🧊 Physics — Properties of Matter
1. Matter
Matter is one of the two basic components of physical science (the other being energy). Any entity exhibiting gravitation and inertia is matter. It has weight and occupies space.
Matter consists of atoms and molecules. It exists in three states:
- Solid: Molecules vibrate about fixed positions — definite shape and volume
- Liquid: Molecules vibrate and move freely — variable shape, fixed volume
- Gas: Molecules move freely with large intermolecular spaces — variable shape and volume
INTERATOMIC FORCE
- Electrostatic attraction between atoms
- Range: ≈ 10⁻¹⁰ m (atomic size)
- Force = −dU/dr (where U = potential energy)
2. Solids
State of matter with definite shape and definite volume. Intermolecular space is minimum.
ELASTICITY
- Property of a body by virtue of which it regains its original configuration after removal of deforming force
- Quartz and phosphor bronze are almost perfectly elastic
- Plasticity: Body does NOT regain original shape (e.g., clay, putty)
HOOKE'S LAW
- Formula: Stress ∝ Strain → Stress / Strain = Constant (E)
- Within the elastic limit, strain is directly proportional to stress
- Modulus of Elasticity: Unit = Nm⁻² or Pascal (Pa)
STRESS & STRAIN
- Stress: Internal restoring force / Area (Nm⁻² or Pa)
- Strain: Fractional change in configuration (no unit)
| Type of Strain | Formula |
|---|---|
| Longitudinal strain | Δl / l |
| Volume strain | ΔV / V |
| Shearing strain | θ |
MODULUS OF ELASTICITY
| Type | Formula | Description |
|---|---|---|
| Young's Modulus (Y) | Y = (F/A) / (Δl/l) | Normal stress / Longitudinal strain |
| Bulk Modulus (K or B) | K = p / (−ΔV/V) | Normal stress / Volumetric strain |
| Modulus of Rigidity (η) | η = (F/A) / θ | Tangential stress / Shearing strain |
KEY POINTS — SOLIDS
- Steel is more elastic than rubber (Ysteel > Yrubber)
- Breaking stress is fixed for a material; breaking force varies with area
- Hollow shafts are stronger than solid shafts
- Girders are I‑shaped to prevent buckling
- Springs are made of steel (higher Young's modulus than copper)
- Elastic limit: Maximum stress before permanent deformation
- Fracture point: Point at which material breaks
- Ductile: Large deformation before fracture (e.g., copper)
- Brittle: Breaks soon after elastic limit (e.g., glass)
- Elastic fatigue: Reduced elasticity under repeated alternating forces
3. Fluids
A substance that begins to flow under an external force. Liquids and gases are fluids.
FLUID DENSITY
- Formula: Density (ρ) = Mass / Volume (SI: kg/m³)
- Density of water = 1000 kg/m³ (maximum at 4°C)
- Relative density: Density of substance / Density of water at 4°C
- Hydrometer: Instrument to measure relative density (based on floatation)
- Water is dipolar in nature — dissolves more substances than any other liquid
FLUID PRESSURE
- Formula: p = F / A (SI: Pascal, Pa)
- Pressure in a liquid column: p = hρg
- 1 torr = 1 mm of mercury column
- 1 bar = 10⁵ Pa
PASCAL'S LAW
- Pressure exerted at any point of a confined fluid is transmitted equally and undiminished in all directions
- Applications: Hydraulic lift, hydraulic press, hydraulic brakes
BUOYANCY & ARCHIMEDES' PRINCIPLE
- Archimedes' Principle: When a body is partially or completely immersed in a liquid, it loses weight equal to the weight of the liquid displaced by the submerged part
- Buoyant force acts upward through the centre of buoyancy
- Law of Floatation: Weight of body = Weight of liquid displaced
FLOATATION FACTS
- Ice floating on water: 11/12 submerged, 1/12 above
- In sea water: 8/9 submerged, 1/9 above
- Easier to swim in sea water (higher density = more buoyancy)
- Density of human body < density of water
4. Surface Tension
Property of a liquid by which it tries to minimise its free surface area.
FORMULA & KEY POINTS
- Formula: Surface Tension (S) = F / l (SI: N/m)
- Raindrops are spherical — minimum surface area for a given volume
- Surface tension decreases with increase in temperature
- Becomes zero at critical temperature
EFFECTS OF IMPURITIES
- Soap, detergent, dettol — decrease surface tension
- Salt — increases surface tension
- Oil — decreases surface tension
CAPILLARITY
- Phenomenon of rising or falling of liquid in a capillary tube
- Formula: h = 2S·cosθ / (ρgr)
- Water rises in capillary tubes (adhesive force > cohesive force)
- Mercury falls in capillary tubes (cohesive force > adhesive force)
- Applications: Blotting paper, tree sap rising, kerosene lamp wick
COHESIVE vs ADHESIVE FORCES
- Cohesive force: Attraction between molecules of same substance (e.g., water-water)
- Adhesive force: Attraction between molecules of different substances (e.g., water-glass)
5. Viscosity
Property of a fluid by which an internal frictional force acts between its layers when in motion.
FORMULA & KEY POINTS
- Formula: F = −η·A·(dv/dx)
- η = coefficient of viscosity (SI: Nsm⁻² or Pa·s)
- 1 poise = 0.1 Nsm⁻²
- Viscosity of liquids decreases with temperature
- Viscosity of gases increases with temperature
- Viscosity of liquids (except water) increases with pressure
- Viscosity of gases is independent of pressure
STOKE'S LAW & TERMINAL VELOCITY
- Terminal velocity: v = (2/9)·r²·(ρ − σ)·g / η
- r = radius of spherical body
- ρ = density of body
- σ = density of liquid
- η = coefficient of viscosity
KEY POINTS — VISCOSITY
- Raindrops have small radius → small terminal velocity → strike earth gently
- In pipe flow: speed is maximum near axis, minimum near walls
- Equation of Continuity: A₁v₁ = A₂v₂ (speed increases in narrower pipes)
6. Bernoulli's Theorem
FORMULA
- p + ½ρv² + ρgh = constant
- For non‑viscous, incompressible liquid in streamline flow
- Sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant
APPLICATIONS
- Venturi tube — measures flow speed
- Aspirator pump — creates suction
- Airplane wing lift — pressure difference creates lift
- Roof blowing off during storms — high wind speed → low pressure above roof
MAGNUS EFFECT
- Spinning ball deviates from its path due to pressure difference created by the spin
- Used in cricket swing bowling
FLOW OF FLUIDS
- Steady (streamline) flow: Fluid particles follow smooth paths
- Turbulent flow: Irregular, chaotic motion (fast rivers, waterfalls)
📌 Summary: Properties of Matter at a Glance
| Topic | Key Formula | Key Point |
|---|---|---|
| Density | ρ = m/V | Water max at 4°C |
| Young's Modulus | Y = FL/AΔl | Steel > Rubber |
| Surface Tension | S = F/l | Decreases with temperature |
| Capillarity | h = 2Scosθ/ρgr | Water rises, mercury falls |
| Viscosity | F = −ηA(dv/dx) | Liquids: decreases with T; Gases: increases with T |
| Terminal Velocity | v = (2/9)r²(ρ−σ)g/η | Raindrops have small terminal velocity |
| Bernoulli's Theorem | p + ½ρv² + ρgh = const | Venturi tube, airplane lift |
| Pascal's Law | p = F/A | Hydraulic lift, brakes |
KEY TAKEAWAYS FOR UPSC
- Density of water: Maximum at 4°C
- Steel is more elastic than rubber
- Surface tension: Decreases with temperature; zero at critical temperature
- Capillarity: Water rises (adhesive > cohesive); Mercury falls (cohesive > adhesive)
- Viscosity: Liquids decrease with T; Gases increase with T
- Bernoulli's principle: Explains Magnus effect, airplane lift, roof blowing off
- Hydrometer: Works on law of floatation
- Ball bearings: Reduce rolling friction
🎯 High-Yield Interactive UPSC Quiz (Physics — Properties of Matter)
Q1. At what temperature is the density of water maximum?
Correct Answer: B. The density of water is maximum at 4°C (277 K).
Q2. Which of the following is more elastic than rubber?
Correct Answer: B. Steel is more elastic than rubber because Ysteel > Yrubber.
Q3. Surface tension of a liquid becomes zero at:
Correct Answer: B. Surface tension becomes zero at the critical temperature of the liquid.
Q4. Which phenomenon explains the rising of water in a capillary tube?
Correct Answer: C. Capillarity explains the rising or falling of liquid in a capillary tube.
Q5. What happens to the viscosity of liquids with increase in temperature?
Correct Answer: A. Viscosity of liquids decreases with increase in temperature.
Q6. Bernoulli's theorem is based on which principle?
Correct Answer: B. Bernoulli's theorem is based on the conservation of energy.
Q7. Which instrument is used to measure relative density of liquids?
Correct Answer: C. Hydrometer is used to measure the relative density (specific gravity) of liquids.
Q8. What fraction of an ice cube is submerged when floating on water?
Correct Answer: C. 11/12 of an ice cube is submerged when floating on water; 1/12 is above water.
Q9. Pascal's law is applied in which of the following?
Correct Answer: C. Hydraulic lift, hydraulic press, and hydraulic brakes work on Pascal's law.
Q10. What is the SI unit of coefficient of viscosity?
Correct Answer: B. The SI unit of coefficient of viscosity is Nsm⁻² (or Pa·s).