Core Concepts and Must-Know Formulas

Stress = F/A; dimensions [ $M^{1}$ $L^{-1}$ $T^{-2}$ ]; unit Pa. Types: tensile, compressive (normal), shear (tangential).
Strain is dimensionless ( $\Delta L$ /L for longitudinal, $\Delta V$ /V for volumetric).
Hooke's Law: stress ∝ strain within the elastic limit. Modulus = stress/strain.
Young's modulus: Y = FL/(A $\Delta L$ ). Used to calculate wire extension: $\Delta L$ = FL/(AY).
Bulk modulus: B = −V(dP/dV). Compressibility = 1/B.
Shear modulus: G = shear stress / shear strain.
All three moduli have dimensions [ $M^{1}$ $L^{-1}$ $T^{-2}$ ] and unit Pa.
Stress-strain curve sequence: Proportional limit → Elastic limit → Yield point → Ultimate stress → Breaking point.
Pascal's law: Pressure transmits equally in enclosed fluid. $F_{1}$ / $A_{1}$ = $F_{2}$ / $A_{2}$ .
Pressure at depth: P = $P_{0}$ + ρgh.
Continuity equation: $A_{1}$ v_{1} = $A_{2}$ v_{2} (incompressible flow).
Bernoulli's equation: P + ½ρ $v^{2}$ + ρgh = constant. Higher v → lower 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 ∝ $r^{2}$ — most tested NEET formula.
Surface tension: S = F/L; [ $M^{1}$ $T^{-2}$ ] (N/m).
Liquid drop excess pressure: $\Delta P$ = 2S/R (one surface).
Soap bubble excess pressure: $\Delta P$ = 4S/R (two surfaces).
Capillary rise: h = 2S cosθ/(ρgr). Positive for θ < 90° (rise), negative for θ > 90° (depression).
Fourier's conduction law: Q/t = KA( $\Delta T$ )/L. K in W $m^{-1}$ $K^{-1}$ .
Stefan-Boltzmann law: P = σ $AT^{4}$ ; T in Kelvin; σ = $5.67 \times 10^{-8}$ W $m^{-2}$ $K^{-4}$ .
Thermal expansion: β = 3α (volume), 2α (area).