A Level Physics: Uncertainties Practice

Part 1: Absolute & Percentage Uncertainty

Q1. Analogue vs. Digital Readings

A student measures the potential difference across a resistor using two different voltmeters:

State the absolute uncertainty for each reading.

Voltmeter A (Analogue): ±0.1 V

Rule: ± half the smallest division (0.2 / 2 = 0.1).

Voltmeter B (Digital): ±0.01 V

Rule: ±1 in the last significant digit displayed.

Q2. Repeated Readings

A wire diameter is measured 5 times with a micrometer:
0.24 mm, 0.26 mm, 0.23 mm, 0.29 mm, 0.25 mm.

Calculate the mean diameter and its absolute uncertainty.

Mean: (0.24+0.26+0.23+0.29+0.25) / 5 = 0.25 mm (to 2 s.f.)

Uncertainty: ±0.03 mm

Rule: Uncertainty = ½ × Range
Range = 0.29 - 0.23 = 0.06 mm
Uncertainty = 0.06 / 2 = 0.03 mm

Final Answer: 0.25 ± 0.03 mm

Q3. Multiplying Quantities (Percentage Rule)

The force on an object is F = 20 ± 1 N and the distance moved is d = 5.0 ± 0.2 m.

Calculate the work done (W = F × d) and the absolute uncertainty in the work done.

Step 1: Calculate Value
W = 20 × 5.0 = 100 J

Step 2: Calculate % Uncertainties
% in F = (1/20) × 100 = 5%
% in d = (0.2/5.0) × 100 = 4%

Step 3: Add % Uncertainties (Multiplication Rule)
Total % Uncertainty = 5% + 4% = 9%

Step 4: Convert back to Absolute
9% of 100 J = 9 J

Final Answer: 100 ± 9 J

Q4. Powers and Indices

The radius of a circle is measured as r = 4.0 ± 5%.

Calculate the percentage uncertainty in the Area (A = πr²).

Answer: 10%

Rule: For A = rⁿ, the % uncertainty is n × (% uncertainty in r).
Here, n = 2.
Total % = 2 × 5% = 10%.

Note: Constants like π have zero uncertainty.

Q5. Gradient Uncertainty

A student plots a graph of Force vs. Acceleration. They draw a Line of Best Fit (LOBF) and a Line of Worst Fit (LOWF) passing through the error bars.

Calculate the percentage uncertainty in the gradient.

Answer: 6.25%

Formula: % Uncertainty = (|m_best - m_worst| / m_best) × 100

Calculation: (|2.40 - 2.55| / 2.40) × 100
= (0.15 / 2.40) × 100 = 6.25%