Question 24
Four identical rods
have a square cross-section. The rods are placed side by side and their total
width is measured with vernier calipers, as shown.
The measurement is
(8.4 ± 0.1) mm and the zero reading on the calipers is (0.0 ± 0.1) mm.
What is the width of
one rod?
A (2.10
± 0.025) mm
B (2.10
± 0.05) mm
C (2.1
± 0.1) mm
D (2.1 ± 0.2) mm
Reference: Past Exam Paper – November 2015 Paper 11 Q5
Solution:
Answer: B.
The
vernier caliper contains a zero error given by 0.0 ± 0.1 mm. The measurement should be corrected to include the zero
error.
Corrected
measurement: W = 8.4 ± 0.2 mm
Width
of 4 rods: W = 8.4 ± 0.2 mm
Width
of 1 rod: x = W / 4 = 2.1 mm
Δx =
¼ × ΔW = 0.2 / 4 = 0.05 mm
The
uncertainty of 0.1 mm does not apply throughout. The purpose of measuring four rods
rather than one rod is to reduce the effect of random error.
Width of 1 rod = 2.1 ±
0.05 mm
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