Measuring Density by Water Displacement

A step-by-step lab — follow the parts in order

Physics · 1A · 7 October 2026

Today's object

Object: _______________

Container: _______________

Write both on your report sheet before you start.

1

Toolbox — the rules of uncertainty

Rule 1 & 2 — reading an instrument

  • Analogue instrument (container): uncertainty of one reading = half a division.
  • Digital instrument (balance): uncertainty = last digit shown.

Rule 3 — subtracting two readings

When you compute V = V₂ − V₁
The uncertainties of the two readings add together.
\text{uncertainty of } V = \text{one full division}

Rule 4 — relative uncertainty

A way to express uncertainty as a percentage of the value.
\text{relative uncertainty} = \frac{\text{uncertainty}}{\text{value}} \times 100\%

It lets you compare the precision of two different measurements.

Rule 5 & 6 — density combines two measurements

For a quotient like \rho = m/V, the relative uncertainties add.
\text{rel. unc. of }\rho = \text{rel. unc. of } m + \text{rel. unc. of } V

Then convert back: absolute uncertainty = relative uncertainty × value, rounded to one significant figure.

Rule 7 — reading the water level

  • Eyes level with the bottom of the meniscus — the curved surface.
  • Container standing flat on the table, not tilted.

Worked example (not your data)

1
V_1=20{,}0\text{ mL},\ V_2=32{,}0\text{ mL} \to V = 12{,}0\pm1{,}0\text{ mL}
rule 3: uncertainties add → one full division
2
\text{rel. unc. of } V = 1{,}0/12{,}0 = 8{,}3\%
rule 4
3
m = 94{,}0\pm0{,}1\text{ g} \to \text{rel. unc.} = 0{,}1\%
rule 2
4
\rho = 94{,}0/12{,}0 = 7{,}83\text{ g/cm}^3,\ \text{rel. unc.} = 8{,}4\% \to \rho = 7{,}8\pm0{,}7\text{ g/cm}^3
rule 5 and 6: add, then convert back to absolute
2

Your turn — follow Parts 1 to 5

Part 1 — The instruments

  • Fill in the instruments table on your sheet: container and balance.
  • Analogue or digital? Range? One division? Uncertainty of one reading?
Not sure about a value — call me.

Part 2 — Measuring the volume (1/2)

1
Fill the container to about two-thirds of its range with water. Read the level: this is V₁.
2
Hold the object close to the water surface and lower it slowly until fully submerged. Do not drop it from above.

Part 2 — Measuring the volume (2/2)

3
Read the new level: this is V₂.
4
V = V_2 - V_1
Then find the uncertainty of V (rule 3) and its relative uncertainty (rule 4).

Part 3 — Measuring the mass

  • Dry the object if it is wet.
  • Place it on the balance and record the mass, with its uncertainty (rule 2).
  • Find the relative uncertainty of the mass.
Remember: 1 mL = 1 cm³.

Part 4 — Density

1
\rho = m \div V \ (\text{g/cm}^3)
2
Add the relative uncertainties of m and V (rule 5) to get the relative uncertainty of ρ.
3
Convert it back into an absolute uncertainty (rule 6). Write the final result as ρ = (value ± uncertainty) g/cm³.

Part 5 — Questions

  • Compare your ρ with the material table. Which material could your object be?
  • Could you identify it with certainty — or could it be more than one material?
  • Name one source of error. Random or systematic?
  • What would you change, to be more confident next time?

Material density table

Materialρ (g/cm³)
Water1,00
Sandstone2,2 – 2,8
Limestone2,3 – 2,7
Granite2,6 – 2,7
Marble2,6 – 2,8
Slate2,7 – 2,8
Basalt2,8 – 3,0
Approximate values: real rocks vary, even within the same type.

Before you hand in

  • Both names on the sheet, group number filled in.
  • Every cell has a number and a unit.
  • One sheet per group.
  • Table and bench clean before you leave.