Question

When a metal wire is stretched by a load, the fractional change in its volume $\Delta V/V$ is proportional to?

• A. $-\frac{\Delta l}{l}$
• B. ${\left(\frac{\Delta l}{l}\right)}^2$
• C. $\sqrt{\Delta l/l}$
• D. None of these

Answer 1

The correct option is A $-\frac{\Delta l}{l}$

$v=\frac{\pi d^{2}l}{4}$

$⟹\frac{\Delta V}{V}=\frac{2\Delta d}{d}+\frac{\Delta l}{l}$

$⟹d\frac{\Delta V}{V}=\frac{(1-2\sigma )\Delta l}{l}$

$(\frac{\Delta d}{d}=\frac{-\sigma \Delta l}{l})$

where $\sigma$ is Poisson's ratio.