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 \(1 / 2\).