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.

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