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A student performs an experiment to determine the Young's modulus of a wire, exactly \( 2 \mathrm{~m} \) long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be \( 0.8 \mathrm{~mm} \) with an uncertainty of \( \pm \) \( 0.05 \mathrm{~mm} \) at a load of exactly \( 1.0 \mathrm{~kg} \). The student also measures the diameter of the wire to be \( 0.4 \mathrm{~mm} \) with an uncertainty of \( \pm 0.01 \mathrm{~mm} \). Take \( g=9.8 \mathrm{~m} / \mathrm{s}^{2} \) (exact). The Young's modulus obtained from the reading is [IIT-JEE 2007]
(a) \( (2.0 \pm 0.3) \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} \) (b) \( (2.0 \pm 0.2) \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} \)
(c) \( (2.0 \pm 0.1) \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} \) (d) \( (2.0 \pm 0.05) \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} \)
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