Cornell Notes — Full Topic (Properties of Solids & Liquids) — Notes

Cue / Question	Notes
What is stress? Define it.	Restoring force per unit area: σ = F/A. Dimensions: [ $M^{1}$ $L^{-1}$ $T^{-2}$ ], unit: Pa. Types: tensile/compressive (normal to surface), shear (tangential).
What is strain?	Fractional deformation (dimensionless). Longitudinal: $\Delta L$ /L. Volumetric: $\Delta V$ /V. Shear: tanφ ≈ φ (small angle).
State Hooke's Law.	Stress ∝ Strain within elastic limit. Constant of proportionality = elastic modulus.
Define Young's Modulus Y.	Y = FL / (A $\Delta L$ ) = stress / longitudinal strain. [ $M^{1}$ $L^{-1}$ $T^{-2}$ ] (Pa). Governs stretching/compression.
Define Bulk Modulus B.	B = −V(dP/dV). Governs volume change under uniform pressure. Compressibility = 1/B.
Define Shear Modulus G.	G = shear stress / shear strain. Governs shape change without volume change.
State Pascal's Law.	Pressure applied to enclosed fluid transmits equally in all directions. Hydraulic press: $F_{1}$ / $A_{1}$ = $F_{2}$ / $A_{2}$ .
State Bernoulli's equation.	P + ½ρ $v^{2}$ + ρgh = constant. Higher velocity → lower pressure. Valid for ideal, non-viscous, incompressible flow.
Terminal velocity formula.	v_t = 2 $r^{2}$ (ρ − σ)g / (9η). Proportional to $r^{2}$ . Doubling radius → 4× terminal velocity.
Surface tension drop vs bubble.	Liquid drop: $\Delta P$ = 2S/R (one surface). Soap bubble: $\Delta P$ = 4S/R (two surfaces). DB-24 mnemonic.

Summary: Properties of Solids & Liquids covers elasticity (Young's, Bulk, Shear moduli), fluid statics (Pascal's law, pressure at depth), fluid dynamics (continuity, Bernoulli), viscosity (Stokes' law, terminal velocity), surface tension (drop vs bubble excess pressure, capillary rise), and heat transfer (conduction, convection, radiation). The critical NEET discriminator is $\Delta P$ = 2S/R for a liquid drop versus $\Delta P$ = 4S/R for a soap bubble, and the v_t ∝ $r^{2}$ relationship for terminal velocity.