Measuring Density

Density tells us how tightly matter is packed. If two boxes are the same size, the denser one has more mass inside. The density formula is:

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

Where $\rho$ is density, $m$ is mass, and $V$ is volume.

Units and measuring tools

• Density units: SI unit is $\text{kg m}^{-3}$. In labs you often use $\text{g cm}^{-3}$. Conversion: 1 g cm⁻³ = 1000 kg m⁻³.
• Mass: electronic balance (in g or kg). Mass is not the same as weight.
• Volume: measuring cylinder (cm³ or dm³), ruler for regular shapes. 1 cm³ = 1 mL; 1000 cm³ = 1 dm³.

Density of a liquid

1. Find mass of empty cylinder ($m_1$).
2. Add liquid, read volume $V$ at the bottom of the meniscus.
3. Find mass of cylinder + liquid ($m_2$); liquid mass $= m_2 - m_1$.
4. Calculate $\rho = m/V$.

Density of a regularly shaped solid

• Measure dimensions with a ruler. For a cuboid: $V = l\times w\times h$. For a cylinder: $V = \pi r^2 h$.
• Measure mass with a balance, then use $\rho = m/V$.

Density of an irregular solid that sinks (displacement)

1. Partly fill a measuring cylinder. Record initial volume $V_1$.
2. Gently lower the object in (no air bubbles). Record final volume $V_2$.
3. Object volume $= V_2 - V_1$. Measure mass, then $\rho = m/V$.

Floating and sinking

• An object floats in a liquid if its density is less than the liquid’s density; it sinks if it is greater.
• For two non-mixing liquids, the less dense liquid floats on the denser one (e.g., oil on water).

Common misconceptions

• Mass (in g or kg) is measured with a balance; weight is a force (in N) and is not used in $\rho = m/V$.
• Volume by displacement works only if the object is fully submerged and sinks.