Neco 2020 Physics Question 47

An experiment to determine the acceleration due to gravity uses a simple pendulum. For three different lengths the average periods (in seconds) are recorded as follows: length \(L_{1}=0.50\,\text{m}\) with \(\overline{T}_{1}=1.42\,\text{s}\); length \(L_{2}=0.75\,\text{m}\) with \(\overline{T}_{2}=1.73\,\text{s}\); length \(L_{3}=1.00\,\text{m}\) with \(\overline{T}_{3}=2.00\,\text{s}\). For each length the standard deviation of the period measurements is \(0.02\,\text{s}\). The length of each pendulum is measured with an uncertainty of \(\pm0.001\,\text{m}\). Using \(g = 4\pi^{2}L/T^{2}\), (a) calculate the value of \(g\) for each length, (b) determine the combined standard uncertainty of the mean value of \(g\) obtained by averaging the three results, assuming the uncertainties in length and period are independent, and (c) name one possible systematic error affecting all measurements and a precaution to minimise it.