Paragraph 1 — Elasticity: Within the elastic limit, stress is directly proportional to strain — this is ________ Law. The constant of proportionality for longitudinal deformation is called ________ modulus, given by Y = ________. For volume deformation, the relevant modulus is ________ modulus B = −V(dP/dV), and its reciprocal is ________. The stress-strain curve passes through: proportional limit → ________ limit → ________ point → ultimate stress → breaking point. Beyond the elastic limit, the material is said to be in the ________ region.

Key (Paragraph 1): Hooke's | Young's | FL/(A$\Delta L$) | Bulk | compressibility | elastic | yield | plastic

Paragraph 2 — Fluid Dynamics and Surface Tension: The equation of continuity for incompressible fluid states $A_{1}$v_{1} = ________, meaning narrower pipes have ________ flow speed. Bernoulli's equation P + ½ρ$v^{2}$ + ρgh = constant shows that higher velocity corresponds to ________ pressure. For a liquid drop of radius R, excess pressure = ________; for a soap bubble, excess pressure = ________. Capillary rise h = 2S cosθ / ________, and water (acute contact angle) shows ________ while mercury (obtuse contact angle) shows ________ in glass tubes.

Key (Paragraph 2): $A_{2}$v_{2} | higher | lower | 2S/R | 4S/R | ρgr | rise | depression

Paragraph 3 — Viscosity and Heat Transfer: Viscous drag on a sphere of radius r moving at speed v through a fluid of viscosity η is given by Stokes' law: F = ________. Terminal velocity is reached when weight equals buoyancy plus , giving v_t = 2$r^{2}$(ρ − σ)g / (). This shows v_t is proportional to ________. Fourier's law of heat conduction: Q/t = KA($\Delta T$)/L, where K has SI unit ________. Stefan-Boltzmann radiation law: P = σ$AT^{4}$, where σ = ________ W $m^{-2}$ $K^{-4}$.

Key (Paragraph 3): 6πηrv | drag | 9η | $r^{2}$ | W $m^{-1}$ $K^{-1}$ | $5.67 \times 10^{-8}$