City Guilds Model Questions Vol1 2023 Engineering Question 23

The volume of an irregular stone is measured by water displacement. The initial water volume is \(V_{1}=250.0\,\text{mL}\) with an uncertainty of \(\pm0.2\,\text{mL}\) and the final volume after immersion is \(V_{2}=310.5\,\text{mL}\) with the same uncertainty. The stone's mass is measured as \(m=0.162\,\text{kg}\) with an uncertainty of \(\pm0.001\,\text{kg}\). The material density is known to be \(\rho=2.70\,\text{g\,cm}^{-3}\) with an uncertainty of \(\pm0.02\,\text{g\,cm}^{-3}\).\ Calculate the percentage relative error of the volume obtained by water displacement and that obtained by the density method (i.e., \(V=m/\rho\)). State which method provides the more reliable (smaller) relative error, giving the percentages to two decimal places.