Nick Names
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City
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Golden City
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Amritsar
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Manchester Of India
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Ahmedabad
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City Of Seven Islands
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Mumbai
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Queen Of Arabian Sea
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Cochin
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Space City
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Bangalore
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Garden City Of India
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Bangalore
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Silicon Valley Of India
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Bangalore
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Electronic City Of India
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Bangalore
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Pink City
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Jaipur
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Gateway Of India
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Mumbai
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Twin City:
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Hyderabad, Secunderabad
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City Of Festivals
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Madurai
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Deccan Queen
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Pune
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City Of Buildings
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Kolkata
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Dakshin Ganga
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Godavari
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Old Ganga
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Godavari
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Egg Bowls Of Asia
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Andhra Pradesh
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Soya Region
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Madhya Pradesh
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Manchester Of The South
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Coimbatore
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City Of Nawabs
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Lucknow
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Venice Of The East
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Cochin
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Sorrow Of Bengal
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Damodar River
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Sorrow Of Bihar
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Kosi River
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Blue Mountains
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Nilgiri
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Queen Of The Mountains
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Mussoorie (Uttarakhand)
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Sacred River
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Ganga
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Hollywood Of India
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Mumbai
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City Of Castles
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Kolkata
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State Of Five Rivers
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Punjab
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City Of Weavers
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Panipat
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City Of Lakes
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Srinagar
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Steel City Of India
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Jamshedpur (Called Tatanagar)
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City Of Temples
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Varanasi
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Manchester Of The North
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Kanpur
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City Of Rallies
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New Delhi
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Heaven Of India
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Jammu & Kashmir
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Boston Of India
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Ahmedabad
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Garden Of Spices Of India
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Kerala
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Switzerland Of India
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Kashmir
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Abode Of The God
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Prayag(Allahabad)
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Pittsburg Of India
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Jamshedpur
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Nick Names of Important Indian Places
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Brief on CENSUS 2011
1) The population of the country as per the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.
The major highlights of the Census 2011 (Provisional figures) are as under:
*The population of India has increased by more than 181 million during the decade 2001-2011.
2) %age growth in 2001-2011 is 17.64; males 17.19 and females 18.12.
*2001-2011 is the first decade (with the exception of 1911-1921---GREAT DEPRESSION) which has actually added lesser population compared to the previous decade.
3) *Uttar Pradesh (199.5 million) is the most populous State in the country followed by Maharashtra with 112 million.
Some of the highlights
Ø Slogan - Our census, Our Future
Ø India's 1st Census - 1872
Ø 2011 Census is - 15th Census
Ø Total Population - 1,21,01,93,422
Ø India's Rank in population - 2nd with 17.5% (1st China with 19%)
Ø Most Populous State - Uttar Pradesh
Ø Least Populous State - Sikkim
Ø Most Literate State - Kerala (93.9%)
Ø Least Literate State - Bihar (63.82%)
Ø National Sex Ratio - Female : Male (940 : 1000)
Ø Highest Sex Ratio (State) - Kerala (1084 : 1000)
Ø Lowest Sex Ratio (State) - Haryana
Ø Highest Sex Ratio (UT) - Puducherry
Ø Least Sex Ratio (UT) - Damn & Dayyu (61 : 1000)
Ø Literacy of Male - 82.14%
Ø Literacy of Female - 65.46%
Ø Population Growth Rate - 17.64%
Ø Highest fertility Rate - Meghalaya
Ø Most literate union territory - Lakshadweep (92.2%)
Ø Least literate Union Territory - Dadra Nagar & Haweli
Ø Most Literate District - Serechhip (Mizoram)
Ø Least Literate District - Dadra Naga & Haveli
Ø Highest Density of Population - Bihar (1102 sq.km)
Ø Lowest Density of Population - Arunachal Pradesh (17)
Ø Total number of districts - 640
Ø Highest Populous District - Thane (Mumbai)
Ø 100% Literacy District - Palakkad (Kerala)
Ø 100% Banking State - Kerala
Ø 100% Banking District - Palakkad (Kerala)
Ø Density of Population in India - 382 sq. km
Ø Increase in population (during 2001-2011) - 181 million
Conservation of Momentum - Detailed Explanation of the Principle!
To study this principle, first of all, we should know what the momentum is? Well, momentum is defined as the mass in motion. It can also be defined as the product of the mass and velocity of an object. It is a vector quantity with a magnitude and a direction.
Conservation of momentum, the general law of physics according to which the momentum never changes in an isolated collection of objects.
Law of Conservation of Momentum
The law of conservation of momentum states that for any two objects colliding in an isolated system, the total momentum before the collision is equal to the total momentum after the collision.
This is because the momentum lost by one object is equal to the momentum gained by the second object. This is also known as the principle of conservation of momentum.
Why is the Momentum Conserved?
Conservation of momentum is a consequence of Newton’s third and second law of motion. Suppose that the two objects A and B collide with each other. Then according to Newton’s third law, the force exerted by object B on object A will be equal to the force exerted by an object A on object B. It implies that the two forces act for the same amount of time . i.e.
FBA = -FAB
According to Newton’s second law,
Force = Rate of Change of Momentum
It follows that the rate of change of momentum of A is equal and opposite to the rate of change of momentum of B. Since these are vectors, they are of equal length but are in opposite directions. This means that B loses momentum at the exact rate A gains momentum so that their total momentum remains the same.
Conservation of Linear Momentum
According to the law of conservation of linear momentum, if no external force is acting on a system of bodies, then the total momentum of the system remains constant.
When the net external force is zero, then the rate of change of momentum is zero. Therefore the law of conservation of momentum can be expressed mathematically as
Initial momentum = Final momentum i.e.
Pi = Pf
Examples based on Conservation of Momentum
The rocket fuel burns push the exhaust gases downwards, and due to this, the rocket gets pushed upwards. Motorboats also work on the same principle, it pushes the water backwards and gets pushed forward to conserve momentum.
Numerical based on the Law of Conservation of Momentum
Question: A shell is fired from a gun with a velocity of 300 m/s making an angle of 60 degrees with the horizontal. It explodes into two fragments when it reaches the highest position. The ratio of the masses of the two pieces is 1 : 3. If the smaller piece stops immediately after the collision. Find the velocity of the other.
Sol: Velocity at the highest point = 300×cos60
=150 m/s
Using momentum conservation,
150×m=3m/4×v
⇒v=200m/s
Hooke's Law - Check Definition, Formula & Applications
What is Hooke’s Law?
Like most other tools that have been designed over the years, a fundamental knowledge of engineering is necessary so it can be used extensively. It implies, in terms of springs, acknowledging the rules of elasticity, torsion, and force that come into effect, all of which is known as Hooke’s law. Its uses are vast, such as an elastic artifact is used to store mechanical energy, making stuff including automobile suspension systems, pendulum clocks, wind-up toys, clocks, rat traps, electronic micromirror cameras, etc. The deforming force can be introduced to the solid by bending, stretching, squeezing, twisting or distorting. The spring is a feat of ingenuity and advanced development. For either, it appears in several variants – the spring of compression, the spring of extensions, the spring of torsions, the spring of coils, etc. – all performing various purposes.
Hooke’s Law Definition
Hooke’s Law definition can be given as a rule of physics that states the force required to expand or compress a spring by some distance is relative to that distance. The law is named after 17th-century British physicist Robert Hooke, who sought to illustrate the relationship between the forces connected to a spring and its flexibility. He stated the law in Latin which has the meaning as “the extension is proportional to the force”.
Hooke’s Law Formula
Hooke’s law formula can be demonstrated numerically as
F =- kX
where F is the force applied to the spring (in either the form of strain or stress); X is indeed the displacement of the spring, with a negative value showing the displacement of the spring when it is stretched; and k is the spring constant and details of how rigid it is. The elastic behavior of solids under Hooke’s law could be attributed to the fact that tiny disturbances of their component particles, molecules, or ions from original positions are indeed directly proportionate to the force which causes deformation.
Hooke’s law is also the first perfect example of an understanding of elasticity – that is the property of an entity or material that tends to cause it to be reestablished in its original form upon being distorted. This tendency of returning to normal form after encountering compression can indeed be referred to as a “restoring force.”
Hooke’s Law Formula
While the metal wire displays elastic behavior as per Hooke’s law since the slight increase in its length if extended by force applied doubles every other time the force is doubled. Hooke’s law may also be defined in terms of stress and strain. Stress is the force of the unit areas in a material that produces as a consequence of the external force applied. The strain is the relative distortion due to stress. The strain is proportional to stress in the case of relatively small stresses.
There seem to be commonly two categories of deformation
Elastic deformation in which if the pressure is removed, the component restores to specifications it had earlier the pressure was implemented i.e. deformation being reversible and non-permanent. However, plastic deformation develops if high pressure is introduced to the component. Stress is now so big that if the component is removed, it still does not leap back to its original position i.e. permanent and irreversible deformation.
Hooke’s law also appears to apply to several other circumstances in which the elastic body is deformed. This can include those from deflating a balloon or trying to pull a rubber band to measuring the wind power necessary to make a high cliff bend and swing.
Hooke’s Law Applications
- The concept of a balance wheel that made it possible to develop a mechanical clock, a handheld wristwatch, a spring scale, and a pressure gauge. Also, because it is a reasonable approximation among all strong bodies (until the forces of deformation are minuscule enough), countless branches of engineering and science are beholden to Hooke for bringing forward this law.
- Nevertheless, like most conventional mechanics, Hooke’s Law only operates within a specific conceptual framework. Since no object can be compressed beyond certain specific sizes (or extended beyond a maximum limit) with no permanent deformation or alteration of state, it will only occur when there is a small amount of force or deformity associated.
Avogadro's Law - Understand the Law with Graphical Representation
Avogadro’s Law
Avogadro’s law states that there is indeed a direct correlation between the number of moles and the volume of gas throughout constant temperature and pressure levels. This law would apply to ideal gases, although there was a minor divergence with real gases.
If we take a real-life example of a tire, It isn’t very convenient to have a flat tire.. It does not really cushion the wheel’s rim, creating a very uncomfortable experience. The stress rises as more gas molecules are pushed into the rigid rubber as air is applied to the tire. how much air must be pumped into a tyre relies on the tire’s pressure level. Insufficient pressure and thus the tire won’t hold its shape and excess pressure may burst tire.
What is Avogadro’s Law?
Hypothesis of Avogadro states that equivalent volumes of gas contain the same amount of molecules at the same pressure and temperature. As a consequence, the volume of a gas is directly related to the number of moles of gas.
“Avogadro’s Law states that when temperature and pressure are kept constant the volume of a gas is directly proportional to the number of moles of the gas”
The law of Avogadro is named after the Italian scientist Amedeo Carlo Avogadro and seems to be closely connected to the ideal gas formula because it incorporates temperature, pressure-volume and volume for a given gas.
Avogadro’s law can be represented at constant pressure and temperature using the following formula:
V ∝ n
V/n = k
V = volume of the gas
n = amount of gaseous substance (often expressed in moles)
k = constant
It is in evidence every time you blow a balloon, the balloon volume rises as you introduce moles of gas by blowing it up.
Graphical Representation of Avogadro’s Law
Therefore, the straight line travels through the origin (that means that perhaps the two volumes are directly proportional), meaning that zero moles of gas must consume zero space.
The law of Avogadro can be derived from the ideal gas equation as follows:
PV = nRT
Where,
- ‘P’ = pressure exerted by the gas on the walls of its container
- ‘V’ = volume occupied by the gas
- ‘n’ = amount of gaseous substance (number of moles of gas)
- ‘R’ = universal gas constant
- ‘T’ = absolute temperature of the gas
Rearranging,
V/n = (RT)/P
the value of (RT)/P is a constant
Thus, V/n = k
For real gases, the rule of Avogadro offers only approximate relations. The divergence of real gasses from optimal behavior decreases at low temperatures and high pressures.
Ohm's Law
Ohm’s law deals with the relationship between current, voltage and ideal resistance. It was given by Georg Simon Ohm in 1827.
Statement of Ohm’s Law
At constant temperature, the current through an ideal resistor is directly proportional to the voltage applied across the resistor. Ideal resistance is defined as the resistance which doesn’t change its resistivity due to change in voltage or current imposed on it and hence is a pure resistance.
Limitation of Ohm’s Law
Ohm’s law is followed by many substances under specific conditions, however, it is not a fundamental law.
The conductors that follow Ohm’s law are called Ohmic conductors. For these conductors, the linear relationship between voltage and current holds true, i.e. V is proportional to I. The resistance is independent of the current I through the conductor. In these conductors, the current I gets reversed in direction when a potential difference, V, is reversed, but the magnitude of current changes linearly with voltage. Therefore, the V-I graph will be a straight line passing through the origin.
Non-Ohmic Conductors
The conductors that don’t obey Ohm’s law are called non-ohmic conductors. The resistance of such conductors is not constant even at a constant temperature. Some examples can be:
- Metallic conductors, which have a straight graph up to a certain current (acts as ohmic) but become non-ohmic at larger currents.
- P-n junction diode, which consists of a p-type and n-type semiconductors. A voltage is applied across the junction, resulting in a current I. I is not proportional to V. Very little currents flow for fairly high negative voltage and a current begins to flow for much smaller positive bias. Thus, the junction diode allows current to flow only in one direction, i.e, it acts as a rectifier.
Some other examples of non-ohmic conductors are incandescent bulbs, semiconductors- like Germanium and Silicon.
The bulb’s tungsten filament heats up when the voltage increases, changing the resistance of the wire. So the bulb filament does not obey ohm’s law. (Bulb is not to be confused with LED, a light-emitting diode)
Summarised Notes for Limitations of Ohm’s Law
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Ideal Gas Equation - Learn Ideal Gas Equation & Limitations
Ideal Gas Equation
PV =nRT is considered as Ideal Gas Equation which describes the behaviour of a gas. This is also known as the General Equation of gas. This equation gives the relationship between pressure, temperature, volume and amount of gas.
Ideal Gas Equation Derivation
Boyle’s Law states that the Volume of the system is inversely proportional to the pressure of the system where the number of moles and temperature remains constant.
Charle’s Law states that the Volume of the system is directly proportional to the Temperature.
According to Avogadro’s Law the volume of the system is directly proportional to the number of moles contained in the system.
Combining all these equations we get,
R: Gas Constant
This equation is known as Ideal Gas Law. According to the Equation, Ideal gas is the one who’s Volume is proportional to the number of moles and temperature and inversely proportional to the pressure. This equation is true for only ideal gases. An ideal gas is a hypothetical condition to a gaseous substance where there are negligible intermolecular forces and molecular size is insignificant as compared to the empty spaces between molecules. The condition which can result in an ideal gas is low pressure and high temperature only.
Value of Gas Constant R
In equation PV=nRT, If P is expressed in atmosphere (atm), V in litres(L), T in kelvin(K), and n in moles(mol). Substituting it in the Ideal Gas Equation, we have
PV together as a unit of energy. So The Unit of R is J/K.mol
This Ideal Gas Equation can be used to find the value of any one of the variable if other four are known. We can also predict the final state(P, V, T, n) of the gas when its initial state(P, V, T, n) of the variables is known. Let, there be two conditions of an ideal gas: initial and final condition.
Initial condition: Pi, Vi, ni, Ti
Final condition: Pf, Vf, nf, Tf
Then,
This will result in
Since both are the values of R, we get
This equation is known as a general gas equation.
Standard Temperature and Pressure (STP)
T = 273.15 K (0 degree Celcius)
P= 105 Pa (1 bar)
The volume of 1 mole of an ideal gas = 22.71 litres (at STP)
The volume of 1 mole of an ideal gas = 22.41 litres (at 1 atm and 0 degrees Celcius)
Limitations of Ideal Gas
An ideal gas is based on assumptions that are not true.
- In reality, Ideal gas does not exist, but the ideal gas equation is very helpful to understand the behaviour of gases during reactions.
- Gases at low density, low pressure and high temperature approximately behave as Ideal Gas.
- Ideal gas law doesn’t work for low temperature, high density and extremely high pressures because at this condition the molecular size and intermolecular forces matters.
- Ideal gas law does not apply for heavy gases(refrigerants) and gases with strong intermolecular forces(like Water Vapour).
Summarised Notes
Check the summarised notes on Ideal Gas Equation to revise quickly.
- The ideal gas equation is given by:
- The general gas equation is given by:
- Standard temperature and pressure are taken as 273.15 K (0 degrees Celcius) and 105 Pa (1 bar) respectively.
Hope this article on the Ideal gas equation has helped you understand the concepts covered here. You can put your comment below in case you have a query or doubt.
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