A metal has Y = 1.2 × 10¹¹ Pa and G = 4.5 × 10¹⁰ Pa. Find its Poisson's ratio and its bulk modulus.

Step 1. Poisson's ratio. $\sigma = \dfrac{Y}{2G} - 1 = \dfrac{1.2 \times 10^{11}\ \text{Pa}}{9.0 \times 10^{10}\ \text{Pa}} - 1 = 0.333$.

Step 2. Bulk modulus. $B = \dfrac{Y}{3(1 - 2\sigma)} = \dfrac{1.2 \times 10^{11}\ \text{Pa}}{3 \times 0.333} = 1.2 \times 10^{11}\ \text{Pa}$.