A laboratory student has to measure the diameter of a steel ball bearing whose true…
PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors
Problem
A laboratory student has to measure the diameter of a steel ball bearing whose true value is expected to be about 1.25cm. Three different instruments are available.
• Ordinary metre scale: least count 1mm
• Vernier callipers: least count 0.01cm
• Screw gauge: least count 0.001cm
During the measurement the laboratory temperature is fluctuating, introducing an additional systematic uncertainty of ±0.002cm in every reading.
Assume that the absolute uncertainty due to instrumental resolution is equal to half the least count.
Attempt all parts.
(i) For each instrument, state the reading you would record if the ball bearing exactly fills 1.25cm on that instrument’s scale. Write the value with the correct number of significant figures.
(ii) For each instrument, calculate the absolute uncertainty arising from instrumental resolution.
(iii) Add the given temperature‐related uncertainty to obtain the total absolute uncertainty for each instrument.
(iv) Determine the percentage uncertainty in the diameter measurement for each instrument.
(v) The experiment requires that the percentage uncertainty must not exceed 0.40%. Identify which instrument(s), if any, satisfy this requirement and give a brief justification based on your calculations.