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Cambridge IGCSE Physics · 0625

Chapter 1: Motion, forces and energy — Part 4

Topic 1.4 · Density

Density

Density is mass per unit volume.

ρ = m / V   Unit: kg/m3 or g/cm3 (1 g/cm3 = 1000 kg/m3).

An object floats in a fluid if its average density is less than the density of the fluid. It sinks if its density is greater.

A metal block has mass 48 kg and measures 0.80 m × 0.40 m × 0.050 m. Calculate its density.

Worked example: volume 0.016 cubic metres, density 3000 kilograms per cubic metre
Find V first (0.016 m3), then ρ = m / V = 3000 kg/m3.

Measuring density

Liquid
Find the mass of a known volume using a measuring cylinder and a balance. ρ = m / V.
Regular solid
Mass on a balance. Volume from length × width × height (or the formula for that shape).
Irregular solid that sinks
Mass on a balance. Volume by displacement: note the water level, immerse the solid, the rise in level is the volume.

An irregular stone has mass 72 g. Lowered into a measuring cylinder, it displaces 24 cm3 of water. Calculate the density of the stone.

Worked example: density by displacement is 72 grams over 24 cubic centimetres equals 3.0 grams per cubic centimetre
Keep g with cm3. ρ = 72 / 24 = 3.0 g/cm3 (= 3000 kg/m3).
Three density experiments: (a) regular solid — mass on a balance and volume from l × w × h; (b) liquid — mass of a known measuring-cylinder volume; (c) irregular solid that sinks — volume by displacement of water in a measuring cylinder.
Diagram 1: Three density experiments: (a) regular solid — mass on a balance and volume from l × w × h; (b) liquid — mass of a known measuring-cylinder volume; (c) irregular solid that sinks — volume by displacement of water in a measuring cylinder.

Immiscible liquids

If two liquids do not mix, the less dense liquid floats on the denser liquid. Compare the given density values.

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