A wire of length 2.0 m and resistivity 1.7 × 10⁻⁸ Ω m is measured by a screw gauge. The pitch is 0.5 mm and the circular scale has 100 divisions. The pitch-scale reading is 0.50 mm, the 26th circular division coincides, and the zero error is -0.01 mm. The resistance of the wire is closest to:
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Question

A wire of length 2.0 m and resistivity 1.7 × 10⁻⁸ Ω m is measured by a screw gauge. The pitch is 0.5 mm and the circular scale has 100 divisions. The pitch-scale reading is 0.50 mm, the 26th circular division coincides, and the zero error is -0.01 mm. The resistance of the wire is closest to:

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G1 Physics · Accepted Answer

LC = 0.5/100 = 0.005 mm. Observed diameter = 0.50 + 26(0.005) = 0.630 mm. Corrected diameter = 0.630 + 0.010 = 0.640 mm = 6.40 × 10⁻⁴ m. Area = πd²/4 ≈ 3.22 × 10⁻⁷ m². Therefore R = ρL/A ≈ 0.106 Ω.