City Guilds Model Questions Vol1 2018 Engineering Question 10

A metal rod is measured with two instruments. - A steel rule has a systematic error of \(+0.2\ \text{mm}\) per \(100\ \text{mm}\) (it reads longer). A single measurement with the rule gives \(150.6\ \text{mm}\). - A Vernier caliper has a zero error of \(-0.03\ \text{mm}\) (reads low) and a random error with standard deviation \(0.05\ \text{mm}\). Three readings are obtained: \(150.32\ \text{mm},\ 150.28\ \text{mm},\ 150.35\ \text{mm}\). Assuming the steel rule's random error is negligible, determine the best estimate of the rod's true length using a weighted average that accounts for the systematic and random errors. Also compute the combined standard uncertainty of the estimate. Express the length to the nearest \(0.01\ \text{mm}\) and the uncertainty to the nearest \(0.01\ \text{mm}\).