Properties of Solids and Liquids Chapter - Physics JEE Main

JEE Main Physics Chapters 

1

Units and Measurement

11

Electrostatics

2

Kinematics

12

Current Electricity

3

Laws of Motion

13

Magnetic Effects of Current and Magnetism

4

Work, Energy and Power

14

Electromagnetic Induction and Alternating Currents

5

Rotational Motion

15

Electromagnetic Waves

6

Gravitation

16

Optics

7

Properties of Solids and Liquids

17

Dual Nature of Matter

8

Thermodynamics

18

Atoms and Nuclei

9

Kinetic Theory of Gases

19

Electronic Devices

10

Oscillations and Waves

20

Communication Systems

Name of the Concept

Key Points of the Concept

Elasticity of Solids and its elastic behaviour

• Some solids can regain its shapee and size after deforming force is removed. This is called elasticity.

• If the body cannot regain its shape and size, then the body is said to be plastic. The body undergo permanent deformation due to its plastic behaviour.

• Stress is the restoring force acting per unit area of cross-section of the body. The unit of stress is N/m2. 

• The different types of stress are longitudinal stress, volume stress and tangential stress.

$\text{stress}=\dfrac{\text{Force}}{\text{Area}}$

• The strain is the ratio of change in dimension to the original dimension when the deforming force is applied.

• The different types of strain are longitudinal strain, volume strain and shearing strain.

Young’s Modulus

• Young’s modulus is the ratio of longitudinal stress to the longitudinal strain.

$\text{Young's modulus}=\dfrac{\text{Longitudinal stress}}{\text{longitudinal strai}}$

$\text{Young's modulus}=\dfrac{F/A}{\Delta l/l}$

• Longitudinal stress occurs in solids only when the deforming force is applied parallel to the length of the wire.

• Longitudinal strain is the ratio of change in length to the original length due to longitudinal stress.

$\text{Longitudinal strain}=\dfrac{\text{change in length}}{\text{original length}}$

$\text{Longitudinal strain}=\dfrac{\Delta l}{l}$

Bulk Modulus

• Bulk modulus is the ratio of normal stress to the volume strain given by the formula,

$\text{Bulk modulus}=\dfrac{\text{Normal stress}}{\text{Volumetric strain}}$

$\text{Bulk modulus}=\dfrac{F/A}{-\Delta V/V}$

$\text{Bulk modulus}=\dfrac{-PV}{\Delta V}$

• Bulk stress or volume stress can act in solids, liquids and gases and it produces volume strain.

• Volume strain is the ratio of change in volume to the original volume given by the formula,

$\text{Volume strain}=\dfrac{\text{change in volume}}{\text{original volume}}$

$\text{Longitudinal strain}=\dfrac{\Delta V}{V}$

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Rigidity modulus

• Modulus of rigidity is the ratio of tangential stress to the shearing strain given by,

$\text{Rigidity modulus}=\dfrac{\text{shearing stress}}{\text{shearing strain}}$

$\eta=\dfrac{F/A}{\text{x/h}}$

• Tangential stress or shear stress is developed when the deforming force is applied tangentially

• Shearing strain is defined as the angle in radians through which the vertical surface gets turned due to tangential force and its formula is given by,

$\text{Shearing strain}=\dfrac{\text{x}}{h}$ 

• The diagram show an example of solid cube undergoing shear stress

Stress-strain curve

• The behaviour of a material can be studied using stress-strain curve.

• The curve obeys Hooke’s law in the region from O to A. According to Hookes law. Stress is proportional to strain.

• In the stress-strain curve given above, the point A corresponds to proportional limit.

•  The yield point or elastic limit is the point upto which the wire shows elastic behaviour and the point B corresponds to the yield point.

• The stress corresponding to the yield point is called yield strength.

• Beyond point B, it loses its elastic behaviour and does not regain its original length even after deforming force is removed.

• The stress corresponding to point  D is called ultimate strength.

Hooke's Law

• Hooke's Law states that the stress (σ) in a material is directly proportional to the strain (ε) produced in it, within the elastic limit. Mathematically, this can be expressed as:

σ = Y * ε

Where:

σ is the stress

ε is the strain

Y is Young's modulus (a material property)

Pressure due to a Fluid Column

• The pressure at any point in a fluid column is determined by the height of the column and the density of the fluid. This concept is crucial in understanding fluid pressure in various applications.

• The pressure due to a fluid column is given by the following equation:

P = ρgh

where:

P is the pressure

ρ is the density of the fluid

g is the acceleration due to gravity

h is the height of the fluid column

Pascal’s Law

• A change in pressure at any point in a confined incompressible fluid at rest is transmitted undiminished to all points in the fluid.

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• The application of pascal’s law are used in hydraulic lift, hydraulic brakes and press.

• In hydraulic lift, a small force is converted to a large force having many times the magnitude of the small force. This is a good example of liquid obeying pascal’s law.

Mercurial Barometer

• Mercurical barometer is used to measure the atmospheric pressure. 

• The fluid pressure corresponds to height of the mercury in the column is equal to the atmospheric pressure.

Archimedes Principle

• According to Archimedes principle, whenever a body is fully or partially submerged in liquid, it experiences a net upward force which is equal to the weight of the liquid displaced.

• The formula to calculate the buoyancy force is given by,

$F_B=\rho_l Vg$

Where ⍴l is the density of the liquid, V is the volume of the body immersed in the liquid and g is the acceleration due to gravity.

• A body will float in a liquid if the buoyancy force acting on the body is equal to the weight  of the body.

Bernoulli’s Theorem

• According to Bernoulli’s theorem, the total energy per unit volume of an incompressible fluid always remains constant at any point of the fluid.

$P+\rho gh+\dfrac{1}{2}\rho v^2=\text{constant}$

$P_1+\rho gh_1+\dfrac{1}{2}\rho v_1^2=P_2+\rho gh_2+\dfrac{1}{2}\rho v_2^2$

Application of Bernoulli’s theorem 

• One of the application of bernouilli’s theorem is the aerodynamic lift.

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• Since the total energy of the fluid remains constant, fluid flowing through upper part of the body will have low pressure compared to the high pressure in the fluid passing through lower side of the body.

• Due to pressure difference, there is a net force or uplift which helps the body to move up.

• Another application is when the ball is moving and spinning in air.

• The ball changes its direction due to pressure difference and this effect is called magnus effect.

Viscosity

• Viscosity is a measure of a fluid's resistance to flow. Understanding viscosity is vital in various applications, such as designing lubricants and understanding the behavior of fluids in pipes.

Stoke’s Law

• When a body falls through a fluid, it drags the layer of the fluid in contact with it, a motion between the different layers of the fluid is set and, as a result the body experiences a retarding force, which is known as Viscous Force.

$F=6\pi\eta rv$

Where η is the coefficient of viscosity, r is the radius of the sphere and v is the velocity of the body.

• When a body is falling through a liquid, it attains a constant speed when the net force acting on the body becomes zero. This is called terminal velocity.

Terminal Velocity, Streamline and Turbulent Flow, Reynolds Number

• Terminal Velocity: Terminal velocity is the constant velocity attained by an object when the drag force equals the gravitational force. It is a critical concept in understanding fluid dynamics.

• Streamline and Turbulent Flow: Understanding the difference between streamline and turbulent flow is important in fluid mechanics, particularly in designing efficient transport systems.

• Reynolds Number: The Reynolds number is a dimensionless quantity that characterizes the flow regime of a fluid. It helps in predicting whether a flow will be laminar or turbulent.

Surface tension and surface energy

• Surface tension is net effect of cohesive forces in downward direction on any surface.

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• The unit of surface tension is N/m.

• Surface energy is the potential energy contained by  the molecules of the liquid surface due to which they stay on the surface against inward force of attraction by other molecules.

• The magnitude of surface energy per unit area and surface tension are equal.

• The relationship between surface tension ans surface energy is given by,

$\text{Surface tension}=\dfrac{\text{Surface energy}}{\text{Area}}$

Angle of Contact

• The angle of contact between a liquid and a solid surface is crucial in understanding the shape of liquid surfaces in various situations.

Heat Transfer - Conduction, Convection, and Radiation

• Heat transfer occurs through conduction (direct contact), convection (through fluid movement), and radiation (through electromagnetic waves). These principles are essential in various fields, from cooking to the design of spacecraft heat shields.

• Explore further elaboration on the distinctions between Conduction, Convection, and Radiation to gain a clearer understanding.

Newton's Law of Cooling

• Newton's Law of Cooling describes the rate of change of temperature of an object in contact with a medium of a different temperature. This law has practical applications in fields such as meteorology and engineering.

• Exploring the diverse aspects of solids and liquids, one can delve into topics such as their mechanical behavior, fluid dynamics, thermal properties, and more.

Sl. No.

Name of the Concept

Formula

1.

Work done in stretching a strain

Work done in stretching a wire having young’s modulus(Y) under a force (F) is given by the formula,

$W=\dfrac{1}{2}\dfrac{YA\Delta l^2}{l}$

2.

Thermal stress on a rod fixed between two rigid supports.

$\text{Thermal stress }=Y\alpha\Delta T$

Where ⍺ is the coefficient of linear expansion and ΔT is the change in temperature

3.

Force constant of the wire having a length(l) and area of cross section(A)

$K=\dfrac{YA}{l}$

4.

Depression produced in the beam of bridge

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$\delta=\dfrac{Wl^3}{4Ybd^3}$

5.

Energy stored per unit volume of wire

$U_V=\dfrac{1}{2}\times\text{stress}\times\text{strain}$

$U_V=\dfrac{1}{2}\times Y\times\text{strain}^2$

6.

Variation Of Pressure With Depth Inside The Fluid

$P_2-P_1=\rho gh$

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7.

Equation of continuity

$A_1V_1=A_2V_2$

Where A1 and A2 are the area of cross section of the pipe at the two ends and V1 and V2 are the corresponding velocity of the fluid.

8.

Velocity of efflux

Velcoity of water flowing out from the container is given by,

$v=\sqrt{2gh}$

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9.

Excess pressure inside a liquid drop

$p=\dfrac{2S}{r}$

Where S is the surface tension and r is the radius of the drop

10.

Excess pressure inside a liquid drop

$p=\dfrac{4S}{r}$

Where S is the surface tension and r is the radius of the bubble.

11.

The height of capillary rise inside a tube

$h=\dfrac{2S\cos\theta}{\rho rg}$

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