Neco 2023 Physics Question 38

In a simple pendulum experiment to determine the acceleration due to gravity, a student measures the length \(L = 1.00\ \text{m}\) with a meter rule that has an uncertainty of \(\pm 0.5\ \text{mm}\). The period \(T\) is measured with a stopwatch that has an uncertainty of \(\pm 0.2\ \text{s}\). Five timing measurements are taken and averaged. The relation used is \(g = \dfrac{4\pi^{2}L}{T^{2}}\).\n\n(a) Calculate the percentage contribution of the length uncertainty and the timing uncertainty to the overall uncertainty in the calculated value of \(g\).\n\n(b) The student can either replace the ruler with one that has an uncertainty of \(\pm 0.1\ \text{mm}\) or replace the stopwatch with a digital timer that has an uncertainty of \(\pm 0.02\ \text{s}\). Assuming all other uncertainties remain unchanged, which single improvement will most effectively reduce the total uncertainty in \(g\)? Justify your answer.