**Category : **SSC

**Elasticity and Plasticity**

The property of the body to regain its original configuration (length, or shape) when the deforming forces are removed is called elasticity. On the other hand, if the body does not have any tendency to regain its original configuration on removal of deforming force the body is called plastic body and this property is called plasticity.

**Perfectly elastic body:**A body which regains its original configuration immediately and completely after the removal of deforming force from it, is called perfectly elastic body. Quartz and phosphor bronze, are closed to perfectly plastic body.**Perfectly plastic body:**A body which does not regain its original configuration at all on the removal of deforming force, however small the deforming force may be is called perfectly plastic body. Putty mid mud are closed to perfectly plastic body.**Stress**

The internal restoring force acting per unit area of a body is called stress. i.e., Stress = Restoring force/Area

**Strain**

The ratio of change in configuration to the original configuration is called strain.

\[strain=\frac{Change\,in\,\,configuration}{Original\,Configuration}\]

Strain being the ratio of two like quantities has no units and dimensions.

**Elastic Limit**

Elastic limit is the upper limit of deforming force up to which, if deforming force is removed, the body regains its original form completely and beyond which, if deforming force is increased, the body loses its property of elasticity and gets permanently deformed.

**Hooke's low**

It states that within the elastic limit stress is directly proportional to strain.

i.e.. Stress \[\propto \]strain or Stress =\[E\times \] strain

Stress or \[\frac{Stress}{strain}=E=Cons\tan t\]

Here E is the coefficient of proportionality and is called modulus of elasticity or coefficient of elasticity of a body:

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**Materials-Ductile, Brittle and Elastomers**

**(i) Ductile materials:** The materials which have large range of plastic extension are called ductile materials. They can be drawn into thin wires, e.g., copper, silver, aluminium, iron, etc.

**(ii) Brittle materials:** The materials which have very small range of plastic extension are called brittle materials. These materials break as soon as the stress is increased beyond the elastic limit, e.g., glass, ceramics, cast iron, etc.

**(iii) Elastomers:** The materials which can be stretched to large values of strain are called elastomers. e.g., rubber, elastic tissue of aorta, etc.

**Young's modulus of elasticity (Y):**It is defined as the ratio of normal stress to the longitudinal strain within the elastic limit. Thus, \[Y=\frac{Normal\,Stress}{Longitudinal\,Strain}\] or, \[Y=\frac{F/\pi {{r}^{2}}}{\Delta l/{{L}_{0}}}=\frac{Mg{{L}_{0}}}{\pi {{r}^{2}}\Delta l}\]

**Thermal Stress**

When a rod is rigidly fixed at its two ends and its temperature is changed, then a thermal stress is set up in the rod. And the corresponding strain developed is called thermal strain, Thermal stress \[=\frac{Force}{Area\,\,of\,\,cross\,\,\sec tion}=\frac{F}{A}=Y\alpha \Delta \theta \] Area of cross section A where \[\alpha \] = coefficient of linear expansion of the rod \[\Delta \theta \] = change in temperature.

**Fluids**

Fluids are the substances that can flow. Therefore liquids and gases both are fluids. The study of fluids at rest is called fluid statics or hydrostatics and the study of fluids in motion is called fluid dynamics or hydrodynamics. Both combined are called fluid mechanics.

**Density (p)**

Mass per unit volume is defined as density. So density at a point of a fluid is represented as \[\rho =\underset{\Delta v\to 0}{\mathop{\lim }}\,\frac{\Delta m}{\Delta V}=\frac{dm}{dV}\]where m is the mass and v is the volume of the fluid,

**Relative Density**

It is defined as the ratio of the density of the given fluid to the density of pure water at 4°C. Relative density (R.D). \[=\frac{Density\,\,of\,\,given\,\,liquid}{Density\,\,of\,\,pure\,\,water\,at\,{{4}^{0}}C}\]The density of water is maximum at 4°C and is equal to. \[1.0\times {{10}^{3}}kg{{m}^{-3}}\]

**Pressure**

If a uniform force is exerted normal to an area (A), then average pressure (\[{{P}_{av}}\]) is defined as the normal force (F) per unit area. i. e., \[{{P}_{av}}=\frac{F}{A}\]

**Properties of Matter**

In limiting sense, pressure\[p=\underset{\Delta A\to 0}{\mathop{\lim }}\,\frac{\Delta F}{\Delta A}\]. Pressure is a scalar quantity.

**SI unit:** pascal (Pa), 1Pa= \[1N/{{m}^{2}}\]

**Practical units:** atmospheric pressure (atm), bar and ton 1 atm \[=1.01325\times {{10}^{5}}Pa=\]1.01325 bar = 760 torr = 760mm of Hg column pressure.

**Pascal's Law of Transmission of Fluid Pressure**

Pascal's law is stated in following ways:

The pressure in a fluid at rest is same at all the points if gravity is ignored.

A liquid exerts equal pressures in all directions.

If the pressure in an enclosed fluid is changed at a particular point, the change is transmitted to every point of the fluid and to the walls of the container without being diminished in magnitude.

**Applications of Pascal's law:** Hydraulic machines, lifts, presses and brakes, are based on the Pascal's law.

**Atmospheric Pressure**

Force exerted by air column on unit cross-section area of sea level is called atmospheric pressure \[({{P}_{0}})\]

\[{{P}_{0}}=\frac{F}{A}=101.3KN/{{M}^{2}}\]

Barometer is used to measure atmospheric pressure which was discovered by Torricelli. Atmospheric pressure varies from place to place and at a particular place from time to time.

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**Buoyancy and Archimed Principle**

If a body is partially or wholly immersed in a fluid, it experiences an upward force due to the fluid surrounding it. This phenomenon offeree exerted by fluid on the body is called buoyancy and force is called buoyant force or upthrust.

**Archimedes’ Principle:** It states that the buoyant force on a body that is partially or totally immersed in a fluid equal to the weight of the fluid displaced by it.

**Bernoulli's Principle**

When incompressible, non-viscous, irrotational liquid i.e., ideal liquid flow from one position to other in streamline path then in its path at every point, the sum of pressure energy, kinetic energy and potential energy per unit volume remains constant. i.e., \[{{P}_{1}}+\rho g{{h}_{1}}+\frac{1}{2}\rho {{V}_{1}}^{2}={{P}_{2}}+\rho g{{h}_{2}}+\frac{1}{2}\rho V_{2}^{2}\]

\[\therefore P+\rho gh+\frac{\rho {{v}^{2}}}{2}=constant\]

**Viscosity**

The property of a fluid due to which it opposes the relative motion between its different layers is called viscosity (or fluid friction or internal friction) and the force between the layers opposing the relative motion is called viscous force. According to Newton, the frictional force or viscous force between two layers depends upon the following factors:

\[F\propto A\frac{dv}{dy}\] or \[F=-\eta A\frac{dv}{dy}\] where, \[\eta \] is a constant called coefficient of viscosity or simply viscosity of fluid.

**Factors Affecting Viscosity**

** (1) Effect of temperature:** On increasing temperature viscosity of a liquid decreases. While it increases in the case of gases.

**(2) Effect of pressure:** On increasing pressure viscosity of a liquid increases but viscosity of water decreases. Viscosity of gases is independent of pressure.

**Stoke's Law**

According to stake's law, the viscous drag force F on a spherical body of radius r moving through a fluid of viscosity \[\eta \] with a velocity called terminal velocity v is given by. \[F=6\pi \eta rv\]

**Terminal Velocity**

It is maximum constant velocity acquired by the body while falling freely in a viscous medium. \[{{V}_{T}}=\frac{2{{r}^{2}}(\rho -\alpha )}{9\eta }\]

**Surface Tension**

Surface tension is basically a property of liquid. The liquid surface behaves like a stretched elastic membrane which has a natural tendency to contract and tends to have a minimum possible surface area. This property of liquid is called surface tension. Surface tension \[T=\frac{Force\,F}{Length\,L}\]

**Examples of surface tension**

Raindrops are spherical in shape.

The hair of a shaving brush cling together when taken out of water.

Oil spread on cold water but remains as a drop on hot water etc.

**Angle of Contact (\[\theta \])**

The angle enclosed between the tangent plane at the liquid surface and the tangent plane at the solid surface at the point of contact inside the liquid is termed as the angle of contact.

**Angle of contact of various solid-liquid pairs**

**Capillarity**

A glass tube with fine bore and open at both ends is known as capillary tube. The property by virtue of which a liquid rise or fall in a capillary tube is known as capillarity. Rise or fall of liquid in tubes of narrow bore (capillary tube) is called capillary action. Rise of kerosene in lanterns, rise of ink in fountain pen etc. are due to capillary action.

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