SSC / Railway / UPSC / BPSC · Exam Fusion Prep | Stress · Strain · Elasticity · Pressure · Fluids · Surface Tension · Viscosity · Bernoulli
| State | Key Mechanical Property | Notes |
|---|---|---|
| Solid | Elasticity | Definite shape and volume |
| Liquid | Pressure, Flotation, Surface Tension, Capillarity, Viscosity | Definite volume, no fixed shape |
| Gas | Atmospheric Pressure | No fixed shape or volume |
| Plasma | — | 4th state of matter |
| Bose-Einstein Condensate | — | 5th state of matter |
Plasma = 4th state & Bose-Einstein Condensate = 5th state. These are commonly asked in MCQs!
Restoring force acting on unit area of the surface of a body when deformed.
Ratio of change in dimension to the original dimension. It is dimensionless (no unit).
Pressure change acting normally on all surfaces produces volume change. Longitudinal stress is also normal stress.
Stress produced when force is applied in the tangential direction on the surface of the object.
| TypeStrain | Formula | Used for |
|---|---|---|
| Longitudinal (Linear) Strain | ΔL / L | Change in length |
| Volumetric Strain | ΔV / V | Change in volume |
| Shearing Strain | Δx / L | Angular deformation |
For a cubic object: θ = 30°, Δx = 2.5 m
tan30° = 2.5/L → L = 2.5√3 = 4.33 m
Volume = L³ = (4.33)³ ≈ 81 m³
Within the elastic limit, Stress is directly proportional to Strain.
Ratio of Longitudinal Stress to Longitudinal Strain
Negative ratio of pressure change to volumetric strain
Ratio of Shear Stress to Shear Strain
| Property | Thrust | Pressure |
|---|---|---|
| Definition | Force in perpendicular direction | Thrust per unit area |
| Formula | — | P = F / A |
| Unit | Newton (N) | N/m² or Pascal |
At high altitude, pressure ↓ → Boiling point of water ↓ → Food takes longer to cook. A pressure cooker increases pressure → raises boiling point → faster cooking.
Ice density (~0.917) < Water density (1.0) → Ice floats on water. Density of water is maximum at 4°C.
Pressure on swimmer at 10 m below surface (water density = 10³ kg/m³):
P = 1.01×10⁵ + 10×10³×10 = 2.01×10⁵ N/m² ≈ 2 atm
Hydraulic machines (lift, brakes, press) all work on Pascal's Law. Small force on small piston → large force on large piston.
When a body is wholly or partially immersed in a fluid, it experiences an upward force (buoyant force) equal to the weight of the fluid displaced by it.
Weight > Buoyant Force → Object sinks to the bottom. Example: Iron nail
Weight = Buoyant Force → Object is in equilibrium inside fluid. Example: a neutrally buoyant submerged submarine
If buoyancy initially exceeds weight, the object rises. Floating equilibrium of a ship or wood block requires buoyancy = weight.
Force per unit length in the plane of the liquid surface, acting at right angles on either side of an imaginary line drawn on that surface.
| Condition | Effect on Surface Tension | Example |
|---|---|---|
| Increase in Temperature | Decreases | Hot soup tastes better (spreads easily) |
| Critical Temperature | Becomes Zero | Liquid-gas distinction disappears |
| Adding soap (other impurities may increase or decrease tension) | Decreases | Soap cleans by reducing surface tension |
| Kerosene on water | Decreases | Kills mosquito larvae |
Phenomenon of rising or falling of liquid in a narrow (capillary) tube due to surface tension.
Capillary rise is inversely proportional to radius of tube — thinner tube, higher the liquid rises.
Property of a liquid that opposes relative motion between its different layers (internal friction of fluids).
Particles move along uniform, orderly paths. Occurs at low velocities.
Particles move in irregular, unpredictable paths. Occurs above critical velocity.
Maximum velocity of streamline flow. Above this velocity, flow becomes turbulent.
Δv = 7.0 cm/s, Δz = 0.2 cm
Velocity gradient = Δv/Δz = 7.0/0.2 = 35 /s
For steady, incompressible, inviscid flow, pressure + kinetic + gravitational energy per unit volume is constant along a streamline.
| Application | How Bernoulli's Principle Works |
|---|---|
| 🛩️ Aeroplane Wings (Lift) | Airflow produces pressure differences and downward flow deflection; angle of attack and circulation also contribute to lift |
| 🔧 Venturimeter | Measures flow speed using pressure difference at narrow section |
| ⚾ Magnus Effect | Spinning ball curves in air due to pressure difference on two sides |
| 🏠 Tin Roof Blowing Off | Fast wind above → low pressure → roof lifts up |
| 🚂 Train Platform Suction | Fast train → low pressure near train → people/objects pulled toward it |
Bernoulli’s speed–pressure relation applies at the same height along a streamline under steady, incompressible, inviscid flow. It is not a universal fast-flow/low-pressure rule.