's density, an object floats if its density is *less than* the liquid's density, and sinks if it's *greater*. You don't need to know the object's actual mass or volume to answer a floating/sinking question, only the two densities being compared.
Worked Example
A student wants to find the density of an irregularly-shaped stone. She first measures its mass on a balance, getting 135 g. She then lowers the stone into a measuring cylinder containing 60 cm³ of water, and the water level rises to 95 cm³.
(a) Explain why the displacement method, rather than direct measurement, is used to find the volume of the stone. [1]
The stone is irregularly shaped, so its volume cannot be calculated directly using a geometry formula.
The displacement method works for any shape.
(b) Calculate the volume of the stone. [2]
Volume of stone = final water level − initial water level
= 95 − 60
= 35 cm³
(c) Calculate the density of the stone, in g/cm³. [2]
Density = mass ÷ volume
= 135 ÷ 35
= 3.9 g/cm³ (2 s.f.)
(d) The density of water is 1.0 g/cm³. State, with a reason, whether the stone would float or sink in water. [2]
The stone's density (3.9 g/cm³) is greater than the density of water (1.0 g/cm³),
so the stone would sink.
Why this question is a good test of the topic: it chains together the displacement method, the density formula, and the floating/sinking reasoning, in one flowing question, exactly how it tends to appear in Paper 2.
Frequently Asked Questions
What's the actual difference between mass and weight?
Mass is the amount of matter in an object (constant everywhere, measured in kg). Weight is the gravitational force acting on that mass (W = mg, varies with location, measured in newtons).
What is gravitational field strength?
The weight per unit mass at a given location, measured in N/kg. Near the Earth's surface, it's taken as 10 N/kg at O Level unless a question states a different value.
How do I find the volume of an irregularly-shaped object?
Using the displacement method, lower it into a partially-filled measuring cylinder (or an overflow can) and measure the volume of liquid it displaces.
How do I know if an object will float or sink?
Compare its density to the liquid's density. It floats if its density is less than the liquid's, and sinks if its density is greater.
Is this topic tested in Paper 1 (MCQ) or Paper 2 (structured)?
Both. MCQs often test the mass-vs-weight distinction and unit conversions, Paper 2 usually includes a displacement-method density calculation similar to the worked example above.
Mixing up mass, weight and density?
Small group O Level Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, taught by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author.