Properties of Matter

Introduction

Properties of Matter covers how materials behave under force, how fluids exert pressure, and why some objects float while others sink. It connects everyday physics — ships floating, soap bubbles forming, water rising in thin tubes — to the quantitative laws that explain them.

In NDA Physics, this chapter contributes a steady stream of questions spread across its sub-topics. It is not as equation-heavy as Kinematics or Gravitation, but it tests a wider range of phenomena. The examiner favours Archimedes’ Principle and buoyancy above all else, followed by pressure in fluids, surface tension, and density comparisons. Elasticity (stress, strain, Young’s modulus) appears less frequently but is tested through units and definitions.

NDA Exam Pattern Insight:

• Most frequently tested: Archimedes’ Principle (floating/sinking conditions), buoyancy as an upward force, density comparisons, pressure in fluids at rest
• Major conceptual traps: Buoyancy is a force not a pressure; strain has no unit; stress has the same unit as pressure; a body sinks when its density > fluid density — not because it is heavy
• Numerical focus: Density from mass and volume, relative density calculations, mixing liquids of different densities, finding density from weight and displaced volume

Understand the Topic

Understand the Topic

Topic Family	Key Concepts	Primary NDA Test Mode
Elasticity	Stress, Strain, Hooke’s Law, Young’s Modulus, elastic limit	Definition MCQ + unit identification
Pressure	P = F/A, fluid pressure P = ρgh, Pascal’s Law	Conceptual MCQ + numerical
Archimedes’ Principle	Buoyant force = weight of displaced fluid	Conceptual MCQ (very high frequency)
Floating and Sinking	Density comparison — float if ρ_object < ρ_fluid	Conceptual MCQ (very high frequency)
Density & Relative Density	ρ = m/V, RD = ρ_substance/ρ_water, no unit	Numerical
Surface Tension	Cohesion, surface energy, effects, temperature effect	Conceptual MCQ
Capillary Action	Water rises, mercury falls, angle of contact	Conceptual MCQ
Viscosity	Resistance to flow, coefficient η, temperature effect	Conceptual MCQ
Streamline Flow	Steady flow, no crossing of streamlines, Bernoulli	Conceptual MCQ
Compressibility	Solid < Liquid < Gas	Ranking MCQ

Highest Yield Areas: Archimedes’ Principle and buoyancy questions together constitute about one-third of all NDA questions in this chapter. Surface tension (what it causes, temperature dependence) and fluid pressure statements are the next most common. Mastering these three areas covers over 65% of the chapter’s NDA question load.

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Core Concepts

Elasticity

When a force is applied to a solid and the solid returns to its original shape after the force is removed, the material is said to be elastic. If it does not return, it is plastic.

• Elastic limit — the maximum stress a material can withstand and still return to its original shape. Beyond this, permanent deformation occurs.
• Hooke’s Law — within the elastic limit, stress is directly proportional to strain. This gives us the linear region on a stress-strain graph.
• Elastic material — steel, rubber (within limits)
• Plastic material — clay, putty, lead (above elastic limit)

💡 Key Fact Steel is more elastic than rubber. This surprises many students — elasticity means the ability to return to original shape, not the ability to stretch. Steel deforms very little under stress and returns perfectly. Rubber deforms a lot but also returns, making it elastic but less “perfectly” so.

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Stress and Strain

Stress is the restoring force per unit area developed inside a material when external forces are applied.

Stress = Force / Area → Unit: Pascal (Pa) = N/m²

Strain is the fractional change in dimension (length, volume, or shape) relative to the original dimension.

Strain = Change in dimension / Original dimension → No unit (dimensionless)

⚠️ NDA Trap — NDA 2025-I Q. 139 “Which is dimensionless?” with options: Stress, Strain, Pressure, Force. Strain is dimensionless — it is a ratio of two lengths (ΔL/L) or two volumes (ΔV/V). Stress and Pressure both have units of Pascal (N/m²). Force has units of Newton. Tested directly — the answer is Strain.

⚠️ NDA Trap — NDA 2017-I Q. 108 “Which physical quantity has the same unit as pressure?” with options: Angular momentum, Stress, Strain, Work. Stress has the same unit as Pressure — both are force per unit area, both measured in Pascal (Pa = N/m²). Angular momentum is kg⋅m²/s; work is Joule. Answer: Stress.

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Young’s Modulus

Young’s Modulus (Y) measures a material’s resistance to being stretched or compressed along one direction. It is the ratio of longitudinal stress to longitudinal strain.

Y = Longitudinal Stress / Longitudinal Strain

• A higher Young’s Modulus means the material is stiffer — harder to stretch
• Steel has a much higher Young’s Modulus than rubber
• Young’s Modulus is a property of the material, not of the object’s size or shape

💡 Key Fact The speed of sound in a medium depends on both the elastic property (such as Young’s Modulus) and the inertia property (density) of the medium. This was directly tested in NDA 2016-II Q. 108 — the correct statement is that sound speed depends on both elastic and inertia properties.

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Pressure in Fluids

Pressure is force per unit area. In a fluid at rest, pressure acts equally in all directions at any given depth.

Fluid pressure at depth h: P = ρgh

where ρ is the density of the fluid, g is gravitational acceleration, and h is the depth.

Key properties of pressure in a fluid at rest:

• Pressure increases with depth
• Pressure at the same depth is the same in all directions
• Pressure does not depend on the shape of the container or the area of the base
• Pressure depends only on height of the fluid column and density of the fluid

⚠️ NDA Trap — NDA 2020 Q. 74 “Pressure exerted by a liquid at the base of a beaker depends on the area of the base.” — Wrong. Fluid pressure at the base = ρgh. It depends on the height of the liquid column and the density — not on the area of the base. A wide beaker and a narrow beaker with the same liquid height exert the same pressure at the base.

⚠️ NDA Trap — NDA 2018-I Q. 82 “Pressure is the same at all points in a fluid at rest.” — Wrong. Pressure increases with depth (P = ρgh). It is the same only at the same depth (same horizontal level). Statements 2 and 3 are correct — pressure is exerted on walls, and pressure exists everywhere in the fluid. Correct answer: 2 and 3 only.

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Compressibility

Compressibility is how easily a material’s volume can be reduced by applying pressure.

Correct ranking: Solid < Liquid < Gas

Gases are the most compressible; solids are the least. This was tested directly in NDA 2016-I Q. 100.

⚠️ NDA Trap — NDA 2016-I Q. 100 The option “Solid < Gas < Liquid” is wrong. Gases are far more compressible than liquids. The correct order from least to most compressible: Solid < Liquid < Gas.

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Archimedes’ Principle

Statement: When a body is partially or completely immersed in a fluid, the fluid exerts an upward force (buoyant force) on the body equal to the weight of the fluid displaced by it.

Buoyant Force = Weight of displaced fluid = ρ_fluid × V_submerged × g

This upward force is called buoyancy or upthrust.

⚠️ NDA Trap — NDA 2021-II Q. 114 and NDA 2022-I Q. 95 “Buoyancy is an upward pressure.” — Wrong. This was tested in two separate papers. Buoyancy is an upward force — not pressure. It has units of Newtons, not Pascals. Tested directly in NDA 2021-II and 2022-I with identical question intent.

⚠️ NDA Trap — NDA 2025-I Q. 137 “The buoyant force equals the mass of the body.” — Wrong. Statement 1 in this question was incorrect. The buoyant force equals the weight of the displaced fluid — not the mass of the body. Statement 2 (buoyant force = weight of displaced fluid) is correct. Answer: 2 only.

💡 Key Fact An object submerged in water has an apparent loss of weight equal to the buoyant force. Weight in air minus apparent weight in water = buoyant force = weight of water displaced. This was tested in NDA 2012-I Q. 106 and NDA 2017-II Q. 109.

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Floating and Sinking

Whether an object floats or sinks depends entirely on a comparison of densities:

• Object density < Fluid density → Object floats
• Object density > Fluid density → Object sinks
• Object density = Fluid density → Object is in neutral equilibrium (neither rises nor sinks)

When an object floats:

• The weight of fluid displaced = weight of the floating object
• The object displaces only as much fluid as needed to support its weight

⚠️ NDA Trap — NDA 2025-II Q. 67 “A body sinks in water when it is heavy.” — Wrong. A body sinks when its density is greater than the density of the fluid. A heavy ship made of steel floats because its average density (total mass / total volume, including air spaces) is less than water. The body being “heavy” is irrelevant — density comparison is what determines floating or sinking.

⚠️ NDA Trap — NDA 2018-I Q. 59 “Whether an object floats or sinks depends on its mass and density of liquid.” — Wrong. It depends on the difference in densities of the object and the liquid. Mass alone does not determine floating — a massive but hollow steel ship floats; a small iron nail sinks.

💡 Key Fact — NDA 2010-II Q. 130 When a ship floats on water, the mass of water displaced equals the mass of the ship. This is a direct consequence of Archimedes’ Principle applied to floating bodies. The displaced water supports the ship’s full weight.

💡 Key Fact — NDA 2023-II Q. 108 An iron nail sinks but an iron ship floats. Both are made of iron. The difference: the average density of the ship (steel hull + large air spaces inside) is less than water. The average density of a solid iron nail is much greater than water. Correct statements: 2 (nail density > water) and 3 (ship density < water). Answer: 2 and 3.

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Stable Floating — Centre of Buoyancy

A floating body is in stable equilibrium when its centre of gravity is below its metacentre. The metacentre is the point through which the buoyant force acts when the body is slightly tilted. If the centre of gravity is above the metacentre, the body topples. This was tested in NDA 2026-I Q. 59.

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Density and Relative Density

Density (ρ) = mass per unit volume.

ρ = m/V → Unit: kg/m³ or g/cm³

Relative Density (RD) = density of a substance relative to the density of water at 4°C.

RD = ρ_substance / ρ_water → No unit (dimensionless)

💡 Key Fact Density of water is maximum at 4°C (277 K) = 1000 kg/m³. This was directly tested in NDA 2021-I Q. 52 and NDA 2024-II Q. 114. The answer is 4°C, not 0°C. At 0°C, ice forms and density drops.

💡 Key Fact Relative Density has no unit — it is a pure ratio. This is a common NDA question in units-and-dimensions format. It is sometimes called specific gravity.

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Surface Tension

Surface tension is the tendency of a liquid’s surface to contract to the smallest possible area. It arises because molecules at the surface experience a net inward pull from molecules below (cohesive forces), while having no molecules above to balance.

Effects of surface tension (results):

• Nearly spherical raindrops — the sphere minimises surface area for a given volume
• Capillary rise of water
• Insects walking on water
• Soap and detergent cleaning action (lowers surface tension, helps spread)
• Formation of soap bubbles and films

NOT a result of surface tension:

• Flow of a liquid — flow is due to gravity and pressure differences, not surface tension

⚠️ NDA Trap — NDA 2015-I Q. 62 “Which one is NOT a result of surface tension?” with options including spherical raindrops, capillary rise, soap cleaning action, and flow of a liquid. The answer is flow of a liquid — flow happens due to pressure gradient and gravity, not surface tension.

⚠️ NDA Trap — NDA 2025-II Q. 66 “Surface tension increases when temperature increases.” — Wrong. Surface tension decreases with increasing temperature. As temperature rises, molecules have more kinetic energy and the cohesive forces weaken, reducing surface tension. Answer: (b) It decreases when temperature increases.

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Capillary Action

When a narrow tube (capillary) is placed in a liquid, the liquid may rise or fall in the tube depending on the interaction between the liquid and the tube material.

Water in a glass capillary tube → rises (adhesive force > cohesive force, angle of contact < 90°)

Mercury in a glass capillary tube → falls (depressed) (cohesive force > adhesive force, angle of contact > 90°)

Length of liquid column when capillary is inclined: When a capillary tube containing a risen liquid column is inclined, the length of the liquid column increases, but the vertical height remains the same. The vertical component of the column length is constant — inclined at 45°, the column is longer but the height is unchanged. Tested in NDA 2011-I Q. 70 — length increases when inclined.

💡 Key Fact Capillary rise is a result of surface tension. The smaller the radius of the capillary tube, the greater the rise. This is why water climbs higher in thinner tubes.

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Viscosity

Viscosity is the property of a fluid that resists flow — the internal friction between fluid layers. A more viscous fluid flows more slowly.

• High viscosity: honey, glycerine, thick oil
• Low viscosity: water, petrol

Effect of temperature on viscosity:

• Liquids: viscosity decreases with increasing temperature (hot honey flows more easily)
• Gases: viscosity increases with increasing temperature

💡 Key Fact Viscosity is not the same as surface tension. Viscosity relates to resistance to flow through the bulk of the liquid; surface tension is a property of the surface layer only.

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Streamline (Laminar) Flow

In streamline (or laminar) flow, every fluid particle at a given point follows the same path as the particle before it. The velocity at any given point remains constant over time.

Key facts about streamline flow:

• Also called steady flow or laminar flow
• Velocity of particles at a given fixed point is the same at all times
• Two streamlines never cross each other
• In steady flow, each particle passing through a point follows the same path

⚠️ NDA Trap — NDA 2015-II Q. 119 “In steady flow, each particle may not follow the same path as a previous particle through the same point.” — Wrong. This is the defining feature of streamline flow: every particle at a given point follows the same path as preceding particles. This statement is the NOT correct statement in that question.

⚠️ NDA Trap — NDA 2016-II Q. 103 “In streamline flow, the velocity of all fluid particles at a given instant is the same.” — Wrong. In streamline flow, the velocity at a given fixed point remains constant over time — but different points in the fluid can have different velocities. The velocity of a particle reaching a given position is constant, not the velocity of all particles at the same instant.

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Bernoulli’s Principle

Bernoulli’s Principle states that for a fluid in steady flow, an increase in the speed of flow leads to a decrease in pressure.

It is based on the law of conservation of energy. The total energy (pressure energy + kinetic energy + potential energy) remains constant along a streamline.

💡 Key Fact — NDA 2014-I Q. 99 Bernoulli’s Principle is based on conservation of energy — not conservation of mass or momentum. This was tested directly with all four conservation laws as options. Answer: Conservation of energy.

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Tables & Comparisons

Stress vs Strain

Property	Stress	Strain
Definition	Force per unit area inside material	Fractional change in dimension
Formula	Stress = F/A	Strain = ΔL/L (or ΔV/V)
SI Unit	Pascal (Pa) = N/m²	No unit — dimensionless
Same unit as	Pressure	Nothing (pure ratio)
NDA tested	Unit identification — same as pressure	Dimensionless — NDA 2025-I

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Elasticity vs Plasticity

Property	Elastic Material	Plastic Material
Behaviour after force removed	Returns to original shape	Does not return
Example	Steel, rubber (within limits)	Clay, putty, lead
Elastic limit	Deforms below this and recovers	Deforms permanently above this

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Floating vs Sinking

Condition	What Happens	Reason
ρ_object < ρ_fluid	Object floats	Buoyant force > weight
ρ_object > ρ_fluid	Object sinks	Weight > buoyant force
ρ_object = ρ_fluid	Object in neutral equilibrium	Weight = buoyant force
Hollow steel ship	Floats	Average density < water (includes air spaces)
Solid iron nail	Sinks	Density > water (no air spaces)

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Water vs Mercury in a Capillary Tube

Property	Water in Glass	Mercury in Glass
Behaviour	Rises in capillary	Falls (depressed) in capillary
Dominant force	Adhesion > Cohesion	Cohesion > Adhesion
Angle of contact	< 90° (acute)	> 90° (obtuse)
Meniscus shape	Concave (curves up at edges)	Convex (curves down at edges)
Practical consequence	Water wets glass	Mercury does not wet glass

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Density vs Relative Density

Property	Density (ρ)	Relative Density (RD)
Definition	Mass per unit volume	Ratio of density to density of water
Formula	ρ = m/V	RD = ρ_substance / ρ_water
Unit	kg/m³ or g/cm³	No unit (dimensionless)
Reference	—	Water at 4°C (1000 kg/m³)
Also called	—	Specific gravity

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Surface Tension vs Viscosity

Property	Surface Tension	Viscosity
Location	Property of the surface only	Property of the bulk of the fluid
Cause	Net inward cohesive force on surface molecules	Internal friction between fluid layers
Decreases with temperature	Yes	Yes (for liquids)
Increases with temperature	No	Only for gases
SI Unit	N/m	Pa⋅s
Examples	Soap films, capillarity, spherical drops	Honey flowing slowly, motor oil

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Formulas

Formula 1 — Stress

Stress = F/A

F	Applied force (N)
A	Cross-sectional area perpendicular to force (m²)
Stress	Internal restoring force per unit area (Pa = N/m²)

Used when: Analysing how much force per unit area a material is experiencing under an applied load.

⚠️ NDA Trap: Stress has the same unit as pressure (Pa). Students often confuse this. Stress = N/m² = Pa, exactly like pressure. Strain is the dimensionless partner — it has no unit at all.

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Formula 2 — Strain

Strain = ΔL / L

ΔL	Change in length (m)
L	Original length (m)
Strain	Dimensionless (pure ratio)

Used when: Determining how much a material has deformed relative to its original size.

⚠️ NDA Trap: Strain has no unit. It is a ratio of two lengths. Students sometimes write Pa or N/m² for strain — this is wrong. Only stress and pressure have those units.

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Formula 3 — Young’s Modulus

Y = Stress / Strain = (F/A) / (ΔL/L)

Y	Young’s Modulus (Pa = N/m²)
F/A	Longitudinal stress (Pa)
ΔL/L	Longitudinal strain (dimensionless)

Used when: Comparing stiffness of materials (higher Y = stiffer material).

⚠️ NDA Trap: Since Young’s Modulus = Stress/Strain and strain has no unit, Young’s Modulus has the same unit as stress: Pa (N/m²). It is not dimensionless despite involving a dimensionless quantity in the denominator.

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Formula 4 — Density

ρ = m/V

ρ	Density (kg/m³)
m	Mass (kg)
V	Volume (m³)

Used when: Finding the density of any substance, or checking whether an object will float or sink by comparing densities.

Key value: Density of water = 1000 kg/m³ = 1 g/cm³ (at 4°C)

⚠️ NDA Trap: When mixing equal volumes of liquids with densities D, 2D, and 3D: average density = (D + 2D + 3D)/3 = 6D/3 = 2D. Not 6D (that would be sum, not average). Tested in NDA 2014-II Q. 121.

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Formula 5 — Relative Density

RD = ρ_substance / ρ_water

Also: RD = Weight of substance in air / Loss of weight in water

RD	Relative Density (dimensionless)
ρ_substance	Density of the material (kg/m³)
ρ_water	Density of water = 1000 kg/m³

Used when: Comparing densities without needing absolute values, or in buoyancy problems.

⚠️ NDA Trap: Relative density has no unit — it is a ratio. Also, relative density of silver with respect to iron (NDA 2013-I) is NOT simply silver’s specific gravity. It is 11/8 = 1.375 ≈ 1.4, not 3.0 or 2.8.

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Formula 6 — Buoyant Force (Archimedes’ Principle)

F_b = ρ_fluid × V_submerged × g

Also stated as: F_b = Weight of fluid displaced

F_b	Buoyant force (N) — always upward
ρ_fluid	Density of the fluid (kg/m³)
V_submerged	Volume of object submerged in the fluid (m³)
g	Gravitational acceleration (m/s²)

Used when: Finding the upward force on a submerged or partially submerged object.

⚠️ NDA Trap: Buoyant force depends on the volume of fluid displaced and the density of the fluid — not on the density or mass of the object itself. Two objects of equal volume submerged in the same fluid experience the same buoyant force, regardless of their materials.

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Formula 7 — Fluid Pressure

P = ρgh

P	Pressure at depth h (Pa = N/m²)
ρ	Density of the fluid (kg/m³)
g	Gravitational acceleration (m/s²)
h	Depth below the free surface (m)

Used when: Finding the pressure at a specific depth in a fluid, or comparing pressures at different depths.

⚠️ NDA Trap: Pressure in a fluid at a given depth does not depend on the area of the container base or the total volume of fluid. A tall narrow column and a wide shallow basin with the same fluid height exert the same pressure at the bottom.

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Worked NDA Numericals

NDA Paper	Given	Formula	Answer
NDA 2013-I Q. 138: Specific gravity of silver = 11, iron = 8. Relative density of silver w.r.t. iron?	RD_Ag = 11, RD_Fe = 8	RD_Ag/RD_Fe = 11/8 = 1.375 ≈ 1.4	≈ 1.4
NDA 2014-II Q. 121: Three liquids D, 2D, 3D mixed in equal volumes. Average density?	Equal volumes → average = (D+2D+3D)/3 = 6D/3	Arithmetic mean of densities	2D
NDA 2019-II Q. 65: Mixed in equal volumes: RD = 4. Mixed in equal masses: RD = 3. Find ρ₁ and ρ₂.	Equal volumes: (ρ₁+ρ₂)/2 = 4 → ρ₁+ρ₂ = 8. Equal masses: 2ρ₁ρ₂/(ρ₁+ρ₂) = 3 → 2ρ₁ρ₂ = 24 → ρ₁ρ₂ = 12. Solve: sum=8, product=12 → ρ=2,6	Harmonic and arithmetic mean	ρ₁=6, ρ₂=2
NDA 2022-II Q. 134: Packet: volume = 1L = 1000 cm³, mass = 800g. Float or sink in water (1 g/cm³) and liquid B (1.5 g/cm³)?	Density of packet = 800/1000 = 0.8 g/cm³. Compare: 0.8 < 1 (water) → floats; 0.8 < 1.5 (B) → floats	ρ_object vs ρ_fluid	Floats in both
NDA 2024-II Q. 92: Pumpkin weighs 7.5 N. Submerged: displaces ¾ L = 0.75 L = 0.00075 m³. g = 10. Find density.	Mass = W/g = 7.5/10 = 0.75 kg. Volume = 0.00075 m³. ρ = m/V = 0.75/0.00075 = 1000 kg/m³	ρ = m/V	1000 kg/m³
NDA 2024-II Q. 114: Water maximum density temperature?	Water density is maximum at 4°C = 277 K (not 0°C, not 100°C)	Direct recall	277 K (4°C)