MATHEMATICS · Subjective · ISC · Physics · Physical World and Measurement · Properties of Bulk Matter
Problem
In a physics project, a student team measures the Young’s modulus of a steel wire using an optical lever arrangement. The experiment involves the following stages:
Stage 1 – Calibration of the main scale: The millimetre scale used to read the reflected beam position is later found to be expanded uniformly by 0.4 %.
Stage 2 – Loading of the wire: Ten extension readings are noted for a fixed load. The readings (in mm) relative to the initial position are:
0.18, 0.22, 0.19, 0.21, 0.60, 0.20, 0.19, 0.18, 0.23, 0.21
Stage 3 – Final calculation: The average extension from Stage 2 is substituted in the working formula to obtain Young’s modulus.
Answer the following parts:
(i) With proper justification, classify the error arising from the scale expansion in Stage 1.
(ii) From the extension data in Stage 2, identify any gross error(s) and obtain the corrected mean extension after suitable treatment of the data.
(iii) Determine the percentage random error associated with the corrected mean extension.
(iv) The working formula for Young’s modulus contains the extension as a directly proportional factor. Calculate the percentage error propagated to Young’s modulus from (a) the systematic error in scale calibration and (b) the random error in extension, and decide which one dominates the final uncertainty.