Question

A copper rod of length $l$ is suspended from the ceiling by one of its ends. Find the relative increment of its volume $\frac{\Delta V}{V}$.

• A. $\frac{\Delta V}{V}=(1-2\mu )\frac{\Delta l}{l}$
• B. $\frac{\Delta V}{V}=(1-3\mu )\frac{\Delta l}{l}$
  
• C. $\frac{\Delta V}{V}=(1-2\mu )\frac{2\Delta l}{l}$
  
• D. $\frac{\Delta V}{V}=(1-3\mu )\frac{3\Delta l}{l}$
  

Answer 1

The correct option is A $\frac{\Delta V}{V}=(1-2\mu )\frac{\Delta l}{l}$

We can take copper rod as cylindrical rod

$v=\pi r^{2}l$

$E=\frac{\Delta l}{l}$ (longitudinal strain)

$E^{\prime }=\frac{\Delta r}{r}=-\mu E$ ,where $\mu$ is Poisson ratio,$E^{\prime }$ is lateral strain

$\frac{\Delta V}{V}=\frac{2\Delta r}{r}+\frac{\Delta l}{l}$

$\frac{\Delta V}{V}=(1-2\mu )\frac{\Delta l}{l}$