A student measures the time T for one complete oscillation of a pendulum of length l. Her results are shown in the table.

Question 5

A student measures the time T for one complete oscillation of a pendulum of length l.

Her results are shown in the table.

l / m                             T / s

0.420 ± 0.001                         1.3 ± 0.1

She uses the formula

T = 2π √(l/g)

to calculate the acceleration of free fall g.

What is the best estimate of the percentage uncertainty in the value of g?

A 0.02%                      B 4%               C 8%               D 16%

Reference: Past Exam Paper – November 2015 Paper 12 Q5

Solution:

Answer: D. 

T = 2π √(l/g)

T² = 4π² l / g                giving  g = 4π² l / T²

Percentage uncertainty in g = (Δg / g) × 100%

Δg / g = (Δl / l) + 2(ΔT / T)

Δg / g = (0.001 / 0.420) + 2(0.1 / 1.3)

Δg / g = 0.156

Percentage uncertainty in g = 0.156 × 100 % = 15.6 % ≈ 16%