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Topic 1 · 1.3–1.4

Mass, weight and density

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • State what mass and weight are; define gravitational field strength and use \( g = \dfrac{W}{m} \); compare masses with a balance.
  • Describe weight as the effect of a gravitational field on a mass EXTENDED.
  • Define density and use \( \rho = \dfrac{m}{V} \); describe how to measure the density of a liquid, a regular solid and an irregular solid.
  • Decide whether an object floats from density data; whether one liquid floats on another EXTENDED.

📚The physics

Mass and weight

Mass is a measure of the quantity of matter in an object at rest relative to the observer; it is measured in kilograms and does not depend on where the object is. Weight is a gravitational force on an object that has mass, measured in newtons.

Gravitational field strength is force per unit mass:

\[ g = \frac{W}{m} \qquad \text{so} \qquad W = mg \]

On the Earth \( g = 9.8 \) N/kg, which is equivalent to the acceleration of free fall, 9.8 m/s2. Weights (and so masses) can be compared using a balance. EXTENDED Weight is the effect of a gravitational field on a mass: move the mass to a weaker field and its weight falls, while its mass stays the same.

The same 60 kg astronaut on the Earth, where g is 9.8 newtons per kilogram and the weight is 588 N, and on the Moon, where g is 1.6 newtons per kilogram and the weight is only 96 N.
Same mass, different weight: the field is weaker on the Moon.

Density

Density is mass per unit volume:

\[ \rho = \frac{m}{V} \]

Units are g/cm3 or kg/m3; 1 g/cm3 = 1000 kg/m3 (water is 1.0 g/cm3).

Three methods. Regular solid: measure length, width and height with a ruler, multiply for the volume, find the mass on a balance, divide. Liquid: find the mass of an empty measuring cylinder, add the liquid and read its volume, find the mass again; the difference is the mass of the liquid. Irregular solid that sinks: read the water level V1 in a measuring cylinder, lower the object in and read V2; the volume of the object is V2 minus V1, or collect the overflow from a displacement can.
Every method finds a mass on a balance and a volume, then divides.
  • Regular solid: measure the sides with a ruler (a calliper for small ones), \( V = l \times w \times h \); mass on a balance.
  • Liquid: find the mass of an empty measuring cylinder, pour in liquid, read the volume, find the mass again; subtract.
  • Irregular solid that sinks: volume by displacement — the rise in water level in a measuring cylinder, or the volume of water that overflows from a full displacement can into a measuring cylinder.

Floating and sinking

An object floats in a liquid if its density is less than the liquid’s and sinks if it is greater. EXTENDED Liquids that do not mix form layers: the less dense liquid floats on the denser one.

A beaker with three layers: oil of density 0.92 grams per cubic centimetre on top, water of density 1.00 in the middle, syrup of density 1.30 at the bottom. A cork floats on the oil, a plastic bead of density 1.10 rests at the top of the syrup, and a steel nut of density 7.8 lies on the bottom.
Each object sinks through anything less dense than itself and floats on anything denser.

✏️Worked example

A student finds the density of a small stone. Its mass is 156 g. The water in a measuring cylinder reads 40 cm3; with the stone in it, 100 cm3. (a) Calculate the density of the stone in g/cm3 and in kg/m3. [3] (b) The stone is placed in a liquid of density 2.9 g/cm3. Does it float? Explain. [1] (c) State one precaution when lowering the stone into the water. [1]

(a) Volume = 100 − 40 = 60 cm3. \( \rho = \dfrac{156}{60} = 2.6 \) g/cm3 = 2600 kg/m3.

(b) Yes: 2.6 g/cm3 is less than 2.9 g/cm3.

(c) Lower it gently on a thread (so no water splashes out and the cylinder does not crack); make sure it is fully submerged; read the meniscus at eye level.

Check it. Most rocks have densities of 2–3 g/cm3, so 2.6 is believable. An answer of 0.38 would mean the fraction is upside down.
Using 100 cm3 as the volume. The stone’s volume is the change in reading, not the final reading.

📝Practise

In the style of the multiple-choice, theory and practical papers. EXTENDED marks Supplement content.

1. (Multiple choice.) Which is a unit of weight? A: gram. B: kilogram. C: newton. D: joule.
C. Weight is a force.
2. (Theory.) A rover has a mass of 900 kg. On Mars, g = 3.7 N/kg. Calculate its weight on Mars, and state its mass there. [2]
W = mg = 900 × 3.7 = 3300 N (3330 N). Its mass is still 900 kg.
3. (Theory.) A scientist has a small piece of rock, a displacement can, a measuring cylinder, a beaker of water and a balance. Describe how to find the volume of the rock. [3] (Modelled on 0625/32 June 2026 Q3.)
Fill the displacement can with water until it overflows, and wait for it to stop dripping. Place the measuring cylinder under the spout. Lower the rock gently into the can (on a thread). Read the volume of water collected in the measuring cylinder at eye level with the bottom of the meniscus: this equals the volume of the rock.
4. (Theory.) The rock in question 3 has a mass of 84 g and a volume of 35 cm3. Calculate its density. [2]
\( \rho = \dfrac{84}{35} = \) 2.4 g/cm3.
5. (Multiple choice.) Densities: petrol 0.70, water 1.00, glycerol 1.26 (g/cm3). Which object floats on glycerol but sinks in water and in petrol? A: 18 g, 20 cm3. B: 30 g, 25 cm3. C: 40 g, 25 cm3. D: 12 g, 20 cm3. (Modelled on 0625/12 June 2026 Q5.)
B: 30 / 25 = 1.2 g/cm3, between 1.00 and 1.26. (A 0.90 floats on water; C 1.6 sinks in all; D 0.60 floats on all.)
6. (Practical.) Describe how to measure the density of cooking oil. [4]
Measure the mass of an empty measuring cylinder on a balance. Pour in some oil and read its volume (eye level with the meniscus). Measure the mass of the cylinder and oil. Mass of oil = difference; density = mass ÷ volume.
7. (Theory.) EXTENDED Paraffin (0.80 g/cm3) and salt water (1.03 g/cm3) do not mix. Which liquid forms the top layer? Explain. [1]
Paraffin: it is less dense, so it floats on the salt water.
8. (Theory.) Convert 7.8 g/cm3 into kg/m3. [1]
7.8 × 1000 = 7800 kg/m3.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “Density” — blocks of different materials in water
  • BBC Bitesize — density and how to measure it