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DensityIB MYP Physics: Revision notes

Section 1

What is density?

Density tells you how much mass there is in a given volume. Dense materials pack a lot of mass into a small space.

density = mass ÷ volume, or ρ = m / V

The units are kg/m³ or g/cm³ (use g with cm³ and kg with m³). To convert, 1 g/cm³ = 1000 kg/m³.

Worked example: a block has mass 324 g and volume 120 cm³. Density = 324 ÷ 120 = 2.7 g/cm³ (2700 kg/m³).

Key termsdensity
Exam tip

Rearrange the formula: m = ρ × V and V = m ÷ ρ.

Section 2

Density of a regular solid

A regular solid has a shape you can measure.

  1. Find the mass with a balance.
  2. Measure the lengths with a ruler and work out the volume (for a cuboid, length × width × height).
  3. Calculate density = mass ÷ volume.
Key termsregular solid

Section 3

Density of an irregular solid

You cannot calculate the volume of an irregular solid, such as a stone, from its dimensions. Use displacement:

  1. Find the mass on a balance.
  2. Fill a displacement can with water up to its spout.
  3. Lower the stone, on a string, into the can.
  4. Collect the water that overflows in a measuring cylinder. Its volume equals the volume of the stone.
  5. Calculate density = mass ÷ volume.
Key termsirregular soliddisplacement can

Section 4

Density of a liquid

  1. Place an empty measuring cylinder on a balance and record its mass (or press tare so it reads zero).
  2. Pour in some liquid and read the volume at the bottom of the meniscus, at eye level.
  3. Find the mass of the cylinder and liquid, and subtract the mass of the empty cylinder.
  4. Calculate density = mass of liquid ÷ volume.

Repeating and averaging makes the result more reliable.

Key termsmeniscus

Section 5

Floating and sinking

Compare the density of the object with the density of the fluid.

  • If the object is less dense than the fluid, it floats.
  • If the object is more dense than the fluid, it sinks.

Water has a density of 1.0 g/cm³. A steel ship floats because its average density, including the air inside the hull, is less than water.

Key termsfloatingsinking
Common mistake

Heavy things do not always sink. Compare densities, not masses.

Section 6

Density and changes of state

When a substance changes state its mass stays the same but its volume changes, so its density changes.

  • Gas: particles are far apart, so the density is very low.
  • Liquid: particles are close together, so the density is much higher.
  • Solid: particles are usually packed slightly closer, so the density is slightly higher than the liquid.

Water is an exception: ice (0.92 g/cm³) is less dense than liquid water (1.00 g/cm³), so ice floats.

Key termschange of state

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Density

  1. A jeweller in Jaipur is testing a solid rectangular metal block. The block has a mass of 324 g and measures 4.0 cm by 5.0 cm by 6.0 cm.
    The density of the block is 2.7 g/cm³. Convert this to kg/m³.2 marks
  2. A ship designer in Busan tests three materials in fresh water, which has a density of 1.0 g/cm³. The density of the wood is 0.60 g/cm³, the density of the plastic is 1.2 g/cm³ and the density of the steel is 7.8 g/cm³.
    Calculate the mass of 50 cm³ of the wood.2 marks
  3. A student in Accra wants to find the density of a small irregular stone. She has a balance, a displacement can filled to the spout with water, a measuring cylinder and some string. She finds that the stone has a mass of 84 g and that the water displaced by the stone measures 30 cm³.
    Outline how the student could have obtained the mass and the volume of the stone.3 marks
See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).