Question

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 $\pm 0.05mm$ at a load of exactly $1.0kg$. The student also measures the diameter of the wire to be $0.4mm$ with an uncertainty of $\pm 0.01mm$. Take $g=9.8m/s^2$(exact). The Young's modulus obtained from the reading is :

• A. $(2.0\pm 0.3){10}^{11}N/m^2$
• B. $(2.0\pm 0.2){10}^{11}N/m^2$
• C. $(2.0\pm 0.1){10}^{11}N/m^2$
• D. $(2.0\pm 0.05){10}^{11}N/m^2$

Answer 1

The correct option is B $(2.0\pm 0.2){10}^{11}N/m^2$

$Y=\frac{4Fl}{\pi D^2\Delta l}=2\times {10}^{11}$

$\frac{\Delta Y}{Y}=\frac{2\Delta D}{D}+\frac{\Delta L}{L}=2\times \frac{0.01}{0.4}+\frac{0.05}{0.8}=0.1125$

Thus, $\Delta Y=2\times {10}^{11}\times 0.1125=0.2\times {10}^{11}$