Problem 1.299

A bar made of material whose Young's modulus is equal to $E$ and Poisson's ratio to $\mu$ is subjected to the hydrostatic pressure $p$. Find: (a) the fractional decrement of its volume; (b) the relationship between the compressibility $\beta$ and the elastic constants $E$ and $\mu$. Show that Poisson's ratio $\mu$ cannot exceed $1 / 2$.