Properties of Solids and Fluids Questions for AGNIVEER VAYU

Elasticity and Stress-Strain

Elasticity is the ability of a material to return to its original shape after deformation. When you apply force to a solid, it deforms. Stress is the force applied per unit area, and strain is the fractional change in dimension. Think of a rubber band: pull it (stress), it stretches (strain), release it, it snaps back. The relationship between stress and strain is linear up to the elastic limit — this is Hooke's law. Beyond the elastic limit, permanent deformation occurs. Agniveer Vayu exams focus heavily on Young's modulus, which measures how stiff a material is.

• Stress = Force / Area (measured in Pascal or N/m²)
• Strain = Change in dimension / Original dimension (dimensionless)
• Young's modulus Y = Stress / Strain (higher Y means stiffer material)
• Elastic limit is the maximum stress before permanent deformation
• Hooke's law applies only within elastic limit: F = -kx

Fluid Pressure and Buoyancy

Fluids (liquids and gases) exert pressure in all directions. Pressure in a fluid increases with depth due to the weight of fluid above. Pascal's principle states that pressure applied to a confined fluid is transmitted equally in all directions — this is how hydraulic brakes work. Buoyancy is the upward force exerted by a fluid on a submerged object. Archimedes' principle: buoyant force equals the weight of fluid displaced. If buoyant force exceeds weight, object floats; if less, it sinks.

• Pressure P = Force / Area; in fluids, P = ρgh (density × gravity × depth)
• Pascal's principle: pressure applied to confined fluid transmits equally
• Buoyant force F_b = ρ_fluid × V_displaced × g
• Object floats if weight = buoyant force (neutral buoyancy)
• Atmospheric pressure at sea level ≈ 101,325 Pa or 1 atm

Viscosity and Surface Tension

Viscosity is the resistance of a fluid to flow — think of honey versus water. Higher viscosity means thicker, slower-flowing fluid. Stokes' law describes the drag force on a sphere moving through a viscous fluid. Surface tension arises because molecules at the surface experience unequal forces, creating a 'skin' effect. Water droplets are spherical because surface tension minimizes surface area. Capillarity is the rise or fall of liquid in a narrow tube due to surface tension and adhesive forces.

• Viscosity η measured in Pascal-seconds (Pa·s); higher η means more resistance to flow
• Stokes' law: F_drag = 6πηrv (for sphere of radius r moving at velocity v)
• Surface tension γ measured in N/m; acts along the surface like an elastic membrane
• Contact angle determines whether liquid wets a surface (acute angle = wetting)
• Capillary rise h = (2γ cosθ) / (ρgr) where r is tube radius

• Confusing stress and strain — stress is force/area (has units), strain is dimensionless ratio. Many candidates swap them in Young's modulus formula.
• Forgetting atmospheric pressure in absolute pressure calculations. Gauge pressure excludes it; absolute pressure includes it. Agniveer exams often ask for absolute pressure.
• Misapplying Archimedes' principle — buoyant force depends on volume of fluid displaced, NOT volume of object. A hollow object displaces more fluid than a solid one of same mass.
• Using Stokes' law outside its valid range — it applies only to laminar flow at low velocities. At high speeds, turbulence dominates.
• Ignoring contact angle in capillarity — if θ > 90°, liquid depresses (negative h), not rises. This reversal trips many candidates.

• STRESS-STRAIN-MODULUS: Think 'SSM' — Stress is the push, Strain is the stretch, Modulus is the stiffness ratio. Y = Stress/Strain always.
• PASCAL'S PRINCIPLE: 'Pressure spreads equally' — like a balloon: squeeze one side, pressure pushes everywhere inside equally.
• ARCHIMEDES FLOAT TEST: 'Weight vs. Buoyancy' — if buoyant force > weight, float; if equal, suspend; if less, sink. Use ρ_object vs. ρ_fluid.
• VISCOSITY DRAG: 'Stokes' 6πηrv' — remember 6π ≈ 19 for quick estimates. Drag increases with radius, velocity, and viscosity.

• Agniveer Vayu typically includes 1-2 numerical problems on Young's modulus and pressure. Practice unit conversions (mm² to m², cm to m) — careless errors cost marks.
• Buoyancy questions often combine with Newton's laws — expect 'find acceleration of floating/sinking object' type problems. Draw free body diagrams.
• Surface tension and capillarity appear as conceptual MCQs (why water wets glass, why mercury doesn't). Memorize contact angle behavior.
• Viscosity questions may involve terminal velocity — when drag force equals weight, object stops accelerating. Set F_drag = mg and solve.
• Recent Agniveer papers emphasize real-world applications: hydraulic brakes (Pascal), oil viscosity in engines (Stokes), water absorption in soil (capillarity). Expect scenario-based questions.