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Date	May 2017	Marks available	3	Reference code	17M.3.SL.TZ1.2
Level	Standard level	Paper	Paper 3	Time zone	1
Command term	State and Calculate	Question number	2	Adapted from	N/A

Question

In a simple pendulum experiment, a student measures the period T of the pendulum many times and obtains an average value T = (2.540 ± 0.005) s. The length L of the pendulum is measured to be L = (1.60 ± 0.01) m.

Calculate, using $g = \frac{{4{\pi ^2}L}}{{{T^2}}}$ , the value of the acceleration of free fall, including its uncertainty. State the value of the uncertainty to one significant figure.

[3]

In a different experiment a student investigates the dependence of the period T of a simple pendulum on the amplitude of oscillations θ. The graph shows the variation of $\frac{T}{{{T_0}}}$ with θ, where T₀ is the period for small amplitude oscillations.

The period may be considered to be independent of the amplitude θ as long as $\frac{{T - {T_0}}}{{{T_0}}} < 0.01$ . Determine the maximum value of θ for which the period is independent of the amplitude.

[2]

Markscheme

$g = \frac{{4{\pi ^2} \times 1.60}}{{{{2.540}^2}}} = 9.7907$

$\Delta g = g\left( {\frac{{\Delta L}}{L} + 2 \times \frac{{\Delta T}}{T}} \right) =$ « $9.7907\left( {\frac{{0.01}}{{1.60}} + 2 \times \frac{{0.005}}{{2.540}}} \right) =$ » 0.0997