A single sheet of aluminium foil is folded twice to produce a stack of four sheets. The total thickness of the stack of sheets is measured to be (0.80 ± 0.02) mm. This measurement is made using a digital caliper with a zero error of (−0.20 ± 0.02) mm.
What is the percentage uncertainty in the calculated thickness of a single sheet?
A 1.0% B 2.0% C 4.0% D 6.7%
Solution:
Answer: C
This challenging question involves both random and systematic error.
The zero error (−0.20) can be removed but its uncertainty (± 0.02) must be added to the measurement uncertainty.
True value of total thickness = 0.80 + 0.20 = 1.0 mm
Total uncertainty in measurement = ± (0.02 + 0.02) = ± 0.04
So the four sheets have a true thickness of (1.00 ± 0.04) mm.
A single sheet would have a thickness of (0.25 ± 0.01) mm.
Percentage error = (0.01 / 0.25) × 100% = 4%
Reference: PYQ - Oct/Nov 2015 Paper 12 Q6
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