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CIRCULAR & PLANETARYMOTION

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Circular MotionCircular Motion

The motion of the body along theThe motion of the body along the

circumference of the circle is calledcircumference of the circle is calledcircular motioncircular motion

Ex: motion of shafts, gear wheels,Ex: motion of shafts, gear wheels,pulleys etcpulleys etc

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Angular DisplacementAngular Displacement

r

ThenThen thethe angleangle (AOB)(AOB)describeddescribed byby radiusradius vectorvector inin aa

givengiven timetime inin aa circularcircular motionmotionisis calledcalled angularangular displacementdisplacementandand isis denoteddenoted by by UU (in(inradians)radians)..

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Angular displacement U = Arc LengthRadius r

SI unit is radian

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Angular VelocityAngular Velocity

Rate of change of angularRate of change of angular

displacement is called angular velocitydisplacement is called angular velocity SI unit is radsSI unit is rads--11

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Relation between angular velocity(Relation between angular velocity())

and linear velocity (v)and linear velocity (v)

velocity ,velocity ,v = rv = r where r is radiuswhere r is radius

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Angular acceleration (Angular acceleration ())

The rate of change of angular velocityThe rate of change of angular velocity

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Relation between angular acceleration(Relation between angular acceleration())and linear acceleration (a)and linear acceleration (a)

Acceleration,Acceleration, a = ra = r where r is radiuswhere r is radius

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Circular forcesCircular forces

Centripetal forceCentripetal force

Centrifugal forceCentrifugal force

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Centripetal forceCentripetal force

The force which acts towards center along theThe force which acts towards center along theradius in a circular motionradius in a circular motion

F = mvF = mv22/r/r F = mF = m22rr

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Centrifugal forceCentrifugal force

TheThe forceforce whichwhich actsacts awayaway fromfrom thethe centercenter alongalongthethe radiusradius inin aa circularcircular motionmotion ItsIts alsoalso calledcalled pseudopseudo force,force, lielie forceforce andand

fictitiousfictitious forceforce

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Newtons Universal Law ofNewtons Universal Law of

GravitationGravitation EveryEvery particleparticle inin universeuniverse attractsattracts thethe otherother

particleparticle withwith aa forceforce whichwhich isis directly directlyproportionalproportional toto thethe productproduct ofof theirtheir massesmasses andandinverselyinversely proportionalproportional toto squaresquare ofof thethe distancedistancebetweenbetween themthem andand thethe forceforce actsacts alongalong thethestraightstraight lineline joiningjoining themthem..

FF mm11 mm22 /d/d22 FF == GG mm11 mm22 /d/d22

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Relation between g and GRelation between g and G

g = GM/Rg = GM/R22

Where GWhere G -- universal gravitational constantuniversal gravitational constant

MM Mass of the earthMass of the earth RR Radius of the earthRadius of the earth

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Variation of g with altitude hVariation of g with altitude h

g = GM/(R+h)g = GM/(R+h)22

g = g [1g = g [1-- (2h/R)](2h/R)]WhereWhere ggaccelerationacceleration duedue toto gravitygravity atat aa heightheight hh

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Variation of g with depth dVariation of g with depth d

g = g [1g = g [1-- d/R]d/R]WhereWhere ggaccelerationacceleration duedue toto gravitygravity atat aa depthdepth dd

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Escape velocity (VEscape velocity (Vee))

The minimum velocity with which a body mustThe minimum velocity with which a body mustbe projected so as to escape from the earthsbe projected so as to escape from the earthsgravitational field.gravitational field.

Ve = 2 GM/RVe = 2 GM/RVe = 2 gRVe = 2 gR

Ve = 11.2 km/s (approx)Ve = 11.2 km/s (approx)

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Orbital velocity VOrbital velocity Voo

The horizontal velocity with which a satellite isThe horizontal velocity with which a satellite islaunched in a particular orbit to revolve roundlaunched in a particular orbit to revolve roundthe earth is called orbiting velocity.the earth is called orbiting velocity.

VVoo = [GM/(R+h)]= [GM/(R+h)]VVoo = GM/R when R>>h= GM/R when R>>h

VVoo = gR= gR

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Relation between VRelation between Vee & V& Voo

VVee = 2 V= 2 Voo

Escape velocity = 2 orbital velocityEscape velocity = 2 orbital velocity

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One mark questionsOne mark questions

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WhichWhich ofof thethe followingfollowing isis notnot anan

applicationapplication ofof centripetalcentripetal force?force?

a)centrifugea)centrifugeb)cream separatorb)cream separatorc)both 1& 2c)both 1& 2d)noned)none

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InIn SI,SI, angularangular accelerationacceleration isisexpressedexpressed inin termsterms ofof

a)rada)rad--ss

b) rad/sb) rad/s22

c) rad/sc) rad/s

d) radd) rad

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SI unit of G isSI unit of G is

a)Na)N--m/kgm/kgb)Nb)N--mm22/kg/kg22

c)Nc)N--kg/mkg/m22

d)Nd)N--kgkg22/m/m22

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The orbital velocity of a spaceThe orbital velocity of a space craftcraftdepends on itsdepends on its

a)sizea)size

b)heightb)heightc)massc)mass

d)shaped)shape

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Dimensional equation of G isDimensional equation of G is

a)LMa)LM22TT --33

b) LMTb) LMT --22

c)Lc)L22 MTMT--22

d)Ld)L 33 MM--11TT --22

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The The work work donedone onon aa unitunit massmass ininbringingbringing itit fromfrom infinityinfinity toto aa point point ininthethe gravitationalgravitational fieldfield isis

a) gravitational constanta) gravitational constantb) gravitational potentialb) gravitational potentialc) gravitational fieldc) gravitational fieldd) gravitational intensityd) gravitational intensity

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TheThe weightweight ofof aa personperson isis ----------------nearnearpolespoles thanthan onon equatorialequatorial lineline

a)morea)more

b)lessb)lessc)maximumc)maximum

d)noned)none

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Orbiting velocity &escape velocityOrbiting velocity &escape velocityare related asare related as

a) Ve=1/2 Voa) Ve=1/2 Vob) Vo= 1/ 2b) Vo= 1/ 2c)Ve= 2Voc)Ve= 2Vod)Vo= 2Ved)Vo= 2Ve

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Acceleration due gravity at a heightAcceleration due gravity at a heighth above earth surface ish above earth surface is

a) zeroa) zero

b) g`=GM/Rb) g`=GM/R22

+h+h22

c) g`=GM/(R+h)c) g`=GM/(R+h)22

d)g`=(R+h)d)g`=(R+h)22

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Relation between acceleration due toRelation between acceleration due togravity & gravitational constant isgravity & gravitational constant is

a) G=gm/ra) G=gm/r22

b) g=GM /rb) g=GM /r22

c) g=GM/ Rc) g=GM/ R22

d) G=gM/ Rd) G=gM/ R22

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According According toto NewtonsNewtons universaluniversalLawLaw of of Gravitation,Gravitation, forceforce ofofattractionattraction betweenbetween twotwo bodiesbodies variesvaries

a)a) directlydirectly asas distancedistance betweenbetween thethe twotwob)b) inverselyinversely asas cubecube of of distancedistance

betweenbetween thethe twotwo

c)c) directlydirectly asas productproduct ofof thethe massmassd)d) inverselyinversely asas distancedistance betweenbetween thethe

twotwo

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AA CyclistCyclist leansleans inwardinward whilewhile movingmovingalongalong aa curvedcurved roadroad toto overcomeovercome thetheeffecteffect ofof

a) Centripetal forcea) Centripetal forceb) Frictional forceb) Frictional forcec) Centrifugal forcec) Centrifugal forced) noned) none

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CentripetalCentripetal forceforce && CentrifugalCentrifugal forceforcecannotcannot bebe refereedrefereed asas actionaction &&reaction,reaction, becausebecause

a) they are frictional forcesa) they are frictional forcesb) they act along the same lineb) they act along the same linec) they act on same bodyc) they act on same bodyd) they are equal & opposited) they are equal & opposite

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WhenWhen aa stonestone tiedtied toto oneone endend ofof aathreadthread isis whirled, whirled, byby holdingholding otherotherendend inin thethe hand,hand, thethe CentripetalCentripetal forceforceisis providedprovided byby

a) nature of threada) nature of threadb) mass of the threadb) mass of the threadc) tension in the threadc) tension in the threadd) weight of the stoned) weight of the stone

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Angular Angular velocity velocity ofof aa body,body, whichwhichcompletescompletes NN rotationrotation inin 11 minmin isis

a)N/30 rad/sa)N/30 rad/sb)2N/60 rad/sb)2N/60 rad/sc)N/2 rad/sc)N/2 rad/sd) 2/N rad/sd) 2/N rad/s

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CentrifugalCentrifugal forceforce actingacting onon aa bodybody ofofmassmass m,m, rotatingrotating inin aa circularcircular pathpathofof radiusradius rr withwith aa speedspeed vv isis

a)mr/va)mr/v22

b)vb)v22/mr/mrc)mvc)mv22 /r v/r v22

d) mvd) mv22/r/r

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In the solar system, the gravitationalIn the solar system, the gravitationalforce of attraction between the Earthforce of attraction between the Earth

& Moon acts as___________ force& Moon acts as___________ force

a) repulsivea) repulsiveb) tangentialb) tangentialc) centripetalc) centripetald) centrifugald) centrifugal

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The orbiting velocity is given byThe orbiting velocity is given by

a) Va) Voo=2GM/R=2GM/Rb) Vb) V

oo= R /GM= R /GM

c) Vc) Voo= 2gr= 2grd) Vd) Voo= GM/R= GM/R

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Centripetal acceleration is given byCentripetal acceleration is given by

a) w =a) w = /t/tb) = wb) = w

22

ww11

/t/tc) v = r wc) v = r wd) a =r d) a =r

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CentrifugalCentrifugal forceforce onon aa rotatingrotating bodybodyalwaysalways actsacts alongalong thethe

a) circumferencea) circumferenceb) radius in the inward directionb) radius in the inward directionc) radius in outward directionc) radius in outward directiond) tangentd) tangent

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EqualEqual anglesangles describeddescribed inin equalequalintervalsintervals ofof timetime isis

a) uniform angular accelerationa) uniform angular accelerationb) uniform angular velocityb) uniform angular velocityc) variable velocityc) variable velocityd) uniform velocityd) uniform velocity

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BankingBanking angleangle isis inverselyinverselyproportionalproportional toto

a) Centripetal forcea) Centripetal forceb) Centrifugal forceb) Centrifugal forcec) radiusc) radiusd) speedd) speed

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TheThe angelangel sweptswept byby aa rotatingrotating bodybodyinin certaincertain amountamount ofof timetime isis

a) angular accelerationa) angular accelerationb) displacementb) displacementc) angular speedc) angular speedd) angular displacementd) angular displacement

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The The accelerationacceleration duedue toto gravitygravity isisminimumminimum

a) on equatoriala) on equatorialb) at north poleb) at north polec) at south polec) at south poled) both 2& 3d) both 2& 3

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AccelerationAcceleration duedue toto gravitygravity ________________withwith increaseincrease inin heightheight aboveabove earthearth

surfacesurface

a) decreasesa) decreasesb) increasesb) increasesc) remains samec) remains samed) becomes zerod) becomes zero

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TheThe orbitalorbital velocityvelocity ofof aa bodybody closerclosertoto earthearth surfacesurface isis

a) gRa) gRb) gRb) gRc) 2gRc) 2gRd) 2gRd) 2gR

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Two Mark QuestionsTwo Mark Questions

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AA bucketbucket filledfilled withwith waterwater isis rotatedrotatedinin verticalvertical circlecircle ofof radiusradius 1010mm.. TheTheminimumminimum speedspeed ofof rotation,rotation, soso thatthat

waterwater doesdoes notnot spillspill outout isis

a) 196m/sa) 196m/sb) 99m/sb) 99m/s

c) 9.9m/sc) 9.9m/sd) 0.99m/sd) 0.99m/s

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The The maximummaximum speedspeed atat which which aavehiclevehicle movesmoves alongalong aa curvedcurved pathpath isis1010 m/sm/s.. IfIf thethe radiusradius isis 55..8989m,m, thenthenthethe bankingbanking angleangle isis

a) 0a) 000b) 60b) 6000

c) 30c) 3000d) 45d) 4500

AA b db d bi ibi i ii i li l hh ff

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AA bodybody orbitingorbiting inin aa circularcircular pathpath ofofradiusradius 22mm makesmakes 6060 rotationrotation inin 11

minuteminute.. TheThe CentripetalCentripetal accelerationaccelerationisis

a)7.9m/sa)7.9m/s22

b)79 m/sb)79 m/s22

c)29.5 m/sc)29.5 m/s22

d)2.95 m/sd)2.95 m/s22

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Given,Given, R=R=64006400km,km, M=M=6610102424 kgkg &&G=G= 66..67671010--1111 SISI unitsunits.. OrbitingOrbiting

velocityvelocity ofof aa satellitesatellite atat aa heightheight ofof100100kmkm aboveabove earthearth isis

a) 78.5a) 78.5 101066 m/sm/sb) 78.5b) 78.5 101033 m/sm/s

c) 7.85 10c) 7.85 1033 m/sm/sd) 7.85d) 7.85 101066 m/sm/s

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TheThe heightheight atat whichwhich gg becomesbecomes 11ofof itsits valuevalue onon earthearth surfacesurface isis

a) Ra) Rb)3Rb)3Rc) 9Rc) 9Rd) 2Rd) 2R

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AA grindergrinder wheelwheel ofof radiusradius 1414mm rotatesrotateswithwith aa speedspeed ofof 4444 m/sm/s.. The The angularangularvelocityvelocity isis

a) 30 rpma) 30 rpmb) 60 rpmb) 60 rpmc) 120 rpmc) 120 rpmd) 240 rpmd) 240 rpm

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WhenWhen aa bodybody rotatesrotates atat 44 rad/srad/s alongalongaa circularcircular path path ofof radiusradius 5050m,m, thethecentripetalcentripetal forceforce present present isis 200200NN..

ThenThen thethe massmass isis

a) 33.3kga) 33.3kgb) 0.25kgb) 0.25kg

c) 75kgc) 75kgd) 0.5kgd) 0.5kg

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A A massmass ofof 55 kgkg movesmoves alongalong thethecircumferencecircumference ofof aa circlecircle ofof radiusradius

250250mm.. IfIf thethe speedspeed isis 1010 m/s,m/s, thenthenthethe centripetalcentripetal forceforce isis

a) 1.25Na) 1.25Nb) 0.8Nb) 0.8N

c) 0.5Nc) 0.5Nd) 87Nd) 87N