Determine density of sinking irregular solids
Combine a balance mass with the increase in cylinder volume after full submersion.
Section P1.4 · Density
Exam scope and assessment notes
Mapped to the named 0973 section using teaching from the corresponding single-science course. A 0973-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade. This qualification reports two grades on the 9–1 scale; confirm the entry route for your zone and exam series.
Before you begin
- Read a measuring cylinder at eye level.
- Subtract initial from final volume.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which cylinder value is the solid's volume?
What you will learn
- Describe displacement for an insoluble sinking solid.
- Calculate density using the solid's own volume.
Measure mass and displacement
Measure the dry solid's mass with a zeroed balance. Choose a liquid in which it sinks without dissolving or reacting, and record the initial cylinder volume. Lower the object carefully until fully submerged, remove trapped bubbles and read the final volume with the same meniscus method. The solid volume is the increase, provided no liquid is lost.
For an original 48 g sample with water readings 38 cm³ before and 54 cm³ after, the sample volume is 16 cm³ and density is 48/16 = 3.0 g/cm³. The cylinder diagram shows those two readings; the supplied mass is a separate balance measurement, not something inferred from the drawing.
Check the method's conditions
A floating object is only partly submerged, so its ordinary displacement reading does not give its full volume. A soluble or reacting object also violates the unchanged-solid assumption. The syllabus method here concerns an irregular solid that sinks in the chosen liquid; another method must be justified for other samples.
Trapped bubbles add volume without adding the sample's measured dry mass. This overestimates volume and underestimates density. Splashing or failing to submerge completely can reduce the recorded increase and overestimate density. Repeat a careful measurement and use a suitably fine cylinder scale; repeating the same flawed method does not remove systematic error.
Sources for this lesson
Pause and explain
A 48 g stone raises water from 38 to 54 cm³. What is density?
Worked example
A 48 g insoluble stone raises water from 38 to 54 cm³. Find density.
Show the worked solution
- Solid volume = 54 − 38 = 16 cm³.
- Density = 48/16.
- ρ = 3.0 g/cm³.
Answer 3.0 g/cm³.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find density for a 48 g stone that raises water from 38 to 54 cm³.
Give me a hint
Find the volume increase before calculating the ratio.
Compare my reasoning
- Volume = 54 − 38 = 16 cm³.
- ρ = 48/16.
- Density = 3.0 g/cm³.
3.0 g/cm³.
Look for these in your work
- Use the displacement difference.
- Keep the dry solid mass.
A 70.2 g solid raises water from 22.0 to 48.0 cm³. Calculate density.
Give me a hint
Both cylinder readings include the same original liquid.
Compare my reasoning
- Volume increase = 26.0 cm³.
- 70.2/26.0 = 2.7.
- Density = 2.7 g/cm³.
2.7 g/cm³.
Look for these in your work
- Subtract readings.
- Give a density unit.
A 48 g sample truly occupies 16 cm³, but attached air bubbles add 4 cm³ to its displacement. Find the incorrect inferred density and compare it with the true value.
Give me a hint
The bubbles change the apparent volume, not the sample mass.
Compare my reasoning
- Apparent volume = 16 + 4 = 20 cm³.
- Incorrect density = 48/20 = 2.4 g/cm³.
- True density is 3.0 g/cm³, so the bubble error gives an underestimate.
2.4 g/cm³ instead of 3.0 g/cm³; an underestimate.
Look for these in your work
- Include the unwanted air volume.
- Explain the error direction.
Common mistakes
- Divide by displaced volume, not the final total reading.
- The object must be fully submerged without trapped air.
- A dissolving or floating sample needs a different justified method.
What can you explain now?
A 70.2 g sample raises water from 22.0 to 48.0 cm³. What is its density?
Compare with the explanation
2.7 g/cm³.
The volume increase is 26.0 cm³; divide 70.2 by 26.0.
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Make it stick
Describe an irregular-solid density method and predict the effects of bubbles and incomplete submersion.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.