1.State Hooke's Law and draw the stress-strain curve for a metallic wire clearly marking yield point and breaking point.
Sol: Stress is proportional to strain within elastic limit: $\sigma = Y \epsilon$. Curve linear up to proportional limit, reaches yield point (plastic deformation starts), and ultimate tensile strength before fracture.
2.A steel wire of length $2\text{ m}$ and cross-sectional area $2\text{ mm}^2$ is stretched by $1\text{ mm}$ under load. Find Young's Modulus if load is $200\text{ N}$.
Sol: $Y = \frac{F L}{A \Delta L} = \frac{200 \times 2}{(2 \times 10^{-6}) \times (1 \times 10^{-3})} = \frac{400}{2 \times 10^{-9}} = 2 \times 10^{11}\text{ N/m}^2$.
3.Define Poisson's ratio $\sigma$ and state its theoretical limits.
Sol: Ratio of lateral strain to longitudinal strain: $\sigma = -\frac{\Delta d / d}{\Delta L / L}$. Theoretical limits: $-1 \le \sigma \le 0.5$. Practical range for metals: $0.2 \text{ to } 0.4$.
