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  4. If a wire having initial diameter of 2 mm produced the longitudinal strain of 0.1%, then the final diameter of wire is (σ =0.5)

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Q. If a wire having initial diameter of 2 mm produced the longitudinal strain of 0.1%, then the final diameter of wire is $(\sigma =0.5)$

MHT CETMHT CET 2005Gravitation

Solution:

Poisson's ratio
$\sigma=\frac{lateral strain}{longitudinal strain}$
$=-\frac{\Delta R / R}{\Delta l / l}$
$\sigma=-\frac{\Delta R}{R}\times\frac{l}{\Delta l}or|\sigma|=\frac{\Delta R}{R}\times\frac{l}{\Delta l}$
= $\frac{\Delta R}{R}|=|\sigma|\left(\frac{\Delta}{l}\right)$
or $\Delta R=0.5\times\frac{0.1}{100}\times\left(\frac{2\times10^{-3}}{2}\right)$
= 0.0005 mm