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In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), using a scale of least count = 1 mm, a weight of mass 1kg (measured using a scale of least count = 1g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count = 0.001 cm). What will be the fractional error in the value of Young's Modulus determined by this experiment ?

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

Correct answer: 1.4%

Solution

The fractional error in the value of Young's Modulus is calculated by considering the uncertainties in the measurements of radius, length, mass, and elongation. Each measurement contributes to the overall uncertainty, and when combined, they yield a total fractional error of 1.4%, making option D the correct choice.

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