OCR A Level Physics: Foundations of Physics — 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: Foundations of Physics study guide | Foundations of Physics revision notes

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Questions

1. State the SI base unit of (a) mass (b) current (c) amount of substance. [3]

2. Distinguish between a systematic error and a random error, giving one example of each. [4]

3. Momentum p is given by p = mv, where m is in kg and v is in m s⁻¹. Show that the SI base units of momentum are kg m s⁻¹, and use this to check whether the equation F = p/t is homogeneous, given that force is measured in kg m s⁻² (newtons). [4]

4. A length is measured as 25.0 cm ± 0.2 cm.

(a) Calculate the percentage uncertainty in this measurement. [2] (b) A second length, 10.0 cm ± 0.1 cm, is added to it. Calculate the absolute uncertainty in the total length. [2]

5. A density is calculated using ρ = m/V, where mass m = 250 g ± 2 g and volume V = 40.0 cm³ ± 0.5 cm³.

(a) Calculate the percentage uncertainty in m and in V. [2] (b) Calculate the percentage uncertainty in the calculated density. [2]

6. A quantity g is calculated from a measured period T using an equation in which g depends on T². The percentage uncertainty in T is 1.5%. Calculate the percentage uncertainty in g. [2]

7. State whether each quantity is a scalar or a vector: (a) energy (b) displacement (c) acceleration (d) mass. [4]

8. A force of 25 N acts at 40° above the horizontal. Calculate its horizontal and vertical components. [3]

9. Two forces act on an object: 12 N due north and 9 N due east. Calculate the magnitude and direction of the resultant force. [4]

Answers

1. (a) kilogram, kg [1]. (b) ampere, A [1]. (c) mole, mol [1].

2. A systematic error is a consistent bias affecting every reading in the same way, such as a zero error on an instrument [2]. A random error is unpredictable variation between repeated readings, such as fluctuation in reaction time when using a stopwatch [2].

3. Momentum = mass × velocity, so its units are kg × (m s⁻¹) = kg m s⁻¹ [1]. For F = p/t, the units on the right-hand side are (kg m s⁻¹) ÷ s = kg m s⁻² [1], which matches the given unit of force, kg m s⁻² [1]; since both sides have the same base units, the equation is homogeneous [1].

4. (a) (0.2 ÷ 25.0) × 100 = 0.8% [2]. (b) Since the two lengths are combined by addition, absolute uncertainties are added: 0.2 + 0.1 = ±0.3 cm [2].

5. (a) Percentage uncertainty in m = (2 ÷ 250) × 100 = 0.8% [1]. Percentage uncertainty in V = (0.5 ÷ 40.0) × 100 = 1.25% [1]. (b) Since density is found by division, percentage uncertainties are added: 0.8% + 1.25% = 2.05% [2].

6. Since g depends on T², the percentage uncertainty in T is doubled: 1.5% × 2 = 3.0% [2].

7. (a) Scalar [1]. (b) Vector [1]. (c) Vector [1]. (d) Scalar [1].

8. Horizontal component = 25 × cos(40°) = 25 × 0.766 = 19.2 N [1] [1]. Vertical component = 25 × sin(40°) = 25 × 0.643 = 16.1 N [1].

9. Since the two forces are perpendicular, use Pythagoras: resultant = √(12² + 9²) = √(144 + 81) = √225 = 15 N [2]. Direction: tan θ = 9 ÷ 12, so θ = tan⁻¹(0.75) = 36.9° east of north [2].

A note on the power rule for uncertainties

Question 6 tests a rule that is easy to forget under exam pressure: when a measured quantity is raised to a power inside an equation, its percentage uncertainty is multiplied by that power, not simply carried through unchanged. This matters specifically because so many A Level physics equations involve a squared term — period squared in a pendulum or spring equation, radius squared in an area or Coulomb’s law calculation, velocity squared in a kinetic energy calculation — so a measurement that looks only moderately uncertain on its own can dominate the uncertainty in a final calculated result once its power in the equation is accounted for. Question 7 in the Practical Skills practice questions makes exactly this point in the context of a real pendulum experiment, and it is worth treating the two topics’ uncertainty rules as one connected skill rather than revising them separately.

Where marks are usually lost

• Quoting an SI base unit incorrectly, for example writing “kilograms” as “kgs” or confusing a base unit with a commonly used non-SI unit.
• Adding absolute uncertainties when quantities are combined by multiplication or division, or adding percentage uncertainties when quantities are combined by addition or subtraction — these two combination rules are frequently swapped.
• Forgetting to multiply a percentage uncertainty by the power when a quantity is squared, cubed, or otherwise raised to a power within an equation.
• Swapping sine and cosine when resolving a vector into components, particularly under time pressure.
• Using Pythagoras’ theorem to combine two vectors that are not actually perpendicular, without checking the angle between them first.

Approaching foundations of physics questions

For any uncertainty question, first identify how the quantities are being combined — addition or subtraction calls for adding absolute uncertainties, while multiplication or division calls for adding percentage uncertainties — before choosing which rule to apply, since applying the wrong one of these two rules is the single most common error across this entire topic. When a measured quantity appears raised to a power in the equation being used, always check for and apply the power rule explicitly, writing out the multiplication rather than assuming it will not matter. For vector questions, sketch a labelled diagram before calculating anything, since this both reduces the chance of a sin/cos mix-up and earns method marks even if a final numerical answer contains an error; and before using Pythagoras’ theorem to find a resultant, confirm the two vectors involved are genuinely perpendicular, since a vector triangle or component-resolution method is required instead whenever they are not.