Measurement, Mass, Weight and Density

This guide covers the measurement-technique half of 1.1 Physical quantities and measurement techniques, plus 1.3 Mass and weight and 1.4 Density, from Topic 1, Motion, forces and energy, for Cambridge O Level Physics 5054, 2026–2028 series.

Where this fits in 5054

Before Topic 1 can talk about motion, forces or energy in any quantitative way, it needs to establish how the basic quantities involved are actually measured, and what mass, weight and density mean physically. This page comes before Kinematics and Motion Graphs, which assumes you can already measure distance and time; the scalar/vector distinction covered there is the other half of subtopic 1.1.

Syllabus coverage

CAMBRIDGE O LEVEL PHYSICS 5054

• Describe how to measure a variety of lengths with appropriate precision using tapes, rulers and micrometers, including reading the scale on an analogue micrometer (1.1)
• Describe how to use a measuring cylinder to measure the volume of a liquid, and determine the volume of a solid by displacement (1.1)
• Describe how to measure a variety of time intervals using clocks and digital timers (1.1)
• Determine an average value for a small distance and for a short interval of time by measuring multiples, including the period of oscillation of a pendulum (1.1)
• State that mass is a measure of the quantity of matter in an object at rest relative to the observer, and that mass resists change from its state of rest or motion (inertia) (1.3)
• Know that weights, and therefore masses, may be compared using a beam balance or equal-arm balance (1.3)
• Describe how to determine mass using an electronic balance, and weight using a force meter (1.3)
• Define gravitational field strength as force per unit mass; recall and use gravitational field strength = weight ÷ mass, and know this is equivalent to the acceleration of free fall (1.3)
• State that a gravitational field is a region in which a mass experiences a force due to gravitational attraction (1.3)
• Define density as mass per unit volume; recall and use density = mass ÷ volume (1.4)
• Describe how to determine the density of a liquid, of a regularly shaped solid, and of an irregularly shaped solid which sinks in a liquid (volume by displacement), including appropriate calculations (1.4)

5054 is not tiered — every candidate covers all of the above.

Measuring length, volume and time

Length is measured with the instrument that matches the size and precision needed: a tape measure for long distances, a ruler for everyday lengths, and a micrometer for small lengths needing sub-millimetre precision. Reading an analogue micrometer means adding the main scale reading (in whole and half millimetres) to the thimble scale reading (in hundredths of a millimetre) at the point where it aligns with the datum line.

Volume is measured directly for a liquid, using a measuring cylinder read at eye level from the bottom of the meniscus. For a solid, volume comes from its shape (regular solids: measure dimensions and calculate) or, for an irregular solid, by displacement — lowering it into a measuring cylinder of liquid and reading the rise in level, which equals the solid’s volume.

Time is measured with clocks or digital timers, choosing the instrument’s resolution to suit the interval.

Worked example. A pendulum is timed for 20 complete oscillations, taking 18.4 s in total. Find the period of one oscillation.

period = total time / number of oscillations = 18.4 / 20 = 0.92 s

This “measure multiples, then divide” method is the general technique for any small distance or short time interval: timing one oscillation directly is imprecise (reaction-time error is a large fraction of a short interval), but timing 20 and dividing spreads that same error over a much larger total, shrinking its effect on the final answer.

Mass and weight

Mass is the quantity of matter in an object, measured at rest relative to the observer. Mass is also what gives an object inertia — its resistance to a change in its state of rest or motion; a more massive object is harder to start moving, and harder to stop.

Weight is the force of gravity acting on that mass — a different quantity from mass, even though the two are proportional near the Earth’s surface. Mass is compared using a beam or equal-arm balance (comparing against known masses) or measured directly with an electronic balance; weight is measured with a force meter (a calibrated spring).

The link between them is gravitational field strength, g, defined as force per unit mass:

gravitational field strength = weight / mass        g = W / m

This is numerically the same value as the acceleration of free fall (≈ 9.8 m/s² near the Earth’s surface, from Kinematics and Motion Graphs) — one describes how fast a mass accelerates when falling freely, the other describes the force per unit mass acting on it, and Newton’s second law (F = ma, in Forces and Motion) is exactly why these turn out to be the same number.

A gravitational field is simply the region around a mass in which another mass experiences a force due to gravitational attraction — this is why weight, unlike mass, changes from place to place: the Moon’s gravitational field is weaker than the Earth’s, so the same mass weighs less there, without its mass changing at all.

Density

Density is mass per unit volume:

density = mass / volume        ρ = m / V

Worked example. A block has a mass of 540 g and a volume of 200 cm³. Find its density.

ρ = m / V = 540 / 200 = 2.7 g/cm³

Measuring density depends on the shape of what’s being measured:

• Liquid — measure a known volume in a measuring cylinder, find its mass on a balance (subtracting the mass of the empty container), then apply ρ = m/V.
• Regularly shaped solid — measure its dimensions to calculate volume directly (e.g. length × width × height for a cuboid), find its mass on a balance, then apply ρ = m/V.
• Irregularly shaped solid that sinks — find its mass on a balance, then find its volume by displacement: lower it into a partially-filled measuring cylinder and read the rise in liquid level.

Common mistakes

• Reading a micrometer without adding both scales. The main scale and the thimble scale both contribute to the final reading — omitting either gives a wrong answer by a large margin.
• Confusing mass and weight. Mass (kg) is a fixed amount of matter; weight (N) is a force that depends on the local gravitational field strength. A 1 kg mass always has a mass of 1 kg, anywhere — but its weight is only ≈ 9.8 N near the Earth’s surface, and different elsewhere.
• Timing one oscillation instead of several. A single period is short enough that reaction-time error dominates the result — always time multiple oscillations and divide.
• Forgetting to subtract the container’s mass when finding the mass of a liquid alone.
• Using the wrong displacement reading. The volume of a submerged solid is the rise in liquid level, not the final reading on its own.

Quick revision checklist

• Choosing and reading the right instrument for length (tape, ruler, micrometer), volume (measuring cylinder, displacement) and time (clock, digital timer)
• The “measure multiples, divide” method for short times and small distances, and why it improves precision
• Mass vs weight: what each measures, and the instrument used for each
• Gravitational field strength, g = W/m, and why it equals the acceleration of free fall
• Density, ρ = m/V, and how it’s determined for a liquid, a regular solid and an irregular solid

Related resources

• Kinematics and Motion Graphs — the other half of subtopic 1.1 (scalars and vectors), plus subtopic 1.2
• Forces and Motion — Newton’s laws and F = ma, which connect mass to the forces acting on it
• Cambridge O Level Physics subject hub

Written against Cambridge O Level Physics 5054, 2026–2028 series. Always check the current syllabus for your examination year.