PAG1: Materials and Density
Density is mass per unit volume, ρ = m/V. For a regular cuboid, measure length, width and height with appropriate resolution and multiply them to obtain volume. Check for a zero offset and read a scale without parallax. Repeated dimension measurements can reveal an uneven shape, but a formula for a perfect cuboid is only as suitable as the object’s geometry.
Before you start
- Use your teacher’s tier checklist: this overview can include Higher-only material, and is not a tier-specific revision list.
- OCR Gateway A separate GCSE Physics J249. P9 groups the practical techniques into PAG1–8; the activities here are suitable examples, and centres can choose alternatives covering the required apparatus and techniques.
- Measure mass and volume, calculate a cuboid volume and convert simple metric units.
- Use the centre’s approved supervised method and equipment limits. These notes prepare you to explain and evaluate practical work; they do not replace carrying it out and recording the evidence.
Watch, pause, try
Video by Science Shorts. This practical overview supports density measurements. Check the board-specific written requirements for regular dimensions, displaced solid volume and liquid mass by difference.
Viewing focus: Choose dimension or displacement measurements for a solid
After watching, attempt these questions before opening the answers. You can also use the written lesson below.
After watching 1: Why do you need two readings for either cylinder displacement or liquid mass by difference?
Show answer and reasoning
Each desired quantity is a change: final minus initial volume excludes the original liquid, and filled minus empty mass excludes the vessel.
After watching 2: Explain the effect of a bubble attached to an immersed solid on its calculated density.
Show answer and reasoning
The bubble increases the apparent displaced volume without increasing the solid’s measured mass. Dividing by an excessive volume underestimates density.
What you'll be able to do
- Choose dimension or displacement measurements for a solid
- Obtain liquid mass by difference
- Calculate density with consistent volume units and evaluate uncertainty
Measure the volume that belongs to the object
Density is mass per unit volume, ρ = m/V. For a regular cuboid, measure length, width and height with appropriate resolution and multiply them to obtain volume. Check for a zero offset and read a scale without parallax. Repeated dimension measurements can reveal an uneven shape, but a formula for a perfect cuboid is only as suitable as the object’s geometry.
An irregular solid can be fully immersed in a suitable liquid and its displacement measured. In a measuring cylinder, subtract the initial reading from the final reading; in an overflow arrangement, collect the displaced volume after excess liquid has finished draining initially. Remove trapped air and account for any suspension thread. The object must not dissolve, absorb liquid or float partly above the surface if this simple method is to give its full volume.
Use a mass difference for a liquid
Weigh a clean empty container, then the same container holding the measured liquid volume. Subtract the empty-container mass. Alternatively, correctly tare the balance with the empty container before adding liquid. Including the container in the liquid mass produces an excessive density. Use the same container and avoid losing material between the mass and volume measurements.
Read the liquid level at eye height using the appropriate meniscus. Choose a cylinder whose graduations suit the volume rather than assuming the biggest vessel gives the best resolution. Record raw masses and volume before calculating. For a given absolute volume-reading uncertainty, a suitably larger measured sample can reduce the relative uncertainty if the apparatus and method remain appropriate.
Connect measurement problems to the calculated density
Trapped bubbles attached to an immersed object can make the observed displacement too large. With the measured object mass unchanged, the inferred density is then too small. Failure to collect some displaced liquid has the opposite volume error and can make the density too large. Derive the effect from the numerator and denominator rather than giving a direction without a reason.
Do not confuse density with mass: a large piece of a low-density material may have more mass than a small piece of a high-density material. Compare results with the appropriate temperature and material context. Repeats can assess scatter, while a balance offset, a consistent meniscus error or an unsuitable shape model needs a targeted correction.
Worked applications
Attempt these problems on paper before opening the worked reasoning. Explain your steps as well as giving a final answer.
Example 1A regular block has mass 108 g and dimensions 3.0 cm × 2.0 cm × 2.0 cm. Calculate density in g cm⁻³ and kg m⁻³.
Example 2An empty container is 45.2 g and the container plus 50.0 cm³ of liquid is 86.2 g. Find liquid density.
Example 3A 67.5 g irregular solid raises a cylinder reading from 30.0 to 55.0 cm³. Find density, then explain the effect if trapped air adds an apparent 2.0 cm³ to the displacement.
Common mistakes to avoid
Key takeaways
- You can choose dimension or displacement measurements for a solid.
- You can obtain liquid mass by difference.
- You can calculate density with consistent volume units and evaluate uncertainty.
Apply it in an exam
Question 1: A 67.5 g irregular solid raises a cylinder reading from 30.0 to 55.0 cm³. Find density, then explain the effect if trapped air adds an apparent 2.0 cm³ to the displacement.
Show answer and reasoning
2.70 g cm⁻³ without that bubble error; an excessive volume gives a lower estimate.
- True illustrative displacement = 55.0 − 30.0 = 25.0 cm³.
- Density = 67.5/25.0 = 2.70 g cm⁻³.
- Using an inflated 27.0 cm³ gives 67.5/27.0 = 2.50 g cm⁻³.
Explore further
- OCR J249 official specification (opens in a new tab)
Check the assessed scope and practical or mathematical requirements.
- Read or explore this topic (opens in a new tab)
An external explanation or interactive activity to use alongside the lesson. It may include extension material.
Return to this tomorrow
Close the notes and answer from memory. Revisit any explanation you cannot yet reconstruct.
- Which volume belongs to an irregular immersed solid?
- What is 2.7 g cm⁻³ in kg m⁻³?
Test yourself
Answer a few questions, then review anything you missed.
Keep practising
Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.