Density

Density — the mass per unit volume of a material:

ρ = m / V

with density in kg/m³, mass in kilograms and volume in cubic metres. The symbol ρ is the Greek letter rho.

Density is often quoted in g/cm³ instead, and the two differ by a factor of 1000:

1 g/cm³ = 1000 kg/m³

Water is 1.00 g/cm³, or 1000 kg/m³. Getting this conversion wrong is the usual way to be out by a factor of a thousand.

Density is a property of the material, not of the object. A steel nail and a steel girder have the same density. Doubling the size of an object doubles both its mass and its volume, leaving the ratio unchanged.

Why a ship floats although steel sinks. A solid lump of steel is denser than water and sinks. A ship is mostly air, so the average density of the whole ship is less than that of water and it floats. It is the average density of the object that decides, not the density of what it is made from.

Measuring the density of a regular solid:

1. Find the mass on a balance.
2. Measure the dimensions with a ruler or callipers and calculate the volume.
3. Divide.

Measuring the density of an irregular solid — find the mass on a balance, then find the volume by displacement: lower the object into a measuring cylinder containing a known volume of water and record the rise, or use a displacement can and collect the overflow. The volume of water displaced equals the volume of the object.

Measuring the density of a liquid — find the mass of an empty measuring cylinder, add a known volume of the liquid, find the new mass, and subtract to get the mass of the liquid alone. Forgetting to subtract the cylinder is a common error and inflates the answer.

Example: a block of mass 240 g measures 4.0 cm × 3.0 cm × 2.0 cm. Its volume is 24 cm³, so its density is 240 ÷ 24 = 10 g/cm³, which is 10 000 kg/m³.