A student performs an experiment to determine the young’s modulus of a wire, exactly 2m long by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8mm with an uncertainty of ± 0.05mm at load of exactly 1.0kg. The student also measures the diameter of the wire to be 0.4mm with an uncertainty of ±0.01mm . Take G = 9.8 m/s2 (exact) then Y=?

# A student performs an experiment to determine the young’s modulus of a wire, exactly 2m long by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8mm with an uncertainty of $±$ 0.05mm at load of exactly 1.0kg. The student also measures the diameter of the wire to be 0.4mm with an uncertainty of $±$0.01mm . Take G = 9.8 m/s2 (exact) then Y=?

1. A

(2.0 $±$ 0.3) $×$1011N /m2

2. B

(2.0 $±$ 0.2) $×$1011N /m2

3. C

(2.0 $±$ 0.1) $×$1011N /m2

4. D

(2.0 $±$ 0.5) $×$1011N /m2

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### Solution:

We know that,

$Y=\frac{4Fl}{{\mathrm{\pi D}}^{2}\mathrm{e}}$

taking log,

$\mathrm{log}Y=\mathrm{log}4Fl-\mathrm{log}\pi {D}^{2}e$

now partially differentiating,

$∆Y=-Y×\left(\frac{2∆r}{r}+\frac{∆e}{e}\right)=0.22×{10}^{11}$

$Y=\left(2±0.2\right)×{10}^{11}N{m}^{-2}$

Hence the correct answer is $\left(2±0.2\right)×{10}^{11}N{m}^{-2}.$

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