A wire of length 'L' and radius ' $\mathrm{r}$ ' is loaded with a weight ' $\mathrm{Mg}$ '. If ' $\mathrm{Y}$ ' 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 $(\Delta \mathrm{r})$ is given by