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To measure the Young's Modulus of a wire, the following quantities are measured: radius r = 0.2 cm (least count 0.001 cm), length L = 1 m (least count 1 mm), mass m = 1 kg (least count 1 g), and elongation delta_L = 0.5 cm (least count 0.001 cm). What is the percentage error in the calculated value of Young's Modulus?

1. 0.14%
2. 0.9%
3. 9%
4. 1.4%

Correct answer: 1.4%

Solution

Substituting the least counts: %Y = 0.1% + 0.1% + 2(0.5%) + 0.2% = 1.4%. The dominant term is 2*%error(r) because r is small relative to its least count.

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