Properties of Solids & Liquids is a high-yield NEET Physics topic (2–3 questions per year) spanning elasticity, fluid statics, fluid dynamics, viscosity, surface tension, and heat transfer. Understanding this topic requires both conceptual clarity and numerical dexterity with the associated formulas and dimensional analysis.

Elasticity describes a material's ability to recover from deformation. Stress (σ = F/A) is the restoring force per unit cross-sectional area, with dimensions [$M^{1}$ $L^{-1}$ $T^{-2}$] and SI unit Pascal (Pa). Strain is the fractional deformation and is dimensionless: longitudinal strain = $\Delta L$/L, volumetric strain = $\Delta V$/V, shear strain = tanφ ≈ φ for small angles. Hooke's Law states that stress is proportional to strain within the elastic limit, with the elastic modulus as the constant of proportionality. Three moduli cover different deformation geometries — Young's modulus Y = FL/(A$\Delta L$) for linear stretching, Bulk modulus B = −V(dP/dV) for volume compression (compressibility = 1/B), and Shear modulus G = shear stress/shear strain for tangential deformation. All three share dimensions [$M^{1}$ $L^{-1}$ $T^{-2}$]. The stress-strain curve progresses through five key points: proportional limit (Hooke's law holds), elastic limit (full recovery possible), yield point (plastic deformation begins), ultimate stress (maximum), and breaking point (fracture). Below the elastic limit is the elastic region; beyond it is the plastic (irreversible) region. NEET commonly tests Young's modulus calculations ($\Delta L$ = FL/AY) and identification of curve regions.

Fluid Statics is governed by Pascal's Law: pressure applied to an enclosed fluid transmits equally in all directions. This underpins the hydraulic press, where $F_{1}$/$A_{1}$ = $F_{2}$/$A_{2}$. Pressure at depth h in a static fluid is P = $P_{0}$ + ρgh, where $P_{0}$ is atmospheric pressure, ρ is fluid density, and g is gravitational acceleration — all with dimensions [$M^{1}$ $L^{-1}$ $T^{-2}$].

Fluid Dynamics for ideal (non-viscous, incompressible) fluids is described by two fundamental equations. The equation of continuity, $A_{1}$v_{1} = $A_{2}$v_{2}, expresses conservation of mass: narrower cross-section means higher velocity. Bernoulli's equation, P + ½ρ$v^{2}$ + ρgh = constant, expresses conservation of energy per unit volume. Its most important consequence is that higher velocity corresponds to lower pressure, explaining airplane lift (faster flow over cambered wing top → lower pressure → net upward force), the Venturi effect, and the working of spray guns and carburettors.

Viscosity quantifies internal friction in a fluid. Newton's viscous force law gives F = ηA(dv/dx), where η is the coefficient of viscosity with dimensions [$M^{1}$ $L^{-1}$ $T^{-1}$] and SI unit Pa·s. Stokes' Law gives the drag force on a sphere of radius r moving at speed v: F = 6πηrv. When a sphere falls through a viscous fluid, it accelerates until it reaches terminal velocity v_t, at which point weight equals buoyancy plus viscous drag. Solving the force balance yields v_t = 2$r^{2}$(ρ − σ)g / (9η), where ρ is sphere density and σ is fluid density. The critical result is that v_t ∝ $r^{2}$: doubling the radius quadruples the terminal velocity. This is the most-tested Stokes' law relationship in NEET numericals.

Surface Tension (S = F/L) arises from cohesive forces between fluid molecules at the surface. Its dimensions are [$M^{1}$ $T^{-2}$] and its SI unit is N/m. The excess pressure across a curved liquid surface depends critically on the number of free surfaces: for a liquid drop (one surface), $\Delta P$ = 2S/R; for a soap bubble (two surfaces — inner and outer), $\Delta P$ = 4S/R. Confusing these two is the single most common error in NEET surface tension problems — the mnemonic "DB-24" helps: Drop = 2S/R, Bubble = 4S/R. Capillary rise follows h = 2S cosθ/(ρgr), where θ is the contact angle. For water on glass (θ ≈ 0°, cosθ = 1), capillary rise occurs; for mercury on glass (θ ≈ 140°, cosθ < 0), capillary depression occurs. Surface energy = S × change in area, and the work done in blowing a soap bubble from radius r_{1} to r_{2} is W = 8πS(r_{2}^{2} − r_{1}^{2}), the factor of 8π accounting for the two surfaces.

Heat Transfer covers three mechanisms. Conduction follows Fourier's Law: Q/t = KA($\Delta T$)/L, where K is thermal conductivity with dimensions [$M^{1}$ $L^{1}$ $T^{-3}$ $K^{-1}$] and unit W $m^{-1}$ $K^{-1}$. Good conductors (copper, aluminium) have high K; insulators (wood, air) have low K. Convection follows Newton's Law of Cooling: dT/dt = −k(T − $T_{0}$), giving exponential temperature decay toward the surroundings temperature $T_{0}$. Radiation is governed by the Stefan-Boltzmann Law: P = σ$AT^{4}$, where σ = $5.67 \times 10^{-8}$ W $m^{-2}$ $K^{-4}$. Critically, T must be in Kelvin. Thermal expansion coefficients are related as β (volume) = 3α (linear) and area coefficient = 2α, following the 1-2-3 rule for dimensions of expansion.

The three most-tested NEET traps in this topic are: (1) using $\Delta P$ = 2S/R for a bubble instead of 4S/R, (2) treating v_t as proportional to r instead of $r^{2}$, and (3) using temperature in Celsius rather than Kelvin in the Stefan-Boltzmann law.