A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Se

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 $\pm 0.05 \mathrm{~mm}$ 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 $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ (exact). The Young's modulus obtained from the reading is\

Professor PC Thomas Classes · Answer

(b) : Young's modulus $=\frac{	ext { stress }}{	ext { strain }}$\ or $Y=\frac{4 F l}{\pi d^{2} \Delta l}$\ $=\frac{4 	imes(1 	imes 9.8) 	imes 2}{\pi 	imes\left(0.4 	imes 10^{-3}ight)^{2} 	imes\left(0.8 	imes 10^{-3}ight)}$\ $=2 	imes 10^{11} \mathrm{~N} / \mathrm{m}^{2}$.\ Now, $\frac{\Delta Y}{Y}=\frac{2 \Delta d}{d}+\frac{\Delta(\Delta l)}{\Delta l}$\ or $\Delta Y=\left(\frac{2 	imes 0.01}{0.4}+\frac{0.05}{0.8}ight) 	imes 2 	imes 10^{11} \mathrm{~N} / \mathrm{m}^{2}$\ $=0.2 	imes 10^{11} \mathrm{~N} / \mathrm{m}^{2}$.\ Hence the Young's modulus obtained from the reading is\ $(2.0 \pm 0.2) 	imes 10^{11} \mathrm{~N} / \mathrm{m}^{2}$.\