Skip to main content
SingaporePhysicsSyllabus dot point

What is density, and how do we measure it for solids and liquids?

Define density, apply the relationship density equals mass over volume, and describe how to measure it

A focused answer to the O-Level Physics outcome on density. Density as mass per unit volume, the relationship and its rearrangements, measuring density for regular and irregular solids and liquids, and floating and sinking.

Generated by Claude Opus 4.87 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

Have a quick question? Jump to the Q&A page

Jump to a section
  1. What this dot point is asking
  2. The answer
  3. Examples in context
  4. Try this

What this dot point is asking

SEAB wants you to define density, to use the relationship ρ=m/V\rho = m/V and its rearrangements, and to describe how to measure density for a regular solid, an irregular solid, and a liquid. You should also be able to use density to decide whether an object floats or sinks in a given liquid.

The answer

What density is

Density is the mass per unit volume of a substance. It tells you how tightly packed the matter is:

ρ=mV\rho = \frac{m}{V}

Mass is in kilograms (or grams) and volume in cubic metres (or cubic centimetres), so density is in kg m−3\text{kg m}^{-3} or g cm−3\text{g cm}^{-3}. Water has a density of 1000 kg m−31000\ \text{kg m}^{-3}, which is 1.0 g cm−31.0\ \text{g cm}^{-3}.

Rearranging the relationship

The same relationship gives mass or volume when the other two are known:

m=ρV,V=mρm = \rho V, \qquad V = \frac{m}{\rho}

Measuring density

The method depends on the shape of the object.

  • Regular solid: measure the mass on a balance, measure the sides with a rule (or calipers), calculate the volume from the shape, then divide.
  • Irregular solid: measure the mass on a balance, find the volume by displacement (lower it into water in a measuring cylinder and read the rise), then divide.
  • Liquid: measure the mass of an empty measuring cylinder, pour in a known volume, measure the mass again; the liquid's mass is the difference, then divide by the volume.

Floating and sinking

An object floats in a liquid if its density is less than that of the liquid, and sinks if its density is greater. This is why wood (less dense than water) floats and a stone (more dense) sinks. Ice floats on water because ice is slightly less dense than liquid water.

Examples in context

Example 1. Ships made of steel. Steel is far denser than water, yet a steel ship floats because its hull encloses a large volume of air, making the average density of the whole ship less than that of water. Change the shape so it encloses less air, and the same steel sinks.

Example 2. Checking purity. A jeweller can test whether a ring is pure gold by measuring its density. Pure gold has a known high density, so a ring with a lower density must contain a lighter metal mixed in. Density depends only on the material, not the size, which makes it a reliable test.

Try this

Q1. Write the relationship for density and state its SI unit. [2 marks]

  • Cue. ρ=mV\rho = \dfrac{m}{V}; SI unit is kg m−3\text{kg m}^{-3}.

Q2. A liquid of mass 48 g48\ \text{g} occupies 60 cm360\ \text{cm}^3. Find its density. [2 marks]

  • Cue. ρ=mV=4860=0.80 g cm−3\rho = \dfrac{m}{V} = \dfrac{48}{60} = 0.80\ \text{g cm}^{-3}.

Q3. Explain how to find the volume of an irregular stone using water. [2 marks]

  • Cue. Lower the stone into a measuring cylinder of water; the rise in the water level equals the stone's volume.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marksA metal block has a mass of 270 g270\ \text{g} and measures 5.0 cm5.0\ \text{cm} by 3.0 cm3.0\ \text{cm} by 2.0 cm2.0\ \text{cm}. (a) Find its volume. (b) Find its density in g cm−3\text{g cm}^{-3}.
Show worked answer →

(a) Volume of a cuboid: V=5.0×3.0×2.0=30 cm3V = 5.0 \times 3.0 \times 2.0 = 30\ \text{cm}^3.

(b) Density: ρ=mV=27030=9.0 g cm−3\rho = \dfrac{m}{V} = \dfrac{270}{30} = 9.0\ \text{g cm}^{-3}.

Markers reward the volume from length times breadth times height, density as mass over volume, and the correct value with units.

Original5 marks(a) Describe how you would find the density of a small irregular stone using a measuring cylinder and a balance. (b) The stone has a mass of 84 g84\ \text{g} and raises the water level from 40 cm340\ \text{cm}^3 to 70 cm370\ \text{cm}^3. Find its density.
Show worked answer →

(a) Measure the stone's mass on a balance. Part-fill a measuring cylinder with water and note the volume. Lower the stone in fully and note the new volume. The rise in water level is the volume of the stone.

(b) Volume of stone =70−40=30 cm3= 70 - 40 = 30\ \text{cm}^3. Density =mV=8430=2.8 g cm−3= \dfrac{m}{V} = \dfrac{84}{30} = 2.8\ \text{g cm}^{-3}.

Markers reward measuring mass with a balance, finding volume by displacement (final minus initial level), and density as mass over the displaced volume with units.

Related dot points