From why a ship floats to why oil rises in a wick, the properties of matter and fluid mechanics chapter explains how solids stretch and liquids push, lift and flow. For the NDA exam this is a high-scoring, formula-light zone: a handful of laws — Pascal, Archimedes and Bernoulli — cover most questions. Master the definitions and you bank these marks fast.
Why This Topic Matters for NDA
The NDA General Ability Test packs Physics with conceptual questions, and properties of matter is a favourite because the answers depend on a clear definition rather than long calculation. Year after year you will see one-liners on buoyancy, pressure, surface tension and Bernoulli's principle.
The good news: this chapter rewards understanding over memory. If you can picture why a needle floats on water or why a hydraulic jack lifts a car, the questions answer themselves. Most asked questions are direct one-liners, and even the numericals use just one short formula, so a focused revision here gives a very strong return for the small time you invest.
For a defence aspirant the topic is also practical. Submarines rise and sink using buoyancy, aircraft fly because of pressure differences over the wings, and hydraulic systems operate the brakes and landing gear of every modern machine. Learning the physics here is genuinely useful, not just exam stuff, and that makes it easier to remember under pressure on exam day.
Matter exists in three common states — solid, liquid and gas. Solids resist a change in shape (rigidity); liquids and gases flow, so together they are called fluids.
Elasticity, Stress and Strain
Elasticity is the property by which a body regains its original shape and size after the deforming force is removed. A body that does not regain its shape is called plastic. Steel, rubber and quartz are elastic, while wet clay and dough are plastic. Interestingly, quartz is one of the most perfectly elastic materials known, while putty is almost perfectly plastic.
Every elastic body has an elastic limit. As long as the applied force stays below this limit, the body returns fully to its original form. Beyond the elastic limit a permanent deformation, called a permanent set, remains even after the force is removed, and if you keep increasing the load the body finally breaks at the breaking point.
Stress
Stress is the restoring force acting per unit area inside a deformed body.
Stress = Force ÷ Area, measured in N/m2 (pascal, Pa). Same units as pressure.
Strain
Strain is the ratio of change in dimension to the original dimension. It has no units because it is a ratio.
- Longitudinal strain = change in length ÷ original length
- Volume strain = change in volume ÷ original volume
- Shear strain = angle of deformation
Hooke's Law and the Three Moduli
Hooke's law states that within the elastic limit, stress is directly proportional to strain. The constant of proportionality is the modulus of elasticity.
Modulus of elasticity = Stress ÷ Strain
Young's modulus (Y) → for change in length (longitudinal)
Bulk modulus (K) → for change in volume
Modulus of rigidity (η) → for change in shape (shear)
A higher modulus means a more rigid material. Steel has a larger Young's modulus than rubber, so steel is far less stretchy — an important and often-asked fact.
The reciprocal of bulk modulus is compressibility. Gases have very high compressibility (low bulk modulus); solids and liquids are almost incompressible.
Pressure in Fluids
Pressure is the normal force exerted by a fluid per unit area. In a liquid column the pressure increases with depth.
Pressure at depth h: P = h × ρ × g
where ρ = density of liquid, g = acceleration due to gravity (≈ 9.8 m/s2), h = depth.
- Pressure depends only on depth, density and g — not on the shape or amount of liquid.
- Pressure acts equally in all directions at a given depth.
- Atmospheric pressure at sea level ≈ 1.013 × 105 Pa, measured by a barometer.
This is why dam walls are built thicker at the bottom — water pressure is greatest where the water is deepest.
Pascal's Law and Hydraulic Machines
Pascal's law states that pressure applied to an enclosed fluid is transmitted equally and undiminished in all directions throughout the fluid.
This single idea powers the hydraulic lift, hydraulic brakes and the hydraulic press. A small force on a small piston produces a large force on a large piston, because the same pressure acts over a much bigger area. The two pistons are connected by an incompressible liquid, usually oil, which transmits the pressure without being squashed.
Picture a car service station: the mechanic pushes down gently on a narrow piston, and the wide piston under the car lifts the whole vehicle. The force is multiplied in the ratio of the two piston areas. The same logic, in reverse, lets your foot press a small brake pedal yet stop a heavy car at all four wheels.
For two pistons: F1 ÷ A1 = F2 ÷ A2
So a larger output area A2 gives a larger output force F2.
A hydraulic machine multiplies force, not work. The large piston moves a smaller distance, so energy is conserved.
Archimedes' Principle and Floating
When a body is wholly or partly immersed in a fluid, it experiences an upward force called buoyancy (or upthrust).
Archimedes' principle: the buoyant force equals the weight of the fluid displaced by the body.
Buoyant force = Vdisplaced × ρfluid × g
Law of Floatation
- If weight of body > buoyant force → body sinks.
- If weight of body = buoyant force → body floats fully submerged.
- If weight of body < weight of equal volume of fluid → body floats partly out.
A body floats when its average density is less than the density of the fluid. A ship made of heavy steel floats because its hollow shape lowers its average density.
An iceberg shows only about 1/10 above water because the density of ice (≈ 0.9) is close to that of water (1.0).
Surface Tension and Capillarity
Surface tension is the property of a liquid surface to behave like a stretched elastic membrane. It arises because molecules at the surface are pulled inward by cohesive forces.
- Surface tension makes a liquid try to acquire the minimum surface area, which is why small drops are spherical.
- It lets a steel needle or a water insect rest on water without sinking.
- Surface tension decreases with rise in temperature and decreases when soap or detergent is added.
Capillarity
The rise or fall of a liquid in a narrow tube is capillarity. Water rises in a thin tube (wets glass); mercury falls (does not wet glass).
Capillary action explains how oil rises in a lamp wick, water moves up through soil, and ink spreads on blotting paper.
Detergents work by lowering surface tension, helping water spread into cloth and lift dirt.
Viscosity and Fluid Flow
Viscosity is the internal friction between layers of a fluid that opposes their relative motion. When one layer of fluid slides over another, this friction tries to slow them down. A thick fluid like honey is highly viscous; water is much less viscous, and air has very little viscosity. This is why honey takes ages to pour but water gushes out instantly.
- For liquids, viscosity decreases as temperature rises (hot honey flows easily).
- For gases, viscosity increases with temperature.
Terminal velocity
A body falling through a viscous fluid speeds up until the drag balances gravity, then moves at a constant terminal velocity. This is why a raindrop does not keep accelerating all the way down.
An ideal fluid is non-viscous and incompressible. Flow is streamline (laminar) at low speed and turbulent at high speed.
Bernoulli's Principle
Bernoulli's principle states that for a flowing ideal fluid, where the speed is high the pressure is low, and where the speed is low the pressure is high. It is a statement of conservation of energy for fluids.
P + ½ρv2 + ρgh = constant along a streamline.
Everyday consequences:
- Aeroplane lift — faster air over the curved top of a wing means lower pressure above, lifting the wing.
- A spinning cricket ball swings because of unequal air speeds on its two sides.
- Two boats moving side by side are drawn together as fast water between them lowers the pressure.
Bernoulli's principle holds for an ideal, non-viscous, streamline flow. Do not apply it blindly to thick or turbulent fluids in the exam.
Worked Example
A body weighs 50 N in air and 40 N when fully immersed in water. Find the buoyant force and the volume of the body. (Take g = 10 m/s2, density of water = 1000 kg/m3.)
So the buoyant force is 10 N and the volume of the body is 1000 cm3 (one litre).
The apparent loss of weight of an immersed body always equals the buoyant force. This shortcut solves most NDA buoyancy numericals in one line.
Common Mistakes to Avoid
Thinking pressure depends on the amount of liquid. It depends only on depth, density and g — a narrow deep tank can have higher pressure than a wide shallow lake.
Believing a hydraulic press creates extra energy. It only multiplies force; the work done stays the same.
Saying surface tension increases with temperature. It decreases as a liquid is heated.
Confusing the moduli: Young's is for length, bulk is for volume, rigidity is for shape.
Previous-Year Question and Quick Recap
Q. A ship floating in sea water moves into a river. What happens to the level of the ship in the water?
Answer: River water is less dense than sea water, so it gives less buoyant force per unit volume. The ship must displace more water to stay afloat, so it sinks a little deeper in river water.
- Elasticity = ability to regain shape; Stress = F/A, strain is unitless.
- Hooke's law: stress ∝ strain; moduli are Young's, bulk, rigidity.
- Pressure in liquid P = hρg, acts equally in all directions.
- Pascal: pressure transmits equally → hydraulic lift and brakes.
- Archimedes: upthrust = weight of fluid displaced; floats if density is lower.
- Surface tension makes drops spherical and drives capillarity.
- Viscosity is internal fluid friction; gives terminal velocity.
- Bernoulli: high speed → low pressure (aeroplane lift).
Frequently asked questions
What is the difference between stress and pressure?
Both are force per unit area with the same unit (pascal). Pressure is an external force applied on a surface, while stress is the internal restoring force per unit area set up inside a deformed body.
Why does a ship float while an iron nail sinks?
A ship is hollow, so its average density is much less than water and it floats by displacing enough water. A solid iron nail has density greater than water, so its weight exceeds the buoyant force and it sinks.
Which principle explains the working of a hydraulic lift?
Pascal's law. Pressure applied to an enclosed fluid is transmitted equally in all directions, so a small force on a small piston produces a large force on a large piston.
Does surface tension increase or decrease with temperature?
Surface tension decreases as temperature rises. Adding soap or detergent also lowers it, which is why warm soapy water cleans clothes more effectively.
What is terminal velocity?
It is the constant maximum velocity a body reaches while falling through a viscous fluid, when the upward viscous drag and buoyancy exactly balance the downward weight, so acceleration becomes zero.
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