Density

O Level / IGCSE Physics · Motion, forces and energy. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Density tells you how much mass is packed into each unit of volume. A material with a high density, such as iron, has a lot of mass in a small space. Density belongs to the material, not to the object: cut a block in half and each half has the same density as before.

To find a density you need two measurements: the mass (on a balance) and the volume. For a regular solid, work out the volume from its measured lengths. For an irregular solid that sinks, use the rise in water level in a measuring cylinder. For a liquid, find its mass by subtracting the mass of the empty container.

Rules to remember

Common mistake

Mixing units, for example dividing a mass in kg by a volume in cm3. Use g with cm3, or kg with m3, and convert only at the end (× 1000 to go from g/cm3 to kg/m3).

Worked example

A glass stopper has a mass of 84 g. It is lowered into a measuring cylinder of water and the reading rises from 42 cm3 to 72 cm3. What is the density of the glass?

  1. Volume of stopper = rise in water level = 72 − 42 = 30 cm3
  2. density = mass ÷ volume = 84 ÷ 30 = 2.8 g/cm3
  3. In kg/m3: 2.8 × 1000 = 2800 kg/m3

Answer: 2.8 g/cm3 (2800 kg/m3).

Practice questions

Try each one, then open the answer.

1. A student finds the volume of a stone by displacement, but drops it in so hard that some water splashes out of the measuring cylinder. How does this affect the density she calculates?

  1. A
    too low, because the measured volume is too small
  2. B
    too high, because the measured volume is too small
  3. C
    too high, because the measured mass is too large
  4. D
    unchanged, because the mass of the stone is not affected
Show answer

Answer: B. The water lost in the splash makes the final reading too low, so the volume found is too small. Density = mass ÷ volume, so dividing by a volume that is too small gives a density that is too high.

2. A block of metal has a mass of 540 g and a volume of 200 cm3. What is its density?

  1. A
    0.37 g/cm3
  2. B
    2.7 g/cm3
  3. C
    340 g/cm3
  4. D
    108 000 g/cm3
Show answer

Answer: B. density = mass ÷ volume = 540 ÷ 200 = 2.7 g/cm3 (this is aluminium).

3. A wooden block has a density of 0.60 g/cm3 and floats in water. It is cut into two equal halves. What is the density of each half, and does it float?

  1. A
    0.30 g/cm3, and it floats
  2. B
    0.60 g/cm3, and it floats
  3. C
    0.60 g/cm3, and it sinks
  4. D
    1.2 g/cm3, and it sinks
Show answer

Answer: B. Cutting the block halves both the mass and the volume, so mass ÷ volume is still 0.60 g/cm3. This is less than the 1.0 g/cm3 of water, so each half still floats.

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