A screw gauge has main-scale division 0.5 mm, 100 circular divisions, and one full circular rotation shifts the main scale by two divisions. Zero reading is: main scale 0, circular 4. With wire, two readings are (4 divisions,20 divisions) and (4 divisions,16 divisions). Find the wire diameter and cross-sectional area.
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Question

A screw gauge has main-scale division 0.5 mm, 100 circular divisions, and one full circular rotation shifts the main scale by two divisions. Zero reading is: main scale 0, circular 4. With wire, two readings are (4 divisions,20 divisions) and (4 divisions,16 divisions). Find the wire diameter and cross-sectional area.

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G1 Physics · Accepted Answer

One rotation shifts the main scale by two divisions of 0.5 mm, so pitch=1.0 mm and circular LC=0.01 mm. Zero reading is 0.04 mm. Corrected diameter readings are 2.16 mm and 2.12 mm, giving mean d=2.14 mm and spread ±0.02 mm. Area A=πd²/4=π(1.14 mm²), with propagated uncertainty about π(0.02 mm²). Correct answer: C.