1.State Hooke's Law of elasticity.
Sol: Within elastic limit, stress is directly proportional to strain: $\text{Stress} = E \times \text{Strain}$.
2.Define Young's Modulus, Bulk Modulus, and Shear Modulus.
Sol: $Y = \frac{\text{Longitudinal Stress}}{\text{Longitudinal Strain}}$, $B = \frac{-\Delta P}{\Delta V / V}$, $\eta = \frac{\text{Shear Stress}}{\text{Shear Strain}}$.
3.What is Poisson's ratio? Write its theoretical range.
Sol: Ratio of lateral strain to longitudinal strain: $\sigma = -\frac{\Delta d / d}{\Delta L / L}$. Theoretical range: $-1 \le \sigma \le 0.5$.
4.Write the expression for strain energy stored in a stretched wire.
Sol: $U = \frac{1}{2} \times \text{Load} \times \text{Extension} = \frac{1}{2} \times \text{Stress} \times \text{Strain} \times \text{Volume}$.
5.A steel wire of length $2 \text{ m}$ and cross-sectional area $1 \text{ mm}^2$ stretches by $1 \text{ mm}$ under load $100 \text{ N}$. Find Young's Modulus.
Sol: $Y = \frac{F L}{A \Delta L} = \frac{100 \times 2}{10^{-6} \times 10^{-3}} = 2 \times 10^{11} \text{ N/m}^2$.
6.Find the elastic potential energy stored in a wire of volume $10^{-4} \text{ m}^3$ stretched under stress $10^7 \text{ N/m}^2$ ($Y = 2 \times 10^{11} \text{ N/m}^2$).
Sol: $U = \frac{\text{Stress}^2}{2Y} \times V = \frac{(10^7)^2}{4 \times 10^{11}} \times 10^{-4} = \frac{10^{14}}{4 \times 10^{11}} \times 10^{-4} = 0.025 \text{ Joules}$.
7.Calculate fractional change in volume of a sphere when subjected to uniform pressure of $100 \text{ atm}$ ($B = 1.4 \times 10^{11} \text{ Pa}$).
Sol: $\frac{\Delta V}{V} = \frac{\Delta P}{B} = \frac{100 \times 1.013 \times 10^5}{1.4 \times 10^{11}} = 7.24 \times 10^{-5}$.
8.Explain why steel is more elastic than rubber.
Sol: For equal applied stress, steel produces smaller strain than rubber, meaning steel has a much higher Young's Modulus ($Y_{steel} > Y_{rubber}$).
