$A$ wire of length $L$ and radius $r$ is loaded with a weight $Mg$. If $Y$ and $\sigma$ denote the Young's modulus and Poisson's ratio of the material of the wire respectively,then the decrease in the radius of the wire $(\Delta r)$ is given by:

• A
  $\frac{MgY}{\pi r \sigma}$
• B
  $\frac{Mg \sigma}{\pi rY}$
• C
  $\frac{\sigma \pi r}{MgY}$
• D
  $\frac{Mgr}{\sigma \pi Y}$