Measuring Density of Solids and Liquids

Measuring density requires finding both mass and volume. The method for finding volume depends on whether the object is a regular solid, an irregular solid, or a liquid.

Regular solids (cubes, cuboids, cylinders)

1. Measure the mass using a balance.
2. Measure the dimensions using a ruler (or calipers for small objects).
3. Calculate the volume from the dimensions.
4. Calculate density: $\rho = m/V$.

For a cuboid: $V = l \times w \times h$. For a cylinder: $V = \pi r^2 h$.

Irregular solids (stones, keys, irregular metal pieces)

Use the displacement method:

1. Measure the mass using a balance.
2. Partly fill a measuring cylinder with water and record the initial volume $V_1$.
3. Lower the object into the water using a thread.
4. Record the new volume $V_2$.
5. Volume of the object = $V_2 - V_1$.
6. Calculate density.

For larger objects, use a displacement (eureka) can: fill it until water reaches the spout, place a measuring cylinder under the spout, lower the object in, and collect the displaced water.

Liquids

1. Place an empty measuring cylinder on a balance and record the mass.
2. Pour the liquid into the measuring cylinder and record the new mass.
3. Mass of liquid = new mass − mass of cylinder.
4. Read the volume from the measuring cylinder (read at the bottom of the meniscus).
5. Calculate density.

Common errors and how to correct them

• Trapping air bubbles on an irregular solid. Tilt the object as you lower it into the water to release trapped bubbles. Bubbles increase the apparent volume.
• Not reading the meniscus correctly. For water in a glass cylinder, read the bottom of the curved meniscus at eye level.
• Forgetting to subtract the empty container mass. The balance shows the combined mass of container and substance. Subtract the container.

How to apply this in an exam

Paper 6 frequently asks you to describe an experiment to find density. Name the instruments (balance, ruler or measuring cylinder), describe the method clearly, state the formula, and mention at least one precaution (eye level for meniscus, removing air bubbles, repeating measurements).