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My Dear Aspirants,

Greetings to all of you! “What we think we become” said Gautama Buddha. We all have dreams. To turn dreams into reality it takes a lot of determination, dedication, self discipline and hard work.

We at VETRII IAS Study Circle are committed to provide the right guidance, quality coaching and help every aspirant to achieve his or her life’s cherished goal of becoming a civil servant.

The class room coaching at VETRII IAS Study Circle is meticulously planned to equip the aspirants with all the relevant facts and fundamentals of the subjects. Further the VETRII IAS Study Circle Study material aim to support the candidate by providing the most relevant study material in a comprehensive manner.

Wishing You All The Very Best !!

M. SHUNMUGAMDirector - Vetrii IAS Study Circle.

COMBINED CIVIL SERVICES

Group I & II/II A Services (Preliminary Examination)General Studies – Degree Standard

TOPICS FOR OBJECTIVE TYPE

UNIT–I: General Science

1. ScientificKnowledgeandScientifictemper-PowerofReasoning-RoteLearningVsConceptualLearning -Scienceasa tool tounderstand thepast,presentandfuture.

2. Nature of Universe - General Scientific Laws – Mechanics - Properties ofMatter,Force,MotionandEnergy-Everydayapplicationofthebasicprinciples ofMechanics, Electricity andMagnetism, Light, Sound,Heat,Nuclear Physics,Laser,ElectronicsandCommunications.

3. Elements andCompounds,Acids, Bases, Salts, PetroleumProducts, Fertilizers, Pesticides.

4. Main concepts of Life Science, Classification of Living Organisms, Evolution,Genetics,Physiology,Nutrition,HealthandHygiene,Humandiseases.

5. Environment and Ecology.

UNIT–II: Current Events

1. History-Latestdiaryofevents -Nationalsymbols -ProfileofStates -Eminent personalitiesandplacesinnews–Sports-Booksandauthors.

2. Polity - Political parties and political system in India - Public awareness and Generaladministration-WelfareorientedGovernmentschemesandtheirutility, Problems in Public Delivery Systems.

3. Geography-Geographicallandmarks.4. Economics - Current socio - economic issues.5. Science-LatestinventionsinScienceandTechnology.

UNIT–III: Geography of India

1. Location - Physical features - Monsoon, rainfall, weather and climate - Water resources - Rivers in India - Soil, minerals and natural resources - Forest andwildlife-Agriculturalpattern.

2. Transport-Communication.3. Socialgeography-Populationdensityanddistribution-Racial,linguisticgroups

and major tribes.4. Naturalcalamity-DisasterManagement–Environmentalpollution:Reasonsand

preventivemeasures-Climatechange-Greenenergy.

UNIT–IV: History and Culture Of India1. Indusvalleycivilization-Guptas,DelhiSultans,MughalsandMarathas-Ageof

VijayanagaramandBahmaniKingdoms-SouthIndianhistory.2. ChangeandContinuityintheSocio-CulturalHistoryofIndia.3. CharacteristicsofIndianculture,Unityindiversity–Race,language,custom.4. IndiaasaSecularState,SocialHarmony.

UNIT–V: Indian Polity1. Constitution of India - Preamble to the Constitution - Salient features of the

Constitution-Union,StateandUnionTerritory.2. Citizenship,Fundamentalrights,Fundamentaluties,DirectivePrinciplesofState

Policy.3. Union Executive,Union legislature – State Executive, State Legislature – Local

governments, Panchayat Raj.4. SpiritofFederalism:Centre-StateRelationships.5. Election-JudiciaryinIndia–Ruleoflaw.6. Corruptioninpubliclife–Anti-corruptionmeasures–LokpalandLokAyukta-

RighttoInformation-Empowermentofwomen-Consumerprotectionforums,Humanrightscharter.

UNIT–VI: Indian Economy

1. Natureof Indianeconomy–Fiveyearplanmodels -anassessment–Planning Commission and Niti Ayog.

2. Sourcesofrevenue–ReserveBankofIndia–FiscalPolicyandMonetaryPolicy- FinanceCommission–ResourcesharingbetweenUnionandStateGovernments- GoodsandServicesTax.

3. Structure of Indian Economy and Employment Generation, Land reforms andAgriculture -Applicationof Science andTechnology in agriculture - Industrial growth - Rural welfare oriented programmes – Social problems – Population, education,health,employment,poverty.

UNIT–VII: Indian National Movement

1. National renaissance – Early uprising against British rule - Indian NationalCongress - Emergence of leaders – B.R.Ambedkar, Bhagat Singh, Bharathiar,V.O.Chidambaranar, JawaharlalNehru,Kamarajar,MahatmaGandhi,MaulanaAbulKalamAzad,ThanthaiPeriyar,Rajaji,SubashChandraBoseandothers.

2. DifferentmodesofAgitation:GrowthofSatyagrahaandMilitantmovements.3. Communalismandpartition.

UNIT–VIII: History, Culture, Heritage and Socio-Political Movements in Tamil Nadu

1. HistoryofTamilSociety,relatedArchaeologicaldiscoveries,TamilLiteraturefromSangamagetillcontemporarytimes.

2. Thirukkural:(a)SignificanceasaSecularliterature.(b)RelevancetoEverydayLife.(c)ImpactofThirukkuralonHumanity.(d)ThirukkuralandUniversalValues-Equality,Humanism,etc.(e)RelevancetoSocio-Politico-Economicaffairs.(f)PhilosophicalcontentinThirukkural.

3. RoleofTamilNaduinfreedomstruggle-EarlyagitationsagainstBritishRule-Roleofwomeninfreedomstruggle.

4. Evolutionof19thand20thCenturySocio-Politicalmovements inTamilNadu- Justice Party, Growth of Rationalism - Self Respect Movement, Dravidianmovement and Principles underlying both these movements, Contributions ofThanthaiPeriyarandPerarignarAnna.

UNIT–IX: Development Administration in Tamil Nadu

1. HumanDevelopment Indicators in TamilNadu and a comparative assessmentacrosstheCountry–ImpactofSocialReformMovementsintheSocio-EconomicDevelopmentofTamilNadu.

2. PoliticalpartiesandWelfareschemesforvarioussectionsofpeople–Rationalebehind Reservation Policy and access to Social Resources - Economic trends in TamilNadu–RoleandimpactofsocialwelfareschemesintheSocio-EconomicDevelopmentofTamilNadu.

3. Social Justice and Social Harmony as the Cornerstones of Socio-Economic Development.

4. EducationandHealthSystemsinTamilNadu.5. GeographyofTamilNaduanditsImpactonEconomicGrowth.6. AchievementsofTamilNaduinvariousFields.7. e-GovernanceinTamilNadu.

UNIT-X: Aptitude and Mental Ability

1. Simplification–Percentage-HighestCommonFactor(HCF)-LowestCommonMultiple(LCM).

2. RatioandProportion.3. Simpleinterest-Compoundinterest-Area-Volume-TimeandWork.4. LogicalReasoning-Puzzles-Dice-VisualReasoning-AlphanumericReasoning

– Number Series.

CONTENTS1. Nature of Universe....................................................1

2. General Scientific Laws..............................................18

3. Mechanics.................................................................22

4. Electricity...................................................................45

5. Heat and Thermodynamics.........................................68

6. Light and Laser..........................................................87

7. Sound...................................................................... 91

8. Nuclear Physics..........................................................100

Appendix I Scientific Instruments..................................................114

Appendix II Inventions and Discoveries.........................................119

Appendix III National Scientific Laboratories..................................133

Appendix IV Physical Quantities, Standards and Units........................138

Appendix V Astronomy and Space Science....................................145

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Chapter

1 Nature of Universe

ORIGIN OF THE UNIVERSE

The following three theories have beenproposed to explain the origin of theUniverse.

(i) Big Bang theory

▪ According to the big bang theory all matter in the universe was concentrated as a single extremely dense and hotfire ball. An explosion occured about20 billion years ago and the matter was broken into pieces, thrown off in alldirectionsintheformofgalaxies.Duetocontinuous movement more and more galaxies will go beyond the boundaryand will be lost. Consequently, the numberofgalaxiesperunitvolumewill

go on decreasing and ultimately we will haveanemptyuniverse.

(ii) Pulsating theory

▪ Someastronomersbelievethatifthetotalmassoftheuniverseismorethanacertainvalue,theexpansionofthegalaxieswouldbestoppedbythegravitationalpull.Thentheuniversemayagaincontract.Afterithas contracted to a certain critical size, an explosion again occurs. The expansionand contraction repeat after every eightbillionyears.Thuswemayhavealternateexpansionandcontractiongivingrisetoapulsatinguniverse.

THE UNIVERSE

• Thesciencewhichdealswiththestudyofheavenlybodiesinrespectoftheirmotions,positionsandcompositionsisknownasastronomy.TheSunaroundwhichtheplanetsrevolveisastar.Itisoneofthehundredbillionstarsthatcompriseourgalaxycalledthe Milky Way.

• Avastcollectionofstarsheldtogetherbymutualgravitationiscalledagalaxy.Thebillionsofsuchgalaxiesformtheuniverse.Hence,theSolarsystem,starsandgalaxiesaretheconstituentsoftheuniverse.

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Vetrii IAS Study Circle Nature of Universe

(iii) Steady state theory

▪ Accordingtothistheory,newgalaxiesarecontinuouslycreatedoutofemptyspacetofillupthegapcausedbythegalaxieswhich escape from the observable partof the universe. This theory, thereforesuggests that the universe has always appearedasitdoestodayandtherateofexpansionhasbeenthesameinthepastandwillremainthesameinfuture.Soasteady state has been achieved so that the totalnumberofgalaxies in theuniverseremains constant.

Galaxy

▪ A large band of stars, gas and dustparticles held together by gravitationalforces is called a galaxy. Galaxies arereally complex in nature consisting ofbillions of stars. Some galaxies emit acomparatively small amount of radioradiationscomparedtothetotalradiationsemitted.Theyarecallednormalgalaxies.OurgalaxyMilkyWayisanormalgalaxyspiralinshape.

▪ The nearest galaxy to us known asAndromeda galaxy, is also a normalgalaxy.It isatadistanceof2×106 light years.(Thedistancetravelledbythelightin one year [9.467 × 1012 km] is called light year). Some galaxies are found toemitmillionsoftimesmoreradiowavescompared to normal galaxies. They arecalledradiogalaxies.

Types of Galaxies

1. SpiralGalaxy2. EllipticalGalaxy3. IrregularGalaxy4. BarredSpiral

Milky Way

▪ TheMilkyWayisthegalaxyinwhichoursolar system is located.Thediameter ofMilky Way is over 100,000 light years.

▪ The Milky Way includes stars smallerthan our Sun as well as many other stars that are thousands of times bigger thanthe Sun.

▪ Itincludesmanyothercelestialbodiesofgases, cloudsofdust, dead stars, newlybornstars,etc.Itisalsothoughttocontainatleast100billionstars.Thegalaxythatisclosest to our Milky Way is Andromeda.

▪ InIndianmythology,thispatchcalledasAkashaGanga.

▪ Our solar system is located within thedisk of the galaxy, about 27,000 lightyearsawayfromthecentreofthegalaxy.

Milky Way Galaxy

MilkyWaylookslikeastreamofmilkacrossthesky.Someoftheimportantfeaturesaregiven below.

(i) Shape and size

▪ Milky Way is thick at the centre and thin at theedges.Thediameterof thedisc is105lightyears.ThethicknessoftheMilkyWayvaries from5000 light years at the

• Astronomical Objects: In 1924, Edwin Hubble first demonstrated existence of galaxiesbeyondMilkyWay.

• Sunspotsarethemagneticstormsonthesurfaceofthesun.

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Vetrii IAS Study Circle Nature of Universe

centreto1000lightyearsat thepositionoftheSunandto<500lightyearsattheedges.TheSun isatadistanceofabout27000lightyearsfromthegalacticcentre.

(ii) Inter-stellar matter

▪ The interstellar space in theMilkyWayisfilledwithdustandgasescalledinterstellarmatter.Itisfoundthatabout90%ofthematterisintheformofhydrogen.

(iii) Clusters

▪ Groups of stars held by mutualgravitational force in the galaxy arecalled star clusters. A star cluster moves asawholeinthegalaxy.Agroupof100to 1000 stars is called galactic cluster. A group of about 10000 stars is calledglobular cluster.

(iv) Rotation

▪ The galaxy is rotating about an axispassingthroughitscentre.Allthestarsinthe Milky Way revolve around the centre andcompleteonerevolutioninabout300millionyears.TheSun,oneofthemanystars revolves around the centre with avelocityof250km/sand itsperiodofrevolution is about 220 million years.

(v) Mass

▪ ThemassoftheMilkyWayisestimatedto be 3 × 1041 kg

Constellation

▪ Aconstellation isarecognizablepatternofstarsinthenightskywhenviewedfromthe Earth. International AstronomicalUnionhas classified 88 constellations tocovertheentirecelestialsphere.

▪ UrsaMajor (SapthaRishiMandalam) isa large constellation and it covers a large partofthesky.Themoststrikingfeatureof this constellation is a group of sevenbright starsknownasbigdipper (sevenSagesinIndianastronomy).

▪ Ursa Minor in Lattin means ‘the littlebear’itliesinthenorthernsky.ThePolestar – Polaris (Dhrua) lies within this constellation. The main group, ‘littledipper’, consists of seven stars and isquitesimilartothatfoundinUrsaMajor.

▪ OrionwasahunterinGreekmythology.The constellation comprises around 81starsoutofwhichallbut10aretoofaintto be seen with naked eye.

Stars

▪ A Star is a luminous heavenly body that radiate energy. With naked eyes, we can see nearly 3000 stars in the night sky and manymorewiththehelpofatelescope.

▪ TheSun is thenearest star to theEarth.ThenextneareststarisAlphaCentauri.

▪ A star is a huge,more or less sphericalmass of glowing gas emitting largeamount of radiant energy. Billions ofstarsformagalaxy.

▪ Therearethreetypesofstars.Theyare(i)doubleandmultiplestars(ii)intrinsicallyvariable starsand (iii)Novaeandsupernovae.

▪ ThenightstarsintheskyhavebeengivennamessuchasSirius(Vyadha),Canopas(Agasti), Spica (Chitra), Arcturus(Swathi),Polaris(Dhruva)...etc.AftertheSun,thestarAlphaCentauriisnearesttoEarth.

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Vetrii IAS Study Circle Nature of Universe

The Solar System

▪ The part of the universe in which theSun occupies the central position of thesystem holding together all the heavenly bodiessuchasplanets,moons,asteroids,comets ... etc., is called Solar system.

▪ The gravitational attraction of the Sunprimarily governs the motion of theplanets and other heavenly bodiesaround it. Mercury, Venus, Earth, Mars, Jupiter,Saturn,UranusandNeptunearetheeightplanetsthatrevolvearoundtheSun.WecanseetheplanetVenusintheearly morning in the eastern sky or in the early evening in the western sky.

▪ The planet Mercury can also be seensometimesafterthesunsetintheWestorjustbeforesunriseintheEast.

▪ TheplanetMarscameclosertotheEarthafter 60,000 years from a distance of 380 × 106 km to a nearby distance of 55.7 × 106km. Itwouldappearagain inthe year 2287.

Sun

▪ The Sun is extremely hot and self-luminous body. It is made ofhydrogeneousmatter.ItisthestarnearesttotheEarth.Itsmassisabout1.989×1030 kg. Its radius is about 6.95 × 108 m. ItsdistancefromtheEarthis1.496×1011 m. Thisisknownasastronomicalunit(AU).

▪ Lightofthesuntakes8minutes20secondstoreachtheEarth.ThegravitationalforceofattractiononthesurfaceoftheSunisabout28timesthatonthesurfaceoftheEarth.

Diameter 1,392,000 km

Volume1,304,000 times, Earth’s

GravitationalPull 28 × Earth’s

Relative Density 1.4kg/m3

Temperature6000°Catsurfaceand 15,000,000°C at the centre

▪ Sun rotates about its axis from East toWest.Theperiodofrevolutionis34daysat the pole and 25 days at the equator.ThedensityofmaterialisonefourththatoftheEarth.

▪ TheinnerpartoftheSunisabrightdiscof temperature 14 × 106 K known asphotosphere.

▪ The outer most layer of the Sunof temperature 6000 K is calledchromosphere.

i)Thesunatmosphere

• Photosphere-14×106 K • Chromosphere-6000K

ii)SunProducesenergybyfusioniii)TwosetsofFusion reactions (hydrogen into helium)

• Proton−Proton Chain • CNO cycles (minor amount to

the energy) Four hydrogen nuclei combine to a helium nucleus. Thismassdifferenceconvertedtoenergy.

• (E = mc2)Thisenergywhichkeepsthesun shining.

Tab

le 4

.1 P

hysi

cal

pro

per

ties

of

the

obje

cts

in t

he

Sola

r sy

stem

(NO

R F

OR

EX

AM

INA

TIO

N)

g E =

9.8

m s

–2,

1 y

ear

= 3

65

.25

7 d

ays

; 1

AU

= 1

.49

6 ×

10

8 k

m ;

RE =

63

78

km

; M

E =

5.9

8 ×

10

24 k

g

Mer

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0.05

60.

387

0.24

158

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ays

5,40

00.

380.

367

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l0.

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Venu

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815

0.72

30.

615

243

days

5100

0.96

0.88

610

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20.

850

(E →

W)

Earth

1.00

01.

000

1.00

023

hou

rs 5

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tes

5520

1.00

1.00

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0.40

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107

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881

24 h

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27.

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530.

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152

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ster

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0.00

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4.60

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400.

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7.9

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urs

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1330

11.2

32.

522

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, CH 4, N

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rn95

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540

29.4

610

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inute

s70

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411.

074

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, CH 4

0.61

30 +

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Uran

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303.

980.

922

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e,0.

3524

(E →

W)

CH4

Nept

une

17.2

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716

4.1

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ours

1660

3.88

1.43

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e, C

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352

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–

Objects

Mass in Earth unit

Semi-major axis of

orbit (AU)

Period of revolution

in years

Rotation period

Mean density

(kg m–3)

Radius in Earth unit

g in Earth unit

Escape speed

(km/s)

Atmosphere

Albedo

Number of satellites

173

Tab

le:

Ph

ysic

al p

rop

ert

ies

of

the o

bje

cts

in t

he S

ola

r sy

stem

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Vetrii IAS Study Circle Nature of Universe

▪ The sun is the star at the centre of thesolar system.

▪ Itistheneareststartotheearth.Asastarit is a rather ordinary one, of averagesize. Many other stars are bigger, heavier, hotterandbrighter.Thenextneareststar,AlphaCentauri.

Planets: Aplanet isaheavenlybodythatorbits the sun or another star and shines onlybythelightitreflects.

Atmosphere

▪ The ratio of the amount of solar energyreflectedbytheplanettothatincidentonit is known as albedo.

▪ ThealbedoofVenusis0.85.Itreflects85%of the incident light, the highest amongthe eight planets. It is supposed to becoveredwiththicklayerofatmosphere.

▪ TheplanetsEarth,Jupiter,Saturn,UranusandNeptunehavehighalbedoes,whichindicatethattheypossessatmosphere.

▪ TheplanetMercuryandthemoonreflectonly6%ofthesunlight.It indicatesthattheyhaveno atmosphere,which is alsoconfirmedbyrecentspaceprobes.

▪ There are two factors which determinewhether the planets have atmosphereor not. They are (i) acceleration due togravityonitssurfaceand(ii)thesurfacetemperatureoftheplanet.

▪ The value of g for moon is very small(¼th of the Earth). Consequently theescapespeedformoonisverysmall.Asthe average velocity of the atmosphericairmoleculesat thesurfacetemperatureof the moon is greater than the escapespeed,theairmoleculesescape.

▪ Mercury has a larger value of g thanmoon.Yet there isnoatmosphereon it.Itisbecause,MercuryisveryclosetotheSunandhenceitstemperatureishigh.Sothe mean velocity of the gas moleculesis very high. Hence, the moleculesovercome the gravitational attraction and escape.

Conditions for life on any planet

Thefollowingconditionsmustholdforplantlifeandanimallifetoexistonanyplanet.

Important Facts

Biggestplanet Jupiter

Biggest satellite Gannymede

Blue Planet Earth

Greenplanet Uranus

Brightestplanet Venus

Brightest star Sirius(Dog star)

Closeststarofsolarsystem

AlphaCentauri

Coldestplanet Neptune

Evening star Venus

Farthestplanetfromsun Neptune

Planetwithmaximumnumberofsatellites Jupiter

Fastest revolution in solar system Mercury

Hottestplanet Venus

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Vetrii IAS Study Circle Nature of Universe

1. Theplanetmusthaveasuitablelivingtemperaturerange.

2. Theplanetmusthaveasufficientandrightkindofatmosphere.

3. The planet must have considerableamountofwateronitssurface.

The Terrestrial Planets

▪ Next to the Sun, the most importantmembers of the solar system are theplanets.Thenineplanets,thenearestfourto the Sun namely Mercury, Venus, Earth andMarsarecalledtheterrestrialplanetsbecause their structure is similar to the earth. The common features of these

planetsare:

1. A thin rocky crust, 2. A mantle rich in iron and magnesium3. Acoreofmoltenmetal’s.

▪ The terrestrial planets have veryfew moons. These planets have thinatmospheres.

Mercury

▪ Mercury is the inner most and smallest planet in the solar system orbiting thesun once every 87.969 Earth days. It isnearlyofthesamesizeasthemoonandismuchsmallercomparedtotheearthwithanequatorialradiusof2,439.7km.

▪ The Mercury usually becomes visiblein September and October just beforesunrise in the eastern sky as a morning star.

▪ Mercury too has no atmosphere and itssurfaceisrockyandmountainoustoo.

Venus

▪ VenusorShukraisthesecondplanetintermsofitsdistancefromthesunorbitingit every 224.7 Earth days.

▪ It is a planet, which our elders oftencalledaneveningoramorningstar.ThemassoftheatmosphereofVenusis96.5%Co2, with of the remaining 3.5% beingnitrogen. Venus has no moon or satellite ofitsown.

The Jovian Planets

▪ The planets outside the orbit of Marsaremuch farther off than the terrestrialplanets.

Important Facts

Densestplanet Earth

Fastest rotation in solar system Jupiter

Morning star Venus

Nearestplanettoearth Venus

Nearestplanettosun Mercury

Redplanet Mars

Slowest revolution in solar system Neptune

Slowest rotation in solar system Venus

Smallestplanet Mercury

Smallest satellite Deimos

Earth’s twin Venus

Onlysatellitewithanatmospherelikeearth Titan

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Vetrii IAS Study Circle Nature of Universe

▪ The planets outside the orbit of Marsare called Jovian planets because theirstructure is similar to that of Jupiter.Theseareallgaseousbodies.Theyhavering systems around them and have large numberofmoons.

Jupiter: Jupiter is the largest of all theplanets.Itsmassismorethanthecombinedmassofallotherplanets.

Saturn (Shani):

▪ Saturnisthemostdistantplanetknownto the early astronomers. Its distancefromthesunisalmosttwotimesthatofJupiter.

▪ Saturn is itsbeautiful rings thatencircle theplanet.Therearethreedistinctrings thatsurroundtheplanet.

▪ Theseringsarenotvisiblewiththenakedeyes and can be observed only with the helpofatelescope.

The Earth: Earthisthethirdplanetintermofdistancefromthesun.

Mars: Thenextplanetintermsofdistancefrom the sun is the Mars or Mongol. Itappears reddish and therefore it is alsocalledtheredplanet.

Uranus

▪ Uranus was the first planet to bediscoveredwiththehelpofatelescope.

▪ WilliamHercheldiscoveredtheplanetin1781.

▪ Hydrogen and methane have beendetectedintheatmosphereofUranus.

Escapespeedofearthis11.2km/s

TheescapespeedisVe = 2gR

Mercury=4km/s

Jupiter=60km/s

Moon=2.5km/s

Sun*=620km/s

*Escapespeedveryhigh

Neptune

▪ Neptune is the eighth planet in termsof its distance from the sun. This is thesecondplanet thatwas discoveredwiththehelpoftelescope.

▪ There are two factors which determinewhethertheplanetshaveatmosphereornot,accelerationduetogravityonitsurfacethesurfacetemperatureoftheplanet.

▪ Mercuryhaslargervalueofgravitythanmoon.Thereisnoatmospherebecauseitsveryclosetothesunandittemperatureishigh.

▪ The value of gravity for moon is verysmall(1/6thoftheearth).

Other objects in the Solar system(i) Asteroids ▪ Asteroids are small heavenly bodies

which orbit round the Sun between the orbitsofMarsand Jupiter.Theyare thepiecesofmuchlargerplanetwhichbrokeup due to the gravitational effect ofJupiter.

▪ About 1600 asteroids are revolving aroundtheSun.Thelargestamongthemhasadiameterofabout700kmiscalled

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Vetrii IAS Study Circle Nature of Universe

Ceres.ItcirclestheSunonceinevery4½years.

(ii) Comets

▪ Acometconsistsofasmallmassofrock−like material surrounded by large masses of substances such as water, ammoniaandmethane.Thesesubstancesareeasilyvapourised.CometsmoveroundtheSuninhighlyellipticalorbitsandmostofthetimetheykeepfarawayfromtheSun.

▪ The comet also develops a tail pointingawayfromtheSun.Somecometsareseenatafixedregularintervalsoftime.

▪ Halley’scometisaperiodiccometwhichmadeitsappearancein1910andin1986.Itwouldappearagainin2062.

(iii) Meteors and Meteorites

▪ The comets break into pieces as theyapproach very close to the Sun. WhenEarth’sorbitcrosstheorbitofcomet,thesebrokenpiecesfallontheEarth.MostofthepiecesareburntupbytheheatgeneratedduetofrictionintheEarth’satmosphere.Theyarecalledmeteors(shootingstars).We can see these meteors in the sky on a clear moonless night.

▪ Some bigger size meteors may survive the heat produced by friction and maynot be completely burnt. These blazingobjects which manage to reach the Earth are called meteorites.

▪ The formation of craters on the surfaceofthemoon,MercuryandMarsisduetothe fact that theyhavebeenbombardedbylargenumberofmeteorites.

NEWTON’S LAW OF GRAVITATION

▪ The law states that every particle ofmatter in the universe attracts every other particle with a force which is directlyproportional to the product of theirmassesandinverselyproportionaltothesquareofthedistancebetweenthem.

Fig.Gravitationalforce. ▪ The gravitational force between them is

F α m1m2

F α1/r2

1 22

m mFr

α

F=G

1 22

m mFr

α

▪ Where G is the universal gravitationalconstant.

▪ ThevalueofG is6.67×10−11 N m2 kg−2

anditsdimensionalformulaisM−1L3T−2. ▪ Acceleration due to gravity on the Earth’s surface,g=9.8ms–2

▪ Centripetal acceleration on the moon, ac = ν2/rwhereristheradiusoftheorbitof themoon (3.84× 108 m) and ν is the speedofthemoon.

Accelerationofmoon.

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Vetrii IAS Study Circle Nature of Universe

▪ Time period of revolution of the moonaroundtheEarth,T=27.3days.

▪ The speed of the moon in its orbit,

2 rTπν =

83 12 3.84 10 1.02 10 ms

27.3 24 60 60−π × ×ν = = ×

× × ×

∴Centripetalacceleration,

2

car

ν=

2

cva =

3 2

8

(1.02 10 )3.84 10r

×=

×

ac = 2.7 × 10−3 m s−2

Special Features of the Law

1. The gravitational force between twobodiesisanactionandreactionpair.

2. The gravitational force is very small inthecaseoflighterbodies.Itisappreciablein the case of massive bodies. Thegravitational forcebetween theSunandtheEarthisoftheorderof1027 N.

Acceleration due to Gravity

▪ GalileowasthefirsttomakeasystematicstudyofthemotionofabodyunderthegravityoftheEarth.

▪ He came to the conclusion that “in theabsence of air, all bodies will fall atthe same rate”. It is the air resistancethat slows down a piece of paper or aparachutefallingundergravity.

▪ If a heavy stone and a parachute aredroppedwherethereisnoair,bothwillfalltogetheratthesamerate.

▪ The value of g at sea-level and at alatitude of 45o is taken as the standard (i.e.,) g = 9.8 m s−2

Acceleration due to Gravity at the Surface of the Earth

Acceleration due to gravity.

▪ The gravitational force experienced bythebodyisF=GMm/R2 where M is the massoftheEarth.

▪ From Newton’s second law of motion,Force F = mg.

Equatingtheabovetwoforces,

2

GMm mgR

= ∴ 2

GMgR

=

Mass of the Earth

From the expression 2GMgR

= , themass of

theEarthcanbecalculatedasfollows:

2 6 224

11

gR 9.8 (6.38 10 )M 5.98 10 kgG 6.67 10−

× ×= = = ×

×

VARIATION OF ACCELERATION DUE TO GRAVITY(i) Variation of g with altitude

Variationofgwithaltitude.

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▪ The acceleration due to gravity at P on

thesurfaceis 2GMgR

= ............. (1)

▪ TheaccelerationduetogravityatQis

h 2

GMg(R h)

=+

............. (2)

dividing (2) by (1) 2

h2

g Rg (R h)

=+

h

2hg g 1R

= −

▪ Thevalueofaccelerationdue togravitydecreases with increase in height above thesurfaceoftheEarth.

(ii) Variation of g with depth

Variationofgwithdepth.

▪ The acceleration due to gravity at P on

the surfaceis 2GMgR

=

▪ TheaccelerationduetogravityatQatadepthdfromthesurfaceoftheEarthis

2d

d 2

GMg

(R h)=

−

d

dg g 1R

= −

▪ Thevalueofaccelerationdue togravitydecreaseswithincreaseofdepth.

(iii) Variation of g with latitude (Non−sphericity of the Earth)

Non−sphericityoftheEarth.

▪ The radius of the Earth at equatorialplaneRe is greater than the radius along thepolesRp by about 21 km.

g α

21

R ▪ The value of g varies inversely as the squareofradiusoftheEarth.

(iv) Variation of g with latitude (Rotation of the Earth)

▪ TheEarthrotatesfromwesttoeastin24hours.Itsangularvelocityis7.3×10−5 rad s−1.Theresultantofthesetwoforcesis

F =

2 2 2(mg sin ) (mg cos mR cos )θ + θ − ω θ

Theforce,F=

2 22R cosmg 1g

ω θ−

g' =

2 2R cosg 1g

ω θ−

Case (i)Atthepoles,θ=90o;cosθ=0 ∴g′=gCase (ii)Attheequator,θ=0;cosθ=1

∴g' = 2Rg 1

g ω−

So,thevalueofaccelerationduetogravityismaximumatthepoles.

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Gravitational Field

▪ A particle or a body placed at a pointmodifiesaspacearounditwhichiscalledgravitationalfield.

▪ The gravitational field is defined as thespacearoundamassinwhichitcanexertgravitationalforceonothermass.

Gravitational Field Intensity

▪ Gravitationalfieldintensityorstrengthatapointisdefinedastheforceexperiencedbyaunitmassplacedat thatpoint. It isdenotedbyE. It isavectorquantity. Itsunit is N kg–1.

▪ ThegravitationalfieldintensityatPis

E = Fm

∴ E =

2GMEr

∴ =

▪ Gravitational field intensity is themeasureofgravitationalfield.

Gravitational Potential difference

▪ Gravitational potential differencebetween two points is defined as theamountofworkdoneinmovingunitmassfromonepoint to anotherpoint againstthegravitationalforceofattraction.

▪ Gravitationalpotentialdifference

dν=−Edr ▪ Here,negativesignindicatesthatworkisdoneagainstthegravitationalfield.

Gravitational Potential: Gravitationalpotentialatapointisdefinedastheamountofworkdoneinmovingunitmassfromthepoint to infinity against the gravitationalfield. It isascalarquantity. Itsunit isNmkg−1.

Expression for Gravitational Potential at a Point

ν= GM

r−

▪ The gravitational potential is negative,since,theworkisdoneagainstthefield.(i.e.,) the gravitational force is alwaysattractive.

Gravitational Potential Energy

U= GMm

r−

▪ Gravitational potential energy is zeroat infinityanddecreasesas thedistancedecreases. This is due to the fact thatthe gravitational force exerted on thebody by the Earth is attractive. Hence,the gravitational potential energy U isnegative.

GEO Centric Theory: Earth at the center, the stars in the distant background, and Sun,Moonandtheplanetsorbitingaroundus.

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Gravitational Potential Energy near the Surface of the Earth

U=

2GMmh

R−

U=mgh

2GM gR

∴ =

Inertial Mass

▪ According to Newton’s second law ofmotion (F = ma), the mass of a bodycan be determined by measuring the accelerationproducedinitbyaconstantforce.(i.e.,)m=F/a.

▪ Intertialmassofabodyisameasureoftheabilityofabodytoopposetheproductionofaccelerationinitbyanexternalforce.

A B

B A

m am a

∴ =

Gravitational Mass

▪ AccordingtoNewton’slawofgravitation,the gravitational force on a body isproportionaltoitsmass.

▪ Gravitationalmassisthemassofabodywhich determines the magnitude ofgravitationalpullbetweenthebodyandthe Earth. A B

B A

m Fm F

∴ =

Escape Speed

▪ Theescapespeedistheminimumspeedwith which a body must be projectedin order that it may escape from thegravitationalpulloftheplanet.

e

2GMvR

=

Theescapespeedisve = 2gR

▪ Theescape speed for earth is 11.2km/s,for theplanetMercury it is 4km/sandforJupiteritis60km/s.Theescapespedforthemoonisabout2.5km/s.

Planetary Motion

▪ The first major theory, called the Geo-centric theory was developed by aGreekastronomer,Ptolemy.TheEarthisconsideredtobethecentreoftheuniverse,aroundwhichalltheplanets,themoonsand the stars revolve in various orbits.

▪ The great Indian Mathematician andastronomerAryabhatof the 5th centuryAD stated that the Earth rotates about its axis. Due to lack of communicationbetween the scientists of the East andthose ofWest, his observations did notreachthephilosophersoftheWest.

▪ NicolausCopernicus,aPolishastronomerproposed a new theory called Helio-centric theory. According to this theory, theSunisatrestandalltheplanetsmovearound the Sun in circular orbits.

Astronomical Unit: TheaveragedistancebetweentheEarthandtheSuniscalledanastronomicalunit.Itisdenotedby‘au’.1au=1.496× 108 km

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Vetrii IAS Study Circle Nature of Universe

▪ ADanishastronomerTychoBrahemadeveryaccurateobservationsofthemotionof planets and a German astronomerJohannes Kepler analysed Brahe’sobservationscarefullyandproposedtheempiricallawsofplanetarymotion.

KEPLER’S LAWS OF PLANETARY MOTION(i) The Law of Orbits

Lawoforbits.

▪ Each planetmoves in an elliptical orbitwiththeSunatonefocus.

▪ A is a planet revolving round the Sun.The position P of the planetwhere it isveryclosetotheSunisknownasperigeeand the positionQ of the planetwhereit is farthest from the Sun is known asapogee.

(ii) The Law of Areas

Lawofareas.

▪ The line joining theSun andtheplanet(i.eradiusvector)sweepsoutequalareasinequalintervaloftimes.

▪ Due to thevariable speedof theplanet.When theplanet is closest to theSun, itcovers greater distance in a given time.

▪ Hence, the speed is maximum at theclosest position. When the planet isfar away from the Sun, it covers lesserdistance in the same time. Hence, thespeedisminimumatthefarthestposition.

Proof for the Law of Areas

Fig.Proofforthelawofareas.

2dA 1 rdt 2

= ω

whereωistheangularvelocity. ▪ Theangularmomentumisgivenby

L=mr2ω 2 Lr

mω =

Hence, dA 1 Ldt 2 m

=

▪ Since, the line of action of gravitationalforcepassesthroughtheaxis,theexternaltorque is zero. Hence, the angularmomentum is conserved.

dA 1 Ldt 2 m

== constant.

(i.e.,)theareasweptbytheradiusvectorinunit time is the same.

Light Year: The distance travelled by light in one year is called a light year. It isdenotedby‘ly’.1ly=9.4607× 1012 km

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The Law of Periods

The square of the period of revolutionof a planet around the Sun is directly proportionaltothecubeofthemeandistancebetweentheplanetandtheSun.(i.e.,)T2 α r3

2

3Tr

= constant

Proof for the Law of Periods

Fig.Proofforthelawofperiods.

The gravitational force of attraction of the

Sunontheplanetis, 2

GMmFr

=

Thecentripetalforceis,F =

2mrν

GMisaconstantforanyplanet, ∴T2 α r3

Distance of a heavenly body in the Solar System

▪ Thedistanceofaplanetcanbeaccuratelymeasuredby the radar echomethod. Inthis method, the radio signals are sent towards the planet from a radar. Thesesignalsarereflectedbackfromthesurface

ofaplanet.Thereflectedsignalsorpulsesare receivedanddetectedonEarth.Thetime t taken by the signal in going to the planetandcomingbacktoEarthisnoted.Thesignaltravelswiththevelocityofthelight c.

▪ The distance s of the planet from the

Earth is given by s = ct2

Size of a Planet

▪ Itispossibletodeterminethesizeofanyplanet once we know the distance S oftheplanet.Theimageofeveryheavenlybody is a disc when viewed through a opticaltelescope.

▪ Theangleθiscalledtheangulardiameteroftheplanet.Thelineardiameterdoftheplanetisthengivenby

d = distance × angular diameterd=s×θ

Surface Temperatures of the Planets

▪ The planets do not emit light of theirown.TheyreflecttheSun’slightthatfallson them.

▪ Stefan’slawofradiationE=σT4 where σ is the Stefan’s constant and E is theradiant energy emitted by unit area in unit time.

Parsec: Aparsecisdefinedasthedistanceatwhichoneastronomicalunitsubtendsanangleofonearcsecond.Itisdenotedby‘pc’1pc=3.2615ly=3.09× 1013 km

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▪ DaytemperatureofMercuryismaximum(340oC) since, it is a planet closest tothe Sun and that of Pluto is minimum(−240oC).

▪ Venusisanexceptionasithasverythickatmosphere of carbon-di-oxide. Thisacts as a blanket and keeps its surfacehot. Thus, the temperature of Venus iscomparitivelylargeoftheorderof480oC.

Mass of the Planets and the Sun

▪ ThemassoftheSunMcanbecalculatedifthedistanceoftheSunfromtheEarthr, the period of revolution of the Eartharound the Sun T and the gravitationalconstantGareknownusingtherelation

M = 2 3

24 rGTπ

• The Hubble Space Telescope and powerful ground-based telescopes are nowbeginning tofindgalaxies thatwere createdaboutonebillionyears after theBigBang. These small galaxies were much closer together than galaxies are today.Collisions were common.

• Liketwoflamesmovingtowardseachother,theymergedintobiggergalaxies.OurMilkyWaygalaxycametogetherinthisway.