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A screw gauge is used to measure the diameter of a wire. The main scale has a pitch of 0.5 mm, and the circular scale is divided into 100 equal parts. A full rotation of the circular scale moves the main scale by two divisions. The following readings were recorded during the measurements: Measurement condition | Main scale reading | Circular scale reading When gauge arms touch without the wire | 0 divisions | 4 divisions First measurement with wire | 4 divisions | 20 divisions Second measurement with wire | 4 divisions | 16 divisions Based on these readings, what are the diameter and cross-sectional area of the wire as determined by the screw gauge?

1. 2.22 ± 0.02 mm, π(1.23 ± 0.02) mm²
2. 2.22 ± 0.01 mm, π(1.23 ± 0.01) mm²
3. 2.14 ± 0.02 mm, π(1.14 ± 0.02) mm²
4. 2.14 ± 0.01 mm, π(1.14 ± 0.01) mm²

Correct answer: 2.14 ± 0.02 mm, π(1.14 ± 0.02) mm²

Solution

The screw gauge readings are corrected for the zero error, and the diameter is calculated as 2.14 mm with an uncertainty of ±0.02 mm. The cross-sectional area is then determined using the formula πr², giving π(1.14 ± 0.02) mm².

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