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A wire of length 100 cm and diameter measured by a screw gauge (main scale reading 1 mm, circular scale reading 25, pitch 1 mm, total circular scale divisions 100) is used in Young's modulus determination by Searle's method. Given: elongation deltaₗ = 0.125 cm under tension F = 50 N, least count for normal length = 0.01 cm, least count for elongation = 0.001 cm. The maximum percentage error in Y is (8*n/10)%, where n is approximately an integer. Find n.

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

d = 1 + 25*0.01 = 1.25 mm = 0.125 cm. L = 100 cm. deltaₗ = 0.125 cm. LC of gauge = 0.01 mm = 0.001 cm. Errors: delta_d/d = 0.001/0.125 = 0.008; delta_L/L = 0.01/100 = 0.0001; delta_(deltaₗ)/deltaₗ = 0.001/0.125 = 0.008. Percentage error in Y = (delta_L/L + 2*delta_d/d + delta_(deltaₗ)/deltaₗ)*100 = (0.0001 + 2*0.008 + 0.008)*100 = (0.0001 + 0.016 + 0.008)*100 = 0.0241*100 = 2.41%. Now 8n/10 = 2.41 => n = 2.41*10/8 = 24.1/8 ~ 3.01 ~ 3.

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