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Question

A student performs an experiment to determine the Young's modulus of a wire, exactly 2 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 mm with an uncertainty of 0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of 0.01 mm. Take g=9.8 ms2 (exact). The Young's modulus obtained from the reading is

A
(2.0±0.3)×1011Nm2
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B
(2.0±0.2)×1011Nm2
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C
(2.0±0.1)×1011Nm2
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D
(2.0±0.05)×1011Nm2
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Solution

The correct option is B (2.0±0.2)×1011Nm2
Y=4FlπD2e
Taking long both the sides
logY=log4FllogπD2e
Now, partially differentiating,
ΔYY=(2ΔDD+Δee)ΔYY=(2×0.010.4+0.050.8)ΔYY=0.1125
Also, Y=FlAe=9.8×2π(0.2)2×0.8=194.96×1092×1011
ΔY=Y×(2Δrr+Δee)ΔY=0.225×1011Y=(2±0.2)×1011Nm2

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