B.1.2—Density

Density

Density is mass per unit volume:

$$\rho=\frac{m}{V}$$

It describes how much mass is concentrated in a given volume.

Calculation method

1. Identify the mass of the object or sample.
2. Use the volume occupied by that same sample.
3. Convert units before substituting.
4. Report density with units such as kg m⁻³ or g cm⁻³.

Useful conversion: 1 g cm⁻³ = 1000 kg m⁻³.

Interpret the result

For equal volumes, the denser sample has the greater mass. For equal masses, the denser sample occupies the smaller volume. A non-uniform object requires its total mass divided by its total external volume unless the question specifies a particular material region.

Worked example from local Question Bank row 36355

A spherical hydrogen nebula has radius $9.0\times10^{15}\,\mathrm{m}$ and number density $1.0\times10^{10}\,\mathrm{atoms\,m^{-3}}$. With $m_H=1.67\times10^{-27}\,\mathrm{kg}$, its mass density is $\rho=(1.0\times10^{10})(1.67\times10^{-27})=1.67\times10^{-17}\,\mathrm{kg\,m^{-3}}$.

$$V=\frac43\pi r^3=3.05\times10^{48}\,\mathrm{m^3}$$
$$m=\rho V=(1.67\times10^{-17})(3.05\times10^{48})=5.1\times10^{31}\,\mathrm{kg}$$

Check the boundary

Do not mix the volume of displaced fluid with the object’s mass, and do not use a material’s density formula with inconsistent units. Density is a scalar, so it has no direction.