Comprehensive WBBSE Class 9 Physical Science Notes Chapter 3 Matter: Structure and Properties can help students make connections between concepts.

## Matter: Structure and Properties Class 9 WBBSE Notes

Fluid : The word fluid comes from a Latin word ‘fluere’ meaning to flow.

Hydrostatics : The branch of Physics which deals with fluid at rest is called hydrostatics.

Hydrodynamics: The branch which deals with fluid in motion is called hydrodynamics.

Density : The density of a substance is its mass per unit volume.

Specific gravity : Specific gravity of a substance is the ratio of the density of a substance to the density of water at 4°C.

Relative density : The specific gravity being ratio of two densities, it is also called relative density.

In C.G.S. system, the density of a substance is numerically equal to its specific gravity.

Hydrostatic pressure : The normal force exerted by the fluid at rest per unit area of the surface in contact with it is called the pressure of fluid or hydrostatic pressure.

Mathematical expression of pressure : If F be the normal force acting on the very small area A of the surface in contact due to the fluid, then the pressure ‘ p ‘ is given by,

p = \(\frac{F}{A}\) t or F = p × A

Thrust : The total normal force exerted by a fluid at rest on a surface in contact with it is thrust.

Unit of pressure :

- CGS : dyne cm
^{-2} - SI : Nm
^{-2}or pascal (Pa)

Dimension of pressure : [ML^{-1}T^{-2}]

Pressure is a scalar quantity as pressure at any point inside a fluid is same in all directions.

Unit of Thrust :

- CGS : dyne
- SI : newton (N)

Pressure at a point in a liquid : Consider a liquid of density ‘d’ contained in a vessel in equilibrium of rest. We are to find the pressure at a point ‘O’ at a depth ‘h’ below the liquid surface. Consider a cylindrical vertical column of liquid of height ‘h’, the area of cross-section of the cylinder being ‘A’. Area ‘A’ is around the point ‘O’.

So, volume of liquid column = hA

mass of the liquid column = h Ad

Weight of the liquid column = h Adg

∴ Force exerted by the liquid column on area A = hAdg

∴ Pressure ‘P’ on A = \(\frac{hAdg}{A}\)

∴ P = hdg

Important points regarding liquid pressure :

- The liquid at rest exerts equal pressure at a point inside the liquid in all directions.
- The liquid at rest exerts equal pressure at all points at the same horizontal level in the liquid.
- The liquid pressure is independent of shape of the liquid surface or the area of the liquid surface, but depends upon the height of liquid column.
- Total pressure at a depth ‘h’ below the liquid surface is equal to (p + hdg), where ‘p’ is the atmospheric pressure and ‘d’ is the density of the liquid.
- Average pressure on the side walls of a containers having liquid of density ‘d’ upto a height ‘h’ is \(\frac{1}{2}\) hdg.
- The liquid pressure is a scalar quantity.
- The thrust exerted by a liquid on the walls of vessel in contact with the liquid acts normally to the surface of the vessel.
- The free surface of a liquid at rest is horizontal.
- The liquid always finds its own level.
- The gauge pressure at a point in a liquid is the difference of total pressure at that point and atmospheric pressure.

Pascal’s Law : The pressure applied at any place to an enclosed fluid at rest is transmitted with undiminished magnitude to every portion of the fluid and acts normally to the surface in contact with the fluid.

Archimedes’ principle : Archimedes’ principle states that a body immersed wholly or partly in a fluid at rest, appears to lose a part of its weight, which is equal to the weight of the fluid displaced.

Buoyancy : The upward thrust which any fluid exerts upon a body partly or wholly submerged in it is called its Buoyancy.

Conditions for Archimedes’ principle and buoyancy :

As Archimedes’ principle involves the weight of a body, so the principle does not hold good when the body is in weightless condition like the state of free fall of the body in an artificial satellite moving in a circular orbit.

The buoyancy does not depend on the depth of the liquid to which the body is immersed or on the shape, mass or material of the body. It depends only on the immersed volume of the body and the density of the displaced liquid at a particular place.

Conditions for floatation of a body :

- When the weight of the body(w) is greater than the weight of the liquid displaced (w), then the body sinks, i.e. w>w.
- When the weight of the body (w) is equal to the weight of the liquid displaced (w), then the body floats completely immersed anywhere within the liquid, i.e. w = w’.
- When the weight of the body is less than the weight of the liquid displaced, then the body floats partly immersed on the surface of the liquid. i.e. w < w

Atmospheric pressure : The weight of a column of air of unit crosssection and which extends from the point under consideration to the top of the atmosphere is called atmospheric pressure.

Standard or Normal temperature and pressure : The standard or normal atmospheric pressure is defined as the pressure exerted by a column of mercury 76 cm high at 0°C at 45° latitude and mean sea-level.

Siphon : A siphon is a simple device for transferring liquid from one vessel to the other without disturbing the whole volume of the liquid or pouring it.

Arrangement of siphon : It consists of a bent tube with one of the arms BD longer than the other AC. The tube is first filled with the liquid to be transferred. The two ends of the tube are then closed with fingers and the shorter limb is placed in the vessel to be emptied below the level of the liquid and two ends are opened. The liquid begins to flow.

Working principle of siphon :

Let ‘p’ be the atmospheric pressure, ‘ d ‘ the density of the liquid and h_{1} and h_{2} be the vertical heights of A and B above the liquid surfaces.

The pressure P_{1} at A = P-h_{1} dg and the pressure P_{2} at B = P-h_{2} dg.

Now as h_{2}>h_{1}, so P_{1}>P_{2},

i.e. Pressure at A > Pressure at B.

Hence the liquid at A is pushed to B. As the liquid moves from A to B the vacancy so produced is filled up by atmospheric pressure forcing more liquid into the tube from the vessel. From the point ‘B’ liquid comes out of longer tube due to gravity and a continuous flow through the siphon takes place.

Conditions for working of a siphon are :

- At first the whole tube must be filled with liquid.
- The end of the longer tube must be below the level of the liquid in the other vessel.
- The height h
_{1}must be less than the height of the corresponding liquid barometer, otherwise the atmospheric pressure will not be able to raise the liquid to the top of the tube. - The siphon will not work in vacuum due to the absence of atmospheric pressure.

Example : 1. We cannot siphon out water from a boat floating on a river to the river. Because the boat is floating in the river and water leaks into the boat from the river, so level of water inside the boat would be same as that of the river outside.

2. There being no atmosphere in the moon, atmospheric pressure is absent there. So normally siphon does not work on the moon. But in the case of pure liquid, the siphon action may be possible even in the moon due to cohesive force of the liquid.

Surface Tension : Surface tension is the property of a liquid by virtue of which the free surface of liquid at rest tends to have minimum area and so it behaves as if covered with a stretched membrane.

Measurement of surface tension : Surface tension is measured as the force acting on unit length of an imaginary line drawn tangentially anywhere on the free surface of the liquid at rest. It acts at right angles to both sides of the line and tangentially to the liquid surface.

Mathematical expression of surface tension :

If ‘F’ be the total force acting on an imaginary line of length l, drawn tangentially on the liquid surface at rest, the force of surface tension ” T ” is given by:

T = \(\frac{F}{l}\)

Units of surface tension :

- CGS : dyne cm
^{-1} - SI : Nm
^{-1 }

Dimensional formula of surface tension : [MT^{-2}]

Surface tension is a scalar quantity as it has no specific direction.

Examples of surface tension :

Raindrops attain spherical shape to acquire minimum area (as we know for a given volume of sphere has minimum surface area) due to surface tension, so that it has minimum surface energy.

An iron needle sinks in water but a greased iron needle placed gently on the water surface at rest is found to float on it. A slight depression on the surface of water can be seen just below the needle, showing that the water surface behaves like a stretched membrane.

A wire ring is dipped in soap solution to form a soap film on it and a loop of cotton thread is gently placed on it. The loop takes an irregular shape. Now on pricking the soap film in the middle position of the loop with a sharp needle, the loop would be found to attain circular shape. It is because the remaining soap film tries to have minimum surface area due to surface tension and for a given perimeter, the area of the circle is maximum.

A little kerosene oil dropped on water is found to spread over the water surface. This is because the surface tension of oil is much less than that of water and so the greater tension of the water stretches the oil in all directions.

Surface energy : It is the amount of work done against the force of surface tension, in forming the liquid surface of a given area at a constant temperature.

Excess of pressure inside a soap bubble or liquid bubble : A soap bubble or a liquid bubble has a very thin film having two surfaces and has air both inside and outside the bubble. So, in this case, excess of pressure ‘ P ‘ inside the bubble is given by :

P = \(\frac{4T}{R}\)

Excess of pressure inside an air bubble in a liquid :

An air bubble inside a liquid has only one surface and so excess of pressure ‘P’ inside it is given by,

P = \(\frac{2 T}{R}\)

If the air bubble is formed at a depth ‘h’ below the free surface of a liquid of density ‘dhr’, then excess of pressure inside the bubble is given by :

P = \(\frac{2T}{R}\) + hdg

Angle of contact: The angle which is tangent to the liquid surface at the point of contact, makes with the solid surface inside the liquid is called angle of contact.

The value of angle of contact :

- the value depends on the nature of the liquid and the solid in contact.
- depends on the medium above the free surface of the liquid.
- is independent of the inclination of the solid with liquid surface.
- is fixed for a given pair of solid and liquid and surrounding medium.

Variation of surface tension :

The presence of impurities in the liquid surface or dissolved in it, considerably affect force of surface tension and depends on the degree of contamination.

The surface tension of a liquid decreases with rise of temperature. The surface tension of a liquid becomes zero at boiling point of the liquid and it vanishes at critical temperature.

Applications of surface tension :

- Surface tension of soap solution is low, and thus it is used for washing. Hot soap solution is still better as surface tension decreases with rise in temperature.
- Surface tension of lubricating oils and paints are kept low, so that they can spread easily.
- Antiseptics have very low surface tensions so that they can spread quickly.
- Oil spreads over the surface of water because the surface tension of oil is less than that of water.
- Rough sea can be calmed by pouring oil on sea-water.
- In soldering, flux is added to reduce the surface tension of molten tin, so that it can spread.

Viscosity : Viscosity is the property of a fluid by virtue of which an internal frictional force comes into play when the fluid is in motion and opposes the relative motion of its different layers.

Co-efficient of viscosity (η) : Co-efficient of a liquid is the tangential force required to maintain a unit velocity gradient between two layers of unit area.

Dimensional formula of :

η = ML^{-1} T^{-1}

Unit of co-efficient of viscosity :

- CGS : Poise
- SI : Pascal-second (PaS) or decapoise

1 decapoise = 1 NSm^{-2}

Decapoise : If 1 newton tangential force is required to maintain a velocity gradient of 1 ms^{-1} m between two layers each of area 1 m^{2} is called 1 decapoise.

Poise : If 1 dyne tangential force is required to maintain a velocity gradient of 1 cms^{-1} / cm between two layers each of area 1 cm^{2} is called 1 poise.

1 decapoise =10 poise

Terminal velocity : It is the constant maximum velocity acquired by a body while falling through a viscous fluid.

The expression of terminal velocity :

v = \(\frac{2 r^2\left(d-d^{\prime}\right) g}{9 \eta}\)

[ Consider a small sphere of radius r and density d falling under gravity in a viscous fluid of density d and coefficient of viscosity η and terminal velocity is r]

Terminal velocity depends upon :

- The terminal velocity of a sphere varies directly as the square of the radius of it.
- The terminal velocity of a sphere is inversely proportional to the co-efficient of viscosity.
- If the density of the material of the sphere be less than the density of the fluid, then the sphere would move upwards to attain terminal velocity.

Variation of viscosity :

- The viscosity of a liquid decreases with increase in temperature.
- The viscosity of all gases increases with increase in temperature.
- With increase in pressure, the viscosity of liquids increases, but viscosity of water decreases.
- With increase in pressure, the viscosity of gases remains unchanged.

Streamline Flow : The streamline or orderly flow of a fluid is that flow in which every particle of the fluid follows exactly the path of its preceding particle and has the same velocity in magnitude and direction as that of its preceding particle while crossing that point.

Laminar Flow : If fluid flowing over a horizontal surface with a steady flow, moves in the form of layers of different velocities which do not mix with each other, then the flow of liquid is called laminar flow.

Turbulent Flow : When a fluid moves with a velocity greater than its critical velocity the motion of the particles of fluid becomes disorderly or irregular and such a flow is called turbulent flow.

Critical velocity : The critical velocity is that velocity of liquid flow, upto which its flow is streamlined and above which its flow becomes turbulent.

Reynold’s number (R): It is the ratio of the inertial force per unit area to viscous force per unit area for a flowing fluid.

Significance of Reynold’s number (R) :

- R < 2000, the flow of a liquid is streamline or laminar.
- R > 3000, the flow of a liquid is turbulent.
- 2000 < R < 3000, the flow is streamline or turbulent.

Energy of a liquid in motion : A liquid in motion possesses three types of energy. These are :

Pressure energy : The energy possessed by a liquid by virtue of its pressure and is measured by the work done in pushing the liquid in the vessel against the pressure without imparting any velocity to it is called the pressure energy of the liquid.

Potential energy : The energy possessed by a liquid by virtue of its height or position above the surface of the earth or any reference level taken as zero level is called the potential energy of the liquid.

Kinetic energy : The energy possessed by a liquid by virtue of its motion or velocity is called the kinetic energy of the liquid.

Bernoulli’s Principle (1738) : For the streamline flow of an ideal fluid (non-viscous and incompressible) the sum of the pressure energy, kinetic energy and potential energy per unit mass is always constant.

Mathematical form of bernoulli’s principle :

For streamline flow of an ideal fluid of density d and passing through any cross-section at a height h with a velocity ‘v’ at pressure p we have

\(\frac{p}{d}\) = Pressure energy per unit mass

gh = Potential energy per unit mass

\(\frac{1}{2}\) vhr^{2} = Kinetic energy per unit mass

According to Bernoulli’s theorem,

\(\frac{p}{d}\) + gh + \(\frac{1}{2}\)v^{2} = const.

or, \(\frac{p}{dg}\) + h + \(\frac{v^2}{2 g}\) = const.

or, p + hdg + \(\frac{1}{2}\)dv^{2} = const.

For the streamline flow of an ideal fluid, the sum of pressure energy per unit volume, potential energy per unit volume and kinetic energy per unit volume is always constant at all cross-sections of the liquid.

Applications of bernoulli’s theorem :

Atomiser or sprayer : It is Based on Bernoulli’s principle. It is used for spraying liquid like perfumes over the body etc.

Blowing off the roofs during storm : During storms or cyclones, sometimes roofs of a hut are found to blow off without causing any damage to the side walls of the house.

Motion of two parallel boats : The boats sailing in the same direction parallel to each other, small distance apart are found to come closer to each other.

Lift on an aeroplane wings: The shape of an aeroplane wings i.e. aerofoil is made in such a way that its upper surface is curved more than its lower surface.

Spinning of a ball (Magnus effect) : A Cricket ball is thrown straight without any spin. The streamlines of air passing are seen evenly passing above and below the ball and the ball continues to move along the original straight direction. But if the ball is released with a spin, the streamlines of air in the same direction as the direction of spinning of the ball, while these are oppositely directed.

Limitations of bernoulli’s theorem :

- It is assumed that velocity of every particle of liquid passing through any particular cross-section of the tube is uniform.
- But acutally, praticles of liquid in the central layer have maximum velocity and those closer to the tubewell have minimum velocity.
- Thus, mean velocity of the particles should be taken.
- The liquid in motion experiences a viscous drag, which should be considered.
- It is assumed here that there is no loss of energy, when the liquid is in motion. But there is always some loss of
- energy as some kinetic energy is lost as heat.
- When the liquid is flowing on a curved path, the energy due to centrifugal force should be considered.

Elasticity : Elasticity is the property by which a body is able to resist deformation, either in shape or in volume or both, and recovers its original configuration when the deforming force is removed.

Types of bodies according to elastic property :

Perfectly rigid body : A body is said to be perfectly rigid, when no relative displacement between its parts occurs under the action of a deforming force, however large it may be.

Perfectly elastic body : A body is said to be perfectly elastic, when it regains its original configuration immediately and completely after the removal of the deforming force, however large it may be.

Perfectly inelastic body : A body is said to be perfectly inelastic or plastic, when it does not regain its original configuration at all on the removal of deforming force, however small it may be.

Partly elastic body : A body is said to be partly elastic when after the removal of the deforming force, it regains only partly its original configuration.

Elastic Limit : Elastic limit is the upper limit of deforming force upto which the body regains its original shape or size completely on removal of deforming force and beyond which on increasing the deforming force, the body loses, its property of elasticity and gets permanently deformed.

Stress : Whenever a deforming force is applied to a body, internal force of reaction comes into play, which tends to resist the deforming force and maintains the original configuration of the body.

This reaction force developed per unit area of the body is called stress.

Types of Stress :

- Normal stress
- Tangential stress.

Normal stress : When the deforming force acts normally over an area of a body, then the internal restoring force set up per unit area of cross-section is called normal stress.

Types of normal stress :

Tensile stress : If there be increase in length or extension of a body in the direction of the applied force, the stress developed is called tensile stress.

Compression stress : If there be decrease in length or compression of a body due to applied force, the stress developed is called compression stress.

Tangential stress : When the deforming force acts tangentially to the surface of a body to produce a change in the shape of the body, then the stress developed in the body is called tangential stress.

Strain : When a deforming force is applied on a body, there is a change in the configuration of the body and the body is said to be strained.

Measurement of strain : The fractional change in the length, volume or shape of a body relative to that in its original configuration is a measure of the strain.

Types of strain :

- Longitudinal strain : If the deforming force produces a change in length alone, the strain produced in the body is called longitudinal strain.
- Volumetric strain : If the deforming force produces a change in volume only, the strain produced in the body is called volumetric strain.
- Shearing strain : If the deforming force produces a change in the shape of the body alone without changing its volume, the strain produced is called shearing strain.

Hooke’s Law : The deformation of an elastic body is directly proportional to the applied force within elastic limit.

Generalised Hooke’s Law : (Modified Hooke’s Law by Scientist Thomas young)

Within elastic limit, stress is proportional to strain.

∴ stress ∝ strain

or, \(\frac{t { stress }}{t { strain }}\) = Constant

This proportionality constant is known as coefficient of elasticity or modulus of elasticity of a body which is independent of magnitude of stress and strain but depends upon the nature of material of the body and the way in which the body is deformed.

Types of modulus of elasticity :

- Young’s modulus of elasticity : It is the ratio of the longitudinal stress to the longitudinal strain within the elastic limit.
- Bulk Modulus of Elasticity : Bulk modulus of elasticity is the volume stress (normal stress) to the volume strain within elastic limit.
- Modulus of rigidity : Modulus of rigidity or shear modulus of a material is the ratio of the shearing stress to the shearing strain within the elastic limit.

Poisson’s Ratio: The ratio of the lateral strain to longitudinal strain of the material of a wire or bar under tension is called its Poisson’s ratio.

Elastic property of Material : A stressstrain curve for a wire of elastic material shown in fig. 3.3. From the figure it is found that OA portion of the curve is a straight line, i.e., stress is linearly related to strain. Hence, the material obey’s Hooke’s law. This is the region of perfect elasticity and ‘A’ represents the elastic limit of the material.

When the stress on the wire is increased beyond ‘A’ i.e., of elastic limit. Hooke’s law is no longer capable of explaining the elastic behaviour. On removal of stress the wire does not regain its original length completely and the wire is said to have acquired permanent set. The wire behaves like a plastic body.

If the process of stretching continued further, a stage is reached when the wire is found to undergo a relatively large strain with almost no increase of stress. This occurs at point ‘B’ called yield point. Beyond this point, metals are called ductile.

Further increase in stress ultimately results in the breaking of the wire and corresponding point ‘C’ on the curve is called breaking point. Breaking stress is the maximum stress that can be applied to a material before it ruptures. If a solid breaks soon after crossing the elastic limit, it is called brittle.