Neco 2017 Physics Question 35

In a simple pendulum experiment the length of the pendulum is measured with a meter rule as \(L_{\text{meas}} = 0.500\ \text{m}\). The rule has a known systematic error of +0.005\,m, so the true length is \(L = 0.505\ \text{m}\). To determine the period, the time for 20 complete oscillations is recorded as \(t = 28.5\ \text{s}\) using a stopwatch that has a random error of ±0.2\,s per timing. (a) Calculate the acceleration due to gravity \(g\) using the corrected length and the measured period. (b) Estimate the combined standard uncertainty in \(g\) considering the random timing error and an assumed random length measurement uncertainty of ±0.001\,m. (c) Suggest one experimental precaution to reduce the systematic length error.