Measurement and Density: Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Measurement and Density revision notes

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Section A

1. State the SI unit and a suitable measuring instrument for length, mass, time and volume. [4]

2. State the equation for density and its SI unit. [2]

Section B

3. A metal block measures 4.0 cm × 3.0 cm × 2.5 cm and has a mass of 240 g.

(a) Calculate its volume in cm³. [2] (b) Calculate its density in g/cm³. [2] (c) Convert this to kg/m³. [2]

4. Describe how you would measure the density of an irregular stone accurately, stating the equipment and the measurements taken. [6]

5. Explain why an object floats or sinks in a liquid, in terms of density, and predict what happens to a block of density 700 kg/m³ placed in water. [3]

6. A student times 20 oscillations of a pendulum rather than one.

(a) Explain why. [2] (b) The 20 oscillations take 28.4 s. Calculate the period. [2] (c) State two ways the student could improve the accuracy of the timing. [2]

7. Explain the difference between the resolution of an instrument and the accuracy of a measurement, giving an example. [3]

Section C

8. Distinguish between mass and weight, and explain why an object’s weight changes on the Moon while its mass does not. [4]

9. State the equation linking gravitational field strength, weight and mass, and explain why g has the same numerical value as the acceleration of free fall. [3]

10. A block has a mass of 540 g and a volume of 200 cm³. Calculate its density in g/cm³. [2]

11. Describe how you would measure the density of a liquid, stating the equipment and how the mass is found. [4]

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Answers

1. Length — metre; a ruler, or vernier callipers or a micrometer for small lengths [1]. Mass — kilogram; a balance [1]. Time — second; a stopwatch or light gates [1]. Volume — cubic metre (or cm³); a measuring cylinder or displacement can [1].

2. density = mass ÷ volume [1]; SI unit kg/m³ [1].

3. (a) 4.0 × 3.0 × 2.5 [1] = 30 cm³ [1]. (b) 240 ÷ 30 [1] = 8.0 g/cm³ [1]. (c) × 1000 [1] = 8000 kg/m³ [1].

4. Measure the mass on a digital balance, recording the reading to the nearest 0.1 g [1] [1]. Part-fill a measuring cylinder with water and record the initial volume at eye level, reading from the bottom of the meniscus [1]. Lower the stone in gently on a thread so no water splashes out, and record the new volume [1]. The volume of the stone is the difference between the two readings [1]. Calculate density = mass ÷ volume, repeating and taking a mean [1].

5. An object floats if its density is less than that of the liquid and sinks if it is greater [1] [1]. A block of density 700 kg/m³ is less dense than water (1000 kg/m³), so it floats [1]. (Background, beyond this subtopic — quantitatively, it floats with about 70% of its volume submerged, since a floating object displaces its own weight of fluid.)

6. (a) The uncertainty from the student’s reaction time is the same whether one or twenty oscillations are timed [1], so dividing by 20 makes the percentage uncertainty in the period about twenty times smaller [1]. (b) T = 28.4 ÷ 20 [1] = 1.42 s [1]. (c) Any two: repeat the timing and take a mean [1]; use a fiducial marker at the centre of the swing, where the bob moves fastest and the timing point is most sharply defined [1]; use light gates or video timing to remove human reaction time altogether [1].

7. Resolution is the smallest change in the quantity that the instrument can detect — for example a ruler with millimetre divisions has a resolution of 1 mm [1]. Accuracy is how close the measurement is to the true value [1]. A high-resolution instrument can still be inaccurate — a balance reading to 0.001 g that has not been zeroed will give precise but systematically wrong results [1].

8. Mass is the quantity of matter in an object, which also gives it inertia — resistance to a change in its state of motion [1]. Weight is the force of gravity acting on that mass [1]. On the Moon, the gravitational field is weaker, so the same mass weighs less there [1], but the amount of matter — the mass — is unchanged [1].

9. g = W/m [1]. This is numerically the same as the acceleration of free fall because Newton’s second law, F = ma, applied to a falling mass gives W = mg, so g describes both the force per unit mass and the resulting acceleration — the same underlying relationship viewed two ways [2].

10. ρ = m/V = 540 ÷ 200 [1] = 2.7 g/cm³ [1].

11. Measure a known volume of the liquid in a measuring cylinder [1]. Find the mass of the liquid on a balance, by weighing the container with the liquid and subtracting the mass of the empty container [1] [1]. Apply density = mass ÷ volume [1].

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Where marks are usually lost

• Converting g/cm³ to kg/m³ by multiplying by 100 instead of 1000.
• Reading a measuring cylinder from the top of the meniscus.
• Saying an object floats because it is “light”.
• Confusing resolution with accuracy.