Derivation and Formulation of Stokes' Law in Particle Size Analysis:

• Balance of Forces: For a spherical particle of radius $r$ falling in a viscous fluid under gravity, terminal settling velocity ($v$) is attained when submerged net buoyant force equals hydrodynamic drag force ($F_d = 6\pi \eta r v$):
  $$\frac{4}{3}\pi r^3 (D_p - D_l) g = 6\pi \eta r v$$
• Solving for Velocity ($v$):
  $$v = \frac{4\pi r^3 (D_p - D_l) g}{3 \times 6\pi \eta r} = \frac{2 g r^2 (D_p - D_l)}{9\eta}$$
  where:
• $g$ = acceleration due to gravity
• $r$ = particle radius
• $D_p$ = particle density (usually $2.65\text{ g/cm}^3$ for quartz)
• $D_l$ = liquid density ($1.0\text{ g/cm}^3$ for water)
• $\eta$ = dynamic viscosity of the suspension fluid.

Terminology of Soil Structural Aggregates:

• Definition of Ped: A ped is a unit of soil structure formed by natural processes of aggregation of primary soil particles (sand, silt, and clay) bound together by organic matter, clay bridges, and polyvalent cations.
• Distinct Concepts:
• Clod: An artificial, cohesive mass of soil formed by human tillage or mechanical disturbance (such as plowing wet soil).
• Pedon: The smallest three-dimensional sampling unit of a soil body exhibiting all its horizons (typically $1 - 10\text{ m}^2$ area).
• Micromorphology: Microscopic investigation of undisturbed soil fabric and optical features.

Physical Nature and Practical Importance of Soil Consistency:

• Valid Characteristics: Soil consistency describes the manifestation of physical forces of cohesion and adhesion within the soil at various moisture contents, reflected by its resistance to deformation, rupture, or flow under applied mechanical stresses.
• Statement 4 is completely false: Soil consistency is the PRIMARY index used by agronomists and agricultural engineers to evaluate soil workability, optimum moisture range for tillage (friable consistency), trafficability, and susceptibility to compaction. Stating that it does not indicate workability contradicts its principal practical application.

Determination of Soil Bulk Density:

• Formula: Bulk density ($\rho_b$) is the mass of oven-dry soil ($M_s$) divided by total core cylinder volume ($V$):
  $$\rho_b = \frac{M_s}{V} = \frac{M_{\text{core+soil}} - M_{\text{core}}}{\pi r^2 h}$$
• Given Parameters:
• Core diameter $d = 4\text{ cm} \implies$ radius $r = 2\text{ cm}$
• Core height $h = 7\text{ cm}$
• Weight of core + dry soil = $170\text{ g}$
• Weight of empty core = $50\text{ g}$
• Computation:
• Mass of dry soil $M_s = 170 - 50 = 120\text{ g}$
• Core volume $V = \pi \times (2)^2 \times 7 = \frac{22}{7} \times 4 \times 7 = 88\text{ cm}^3$
• Bulk density $\rho_b = \frac{120}{88} \approx 1.3636\text{ g/cm}^3$
  Since $1\text{ g/cm}^3 = 1\text{ Mg m}^{-3}$, $\rho_b = 1.36\text{ Mg m}^{-3}$.