Question

A wire of radius 0.2 mm is extended by 0.1% of its length when it supports a load of 1 kg. Calculate Young’s modulus for the material of the wire.’

Answer 1

The Young's modulus can be obtained as

$E=\dfrac{F/S} {\Delta l/l},$ where F is the force exerted on wire, namely F=mg, S is the area of the wire section, $\Delta l/l = 0.1\%=10^{-3}.$

Therefore,

$E=\dfrac{mg/(\pi r^2)}{10^{-3}}=\dfrac {1\,\text{kg}\cdot9.81\,\text{N/m}/(\pi (2\cdot10^{-4}\,\text{m})^2)}{10^{-3}}= 7.8\cdot10^{10}\,\text{Pa}=78\,\text{GPa}$