Alice and Bob are re-enacting Cao Chong’s weighing experiment.They found two types of rocks, ~50 kg in weight and ~20 kg inweight, respectively. Now for an elephant that weighs ~1 ton, themeasurement could be done with 20 of 50 kg rocks, or 50 of 20 kgrocks.
Alice argues that the first approach gives a more precise resultas more rocks will introduce more error. Bob argues that the secondapproach is better as the error from different rocks tends tocancel out each other.
Calculate the uncertainty of the final result for the twoapproaches for the following two cases: (A) The absolutemeasurement uncertainty for each rock is fixed at 0.5 kg. (B) Therelative measurement uncertainty for each rock is fixed at 2%.Which of the above two approaches win out for the two cases? (C) Isthere a mathematical form of uncertainty-weight relationship foreach rock that would lead to equal uncertainty of the final resultsfor the two approaches?
