ELASTIC MODULI (all [$M^{1}$ $L^{-1}$ $T^{-2}$], unit: Pa)

• Young's Y = FL/(A$\Delta L$) — wire stretching
• Bulk B = −V(dP/dV) — volume compression; Compressibility = 1/B
• Shear G = shear stress / shear strain — layer sliding

FLUID STATICS

• Pressure at depth: P = $P_{0}$ + ρgh
• Pascal's law: $F_{1}$/$A_{1}$ = $F_{2}$/$A_{2}$ (hydraulic press)

FLUID DYNAMICS

• Continuity: $A_{1}$v_{1} = $A_{2}$v_{2} (narrow → faster)
• Bernoulli: P + ½ρ$v^{2}$ + ρgh = constant (high v → low P)

VISCOSITY

• η: [$M^{1}$ $L^{-1}$ $T^{-1}$] (Pa·s)
• Stokes drag: F = 6πηrv
• Terminal velocity: v_t = 2$r^{2}$(ρ−σ)g/(9η) ← v_t ∝ $r^{2}$

SURFACE TENSION (DB-24)

• S = F/L; [$M^{1}$ $T^{-2}$] (N/m)
• Drop: $\Delta P$ = 2S/R (1 surface)
• Bubble: $\Delta P$ = 4S/R (2 surfaces) ← most tested trap
• Capillary: h = 2S cosθ/(ρgr); water ↑, mercury ↓

HEAT TRANSFER

• Conduction: Q/t = KA($\Delta T$)/L; K: [$M^{1}$ $L^{1}$ $T^{-3}$ $K^{-1}$]
• Radiation: P = σ$AT^{4}$; σ = $5.67 \times 10^{-8}$ W $m^{-2}$ $K^{-4}$
• Thermal expansion: β = 3α (volume), 2α (area)

STRESS-STRAIN CURVE ORDER: P → E → Y → U → B (Proportional → Elastic → Yield → Ultimate → Break)

TOP NEET TRAPS:

1. Bubble = 4S/R, Drop = 2S/R
2. v_t ∝ $r^{2}$ (NOT r)
3. Strain is dimensionless
4. β = 3α (NOT 2α)
5. Stefan-Boltzmann needs T in Kelvin