AS Physics: Physical Quantities, Units and Measurement — 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: Physical Quantities and Units revision notes

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Questions

1. State the five SI base quantities and units required at this level (Cambridge 9702), and the quantity each measures. [3]

2. Express the newton and the joule in SI base units. [2]

3. Use homogeneity to check whether v² = u² + 2as is dimensionally consistent, and state what this does not prove. [3]

4. Classify each as scalar or vector: speed, displacement, energy, momentum, temperature, force. [3]

5. Two forces of 8.0 N and 6.0 N act at right angles.

(a) Calculate the magnitude of the resultant. [2] (b) Calculate its direction relative to the 8.0 N force. [2]

6. A force of 45 N acts at 25° above the horizontal.

(a) Calculate the horizontal and vertical components. [2] (b) Explain how you decided which used cosine. [1]

7. A length is measured as 84.2 mm with a rule having 1 mm divisions, and a second length as 21.6 mm.

(a) State the uncertainty in each reading. [1] (b) Calculate the uncertainty in their difference. [2] (c) Calculate the percentage uncertainty in the difference and comment. [3]

8. A cube’s side is measured to 2%. Calculate the percentage uncertainty in its volume. [2]

9. A student repeats a timing measurement several times and finds the readings cluster tightly together, but consistently below the accepted value. Explain, in terms of systematic and random error, why the readings are precise but not accurate. [3]

10. A rectangular block has length l = (12.0 ± 0.1) cm and width w = (5.0 ± 0.1) cm. Calculate the percentage uncertainty in the area. [3]

11. Convert 250 μA to amperes, and 3.2 mm to metres, giving each answer in standard form, and state which SI prefix each conversion uses. [2]

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Answers

1. kilogram (mass), metre (length), second (time) [1]; ampere (current), kelvin (temperature) [1] [1]. (The full SI system has seven base units in total, adding the mole for amount of substance and the candela for luminous intensity, but Cambridge 9702 only requires recall of these five.)

2. N = kg m s⁻² [1]; J = kg m² s⁻² [1].

3. LHS: (m s⁻¹)² = m² s⁻². RHS: (m s⁻¹)² = m² s⁻², and 2as = (m s⁻²)(m) = m² s⁻² [1]. Both sides have the same base units, so the equation is homogeneous [1]. This does not prove the equation is correct, because a dimensionless constant could still be wrong [1].

4. Scalars: speed, energy, temperature [1] [1]. Vectors: displacement, momentum, force [1].

5. (a) R = √(8.0² + 6.0²) [1] = 10.0 N [1]. (b) θ = tan⁻¹(6.0 ÷ 8.0) [1] = 36.9° from the 8.0 N force [1].

6. (a) Horizontal = 45 cos 25° = 40.8 N [1]; vertical = 45 sin 25° = 19.0 N [1]. (b) The angle is measured from the horizontal, so the horizontal component is adjacent to the angle and uses cosine [1].

7. (a) ±0.5 mm each [1]. (b) For a difference, absolute uncertainties add: 0.5 + 0.5 = ±1.0 mm [1] [1]. (c) Difference = 84.2 − 21.6 = 62.6 mm [1] % uncertainty = (1.0 ÷ 62.6) × 100 = 1.6% [1]. Subtracting two similar values would give a much larger percentage uncertainty, so it is best avoided where possible [1].

8. Volume ∝ (side)³, so % uncertainty = 3 × 2% [1] = 6% [1].

9. The tight clustering shows precision — the random error affecting the readings is small [1]. But every reading is displaced in the same direction from the true value, which is the signature of a systematic error (for example a zero error or a consistent reaction-time delay) [1]. Systematic error affects accuracy, not precision, so the readings can be precise (close to each other) without being accurate (close to the true value), and repeating and averaging would not remove the offset [1].

10. % uncertainty in l = (0.1 ÷ 12.0) × 100 ≈ 0.83% [1]; % uncertainty in w = (0.1 ÷ 5.0) × 100 = 2.0% [1]. Since area = l × w, the percentage uncertainties add: 0.83% + 2.0% ≈ 2.8% [1].

11. 250 μA = 250 × 10⁻⁶ A = 2.5 × 10⁻⁴ A, using the micro (10⁻⁶) prefix [1]; 3.2 mm = 3.2 × 10⁻³ m = 3.2 × 10⁻³ m, using the milli (10⁻³) prefix [1].

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Where marks are usually lost

• Assuming homogeneity proves an equation correct.
• Swapping sine and cosine when resolving.
• Adding percentage uncertainties when subtracting quantities.
• Forgetting to multiply by the power when a quantity is cubed.
• Rounding an intermediate value before using it in a later step, which drifts the final answer — carry extra significant figures through the working and only round at the end. Also, give a final numerical answer as a decimal to the precision asked for, not left as a surd or a fraction.
• Confusing precision with accuracy — tightly clustered readings can still all be wrong if a systematic error is present.
• Losing track of a prefix’s power of ten when converting between units, especially with micro (10⁻⁶) and milli (10⁻³).

Work through the Physical Quantities and Units revision notes alongside these questions: the notes summarise the base units, prefixes and error definitions in condensed form, while these questions test whether you can apply the uncertainty-combination rules and the precision-versus-accuracy distinction to a specific numerical situation rather than just recall the rule.