⚙️ Mechanical Properties of Matter — At a Glance
5
States of Matter
3
Types of Stress
3
Moduli of Elasticity
Pascal
Unit of Pressure
  • Matter is made up of molecules and atoms
  • Each state of matter has distinct mechanical properties
  • Key laws: Hooke's Law · Pascal's Law · Archimedes' Principle · Bernoulli's Theorem
  • Key quantities: Stress, Strain, Elasticity, Pressure, Density, Surface Tension, Viscosity
🧱 States of Matter & Their Properties
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
⚠️ Exam Trap — States

Plasma = 4th state & Bose-Einstein Condensate = 5th state. These are commonly asked in MCQs!

🔩 Stress
📘 Definition

Restoring force acting on unit area of the surface of a body when deformed.

Stress = F / AForce per unit area | Unit: N/m²
  • Unit: N/m² (Pascal)
  • It is the internal force resisting deformation
📏 Strain
📘 Definition

Ratio of change in dimension to the original dimension. It is dimensionless (no unit).

Strain = ΔDimension / Original DimensionDimensionless quantity
  • Dimension parameters: Length, Area, Volume
  • No unit — it is a pure ratio
📂 Types of Stress
Type 1
Longitudinal Stress
  • Compressive Stress — stress due to decrease in length
  • Tensile Stress — stress due to increase in length
Type 2
Normal Stress

Stress produced when force is applied perpendicular to the surface of the object.

Type 3
Shear Stress

Stress produced when force is applied in the tangential direction on the surface of the object.

📂 Types of Strain
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
📘 Shear Strain Example

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

📐 Hooke's Law
📘 Statement

Within the elastic limit, Stress is directly proportional to Strain.

Stress ∝ Strain  →  E = Stress / StrainE = Coefficient of Elasticity (Modulus of Elasticity) | Unit: N/m²
Unit
N/m²
Dimension
[ML⁻¹T⁻²]
Named after
Robert Hooke
🔢 Three Moduli of Elasticity
Modulus 1
Young's Modulus (Y)

Ratio of Longitudinal Stress to Longitudinal Strain

Y = MgL / πr²ΔLYoung's Modulus Formula
Modulus 2
Bulk Modulus (β)

Ratio of Normal Stress to Volumetric Strain

β = -PV / ΔVBulk Modulus Formula (negative sign: compression)
Modulus 3
Modulus of Rigidity (η)

Ratio of Shear Stress to Shear Strain

η = F/Aθ = FL/AΔxModulus of Rigidity Formula
⚠️ Exam Trap
  • Y → length change (solids) | β → volume change | η → shape change
  • Bulk modulus has a negative sign (volume decreases on compression)
  • For liquids & gases: only Bulk Modulus applies (no Y or η)
💨 Thrust vs Pressure
Property Thrust Pressure
Definition Force in perpendicular direction Thrust per unit area
Formula P = F / A
Unit Newton (N) N/m² or Pascal
🌫️ Atmospheric Pressure
  • Force applied by the atmosphere on a surface
  • Unit: Bar or 1 atm = 10⁵ Pascal
  • Measuring instrument: Barometer
  • Decreases as we go above Earth's surface
📘 Barometer Reading
  • Suddenly falls ↓ → Storm (Toofan)
  • Falls slowly ↓ → Rain (Baarish)
  • Rises slowly ↑ → Clear weather (Saaf mausam)
🏔️ Examples of Atmospheric Pressure Effects
  • Cooking is difficult in mountains — atmospheric pressure ↓ → boiling point ↓
  • Ink leaks from fountain pen in an aeroplane — cabin pressure difference
  • Nose bleeds at high altitudes — lower external pressure
⚠️ Exam Trap — Boiling Point

At high altitude, pressure ↓ → Boiling point of water ↓ → Food takes longer to cook. A pressure cooker increases pressure → raises boiling point → faster cooking.

⚖️ Density & Relative Density
Density (ρ)
Mass per unit volume
ρ = M / VUnit: kg/m³
Relative Density
Density ratio (no unit)
RD = ρ_substance / ρ_water(4°C)Measured by Hydrometer
Pure Water
10³ kg/m³
Ice
0.9 g/cm³
Max density of water
at 4°C
⚠️ Exam Trap — Ice Density

Ice density (0.9) < Water density (1.0) → Ice floats on water. Density of water is maximum at 4°C.

🌊 Pressure in Fluids (Hydrostatic Pressure)
P = hρgPressure at depth h in a fluid (Hydrostatic Pressure)
P_total = Pₐ + hρgTotal pressure = Atmospheric Pressure + Fluid Pressure
📘 Solved Example

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

⚖️ Pascal's Law
  • Law 1: If g is negligible → pressure is same at every point in the fluid
  • Law 2: Pressure applied on an enclosed fluid is transmitted equally in every direction
Application 1
Hydraulic Lift
Application 2
Hydraulic Brakes
⚠️ Exam Trap — Pascal's Law

Hydraulic machines (lift, brakes, press) all work on Pascal's Law. Small force on small piston → large force on large piston.

📦 Archimedes' Principle
📘 Statement

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.

  • Upthrust / Buoyant Force = Weight of fluid displaced
  • Apparent weight in fluid = Actual weight − Buoyant force
  • First study of upthrust by Archimedes
Application 1
Life Preservers
Application 2
Submarines
Application 3
Lactometers
🚢 Laws of Flotation
Case 1 — W > F (Buoyancy)
Object Sinks

Weight > Buoyant Force → Object sinks to the bottom. Example: Iron nail

Case 2 — W = F (Buoyancy)
Object Floats Fully Submerged

Weight = Buoyant Force → Object is in equilibrium inside fluid. Examples: Cork, Submarine

Case 3 — W < F (Buoyancy)
Object Partially Floats

Weight < Buoyant Force → Object floats with part above surface. Examples: Ship, Block of wood

🧊 Floating of Ice
1/10
Part above water
9/10
Part submerged
⚠️ Exam Trap — Ice Melting
  • When ice melts completely, water level remains unchanged
  • Ice is less dense than water → floats (density of ice = 0.9 g/cm³)
  • This is why icebergs float — and 9/10 is below surface (danger for ships!)
  • Lactometer & Hydrometer work on the principle of flotation
💧 Surface Tension
📘 Definition

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.

T = F / l  =  mg / lSurface Tension Formula | Unit: N/m or J/m²
Unit
N/m or J/m²
Nature
Property of Liquids
🔬 Facts About Surface Tension
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 Impurity (e.g., soap) Decreases Soap cleans by reducing surface tension
Kerosene on water Decreases Kills mosquito larvae
  • Brush hair sticks together when wet — surface tension
  • Needle floats on water — surface tension
  • Raindrops are spherical — surface tension minimizes surface area
🌿 Surface Energy & Capillarity
Surface Energy = W / ΔAWork done per unit increase in surface area | Unit: J/m²
📘 Capillarity

Phenomenon of rising or falling of liquid in a narrow (capillary) tube due to surface tension.

  • Rising of water in plant roots and stems
  • Blood circulation in body vessels (capillaries)
  • Spreading of water on solid surface (wetting)
  • Rising of oil in a lantern wick
⚠️ Exam Trap — Capillarity

Capillary rise is inversely proportional to radius of tube — thinner tube, higher the liquid rises.

🍯 Viscosity
📘 Definition

Property of a liquid that opposes relative motion between its different layers (internal friction of fluids).

F = −ηA(Δv/Δz)Viscous Force Formula | η = coefficient of viscosity
η = FΔz / AΔvCoefficient of Viscosity | SI Unit: kg/m·s = Poiseuille (Pl)
SI Unit
kg/m·s (Pl)
Also called
Poiseuille (Pl)
Δv/Δz
Velocity Gradient
📊 Order of Viscosity (High → Low)
Honey
>
Water
>
Kerosene
>
Petrol
>
Gas
⚠️ Exam Trap — Viscosity vs Temperature
  • Liquids: Viscosity decreases with rise in temperature
  • Gases: Viscosity increases with rise in temperature
  • Viscosity is a property of both liquids and gases (NOT solids)
🌀 Flow Types in Liquids
Streamline Flow
Laminar / Regular Flow

Particles move along uniform, orderly paths. Occurs at low velocities.

Turbulent Flow
Irregular / Chaotic Flow

Particles move in irregular, unpredictable paths. Occurs above critical velocity.

📘 Critical Velocity

Maximum velocity of streamline flow. Above this velocity, flow becomes turbulent.

📘 Velocity Gradient Example

Δv = 7.0 cm/s, Δz = 0.2 cm
Velocity gradient = Δv/Δz = 7.0/0.2 = 35 /s

✈️ Bernoulli's Theorem
📘 Statement

When an ideal fluid flows in streamlined motion, the total energy per unit volume (pressure energy + kinetic energy + potential energy) remains constant at every point.

P + ρgh + ½ρv² = constantBernoulli's Equation
P + ρgh
Static Pressure
½ρv²
Kinetic Pressure
Based on
Energy Conservation
⚠️ Exam Trap — Bernoulli
  • Applies to ideal, incompressible fluid in streamline flow
  • Higher velocity → Lower pressure (and vice versa)
  • Venturimeter measures fluid flow speed using Bernoulli's principle
🌍 Applications of Bernoulli's Theorem
Application How Bernoulli's Principle Works
🛩️ Aeroplane Wings (Lift) Air moves faster over curved top surface → lower pressure on top → net upward 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
📘 Key Concept

Bernoulli's Theorem: Fast flow = Low pressure, Slow flow = High pressure. This is the fundamental principle behind flight, suction, and many everyday phenomena.

🎯 High-Frequency BPSC/BSSC Exam Points
  • Plasma = 4th state, Bose-Einstein Condensate = 5th state of matter
  • Stress = F/A (N/m²) | Strain = ΔDimension/Original (no unit)
  • Hooke's Law: Stress ∝ Strain; E = Stress/Strain (unit: N/m²)
  • Young's (Y) → length | Bulk (β) → volume | Rigidity (η) → shape
  • 1 atm = 10⁵ Pascal | Barometer measures atmospheric pressure
  • Barometer falls suddenly → Storm; rises slowly → Clear weather
  • Density of water = 10³ kg/m³ (maximum at 4°C); Ice = 0.9 g/cm³
  • Pascal's Law applications: Hydraulic Lift, Hydraulic Brakes
  • Archimedes: Buoyant force = Weight of fluid displaced
  • Ice floats: 1/10 above, 9/10 below water; water level unchanged on melting
  • Surface tension: T = F/l | Unit: N/m or J/m²
  • ST ↓ with temperature ↑; ST = 0 at critical temperature
  • Viscosity of liquids ↓ with temp↑; gases ↑ with temp↑
  • Viscosity order: Honey > Water > Kerosene > Petrol > Gas
  • Bernoulli: P + ρgh + ½ρv² = constant | Based on energy conservation
  • Bernoulli applications: Aeroplane wings, Venturimeter, Magnus effect
📋 Formula Quick Reference
Stress = F/AUnit: N/m²
Strain = ΔL/L (or ΔV/V)No unit
E = Stress / StrainModulus of Elasticity
P = F/A = hρgPressure / Hydrostatic
T = F/lSurface Tension
P + ρgh + ½ρv² = CBernoulli's Equation
⚠️ Most Common Exam Traps
  • Strain has NO unit (dimensionless)
  • Plasma = 4th state (NOT gas or liquid)
  • Viscosity of liquids decreases with temp (opposite of gases)
  • Ice melting: water level does NOT change
  • Hydrometer → measures Relative Density; Lactometer → quality of milk
  • Hydraulic systems → Pascal's Law (not Bernoulli)
  • Aeroplane wing lift → Bernoulli's Theorem
  • Barometer falling suddenly = Storm (NOT slowly)
  • Boiling point decreases at high altitude (pressure ↓)
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