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2mL23 ConstantGmr2 Gmwork done massrU r GMm· Gravitational Potential EnergyVg · Gravitational potentialI · Gravitational field Intensity(iii) Law of Periods: T awhere, a length ofsemi-major axisdt F Gm1 m2, G 6.67 10 11 Nm2 kg 2r2(i)(ii)(iii)(iv)elness(g)vorb gR 2 gR(iii) with rotation of earth about its own axisg’ g– Rω 2 cos 2 λ ,0At poles, λ 90 , g maximum0At equator, λ 0 , g minimumi.e. g decreases with depthg′ g 1 d , RE 2h g ′ g 1 , RE i.e. g decreases with heightR2eG Mewith heightg Acceleration possessed by anobject during free falldue to earth’s gravitational pull,During free fall under gravityinside a spacecraft or satellitea body is weightless i.e., effectiveweight becomes zero.2ve2 GM / R1 Mm GMm GMm – G2r r 2rE K.E P.ETotal Energy of a satelliteOrbitals speed(ii) with depth(i)gravityWeakest force in Nature.Central as well as conservative.Always attractive in nature.Applicable for all bodies irrespectiveof their shape, size and position.forc eAcceleration due toCharacteristicsofgravitationalw ofNe a wltoGravitationWhen two mass bodies are separted by a distance,they experience an attractive forcewhich is directly proportional to the product oftheir masses and inversaly proportional to thesquare of their separation.lnatioattialtenodpandlFiemotionw- of planetaryer ’s LaKeplSatlitHeavenly object that revolvesaround a planet v esc Earth ’s v esc 11.2km/sEscape speedChapter - 8ssdA(i) Law of Orbit: Everyplanet revolves aroundthe Sun in an ellipticalorbit and Sun is at itsone focus.(ii) Law of Area: The radiusvector drawn from theSun to a planet sweepsout equal areas in equalintervals of time.Geostationary satellitePolarsatelliteHeight from earth’s surface 880kmTime period 84minOrbital velocity 7.92km/seHeight from surface of earth 36000kmRadius of orbit 42,400kmTime periods 24 hoursOrbital velocity 3.1km/sMind map : learning made simpletl eGraviWheign’G s unra ivit a v e r s atio ln8OSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI

Deforming force applied normal Fn AAreaForce Changing Volume FV AAreapelongitudinal stress F / A longitudinal strain l / lF l Mg l π r 2lAlY Y Young’s modulus of elasticityProperty of material byvirtue of which it regains itoriginal shape & size after theremoval of deforming forceStress9 1 39 Bη or Y Y B ηη 3B(iv)Es ModulusYoung’Restoring force per unit areai.e., stress AFs(iii) Shearing area or tangential stressTangential ForceF tAArea (ii) Volumetric stress (i) Longitudinal stressσ (iii)3B 2 η2η 6BRelation between Y, B, η & σ(i)Y 3B (1 2 σ)Y 2η (1 σ)(ii)Mechanical Propertiesof SolidsElasticityElastic potential energy in a stretched1wire stress strain volume of the wire2Ty P 1B ; compressibility V BVhydraulic stressB volume strainBulk modulus or volume modulus of elasticityBulk ModulusTypes of Modulus of ElasticityWithin the elastic limit, stress isdirectly proportional to strain.i.e., stress strainHooke’slawVchange in length l original lengthlooin volume V ε changeoriginal volumeV Shearing strain angular displacement of theplane perpendicular to the fixed surface θVolumetric strainLongitudinal strainTη η σsFF A εs θAθtangential stressshearing strainRigidity or shear modulus of elasticityRatio of change inconfiguration to originalconfigurationchange in configurationStrain original configurationModulus of RigidityStrain(iii)(ii)(i)Laternal strain (β) d / d Longitudinal strain (α ) l / lValue of σ lies between 0 and 0.5Poision’s ratio(σ) Chapter - 9esrgyneeltiatenocPstilaypMind map : learning made simpleOSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI9

21222hρm gρ (a 2 – a 2)of continuitym a1v1ρ1 a2v2ρ2for an incompressible liquid,ρ1 ρ2 then a1v1 a2v2or av constant Pascal’s law : The pressure exertedat any point on an enclosed liquid istransmitted equally in all direction.Hydraulic brakes and hydraulic liftsare based on Pacal’s law. EquationFlVenturimeterApplicationsowoffl u( ) E A That can flow like liquids and gasesMechanical Propertiesof fluidsForm uViP)soluste P resure(Total or actual pressure at a point.Absolute pressure atmospheric pressure gauge pressureGalaeit yDifference between the absolute pressure at a pointand the atmospheric pressure.Pg absolute pressure(P) – atmospheric pressure(Pa)density of substancedensity of water at 4oCDensity of water at 4 C i.e.,maximum density of water 1.0 103 kg/m3Volume(v)Density(ρ) Mass(m)Ftension S lwork done in increasing area W Surface Energy increase in surfacearea A2Scosθ Capillary rise or fall, h r ρg Excess Pressure inside a drop (liquid)2SPexcess R Excess Pressure inside a bubble (soap)4SPexcess RStroke’s law F 6 ηvrOpposing force between different layers offluid in relative motionViscous drag F ηA dvdxη coefficient of viscosityLift of an aircraft wing.Sprayer or atomizerBlowing off the roofs during windstorm. SurfaceoooChapter - 10Relative Density or specific gravity )(PgresusreePguPressure (atm) exerted by the atmosphere.At sea level, 1 atm pressure exerted by 0.76mof Hg hρg 0.76 13.6 103 9.8 1.013 105 Nm-2 101.3kPaPa)re(usesPricrhePressure(P) thrust(F) limA 0dFarea(A)dAPressure exerted by a liquid column of height h, (p) hρgidsss coFor an incompressible non-viscous streamline,irrotational flow of fluid,1P ρ v 2 ρ gh constant2uidsof FlswLa12Streamline : In liquid flowwhenthe Velocityis less than critical velocity, each particle of theliquid passing through a point travels alongthe same path and same velocity as thepreceding particles.Turbulent : When velocity of liquid flow isgreater than critical velocity and particlesfollow zig-zag path.Q a 1a2Velocity of efflux of liquid through an orificeV 2 ghTo ric ell’sDevice used to measure the rate of flow of liquid.Volume of liquid flowing per secondMind map : learning made simpleLawAbAtmospBernoulli’sprinciple10OSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI

1or λ m b44)Stefan’sBoltzmann lawWiendisplacement lawKrichofTemperatureα L – l0 l l0 Τl0(T – T0)anl coThermal Propertiesof MatterT h er mngolicofolawn’sotNewTypes (In solids)Increase in dimensions dueto increase in temperaturedPrincipleofA – A0 AdAβ A T A dT A0(T–T0)Increase in area of a solid on heating.Coefficient of superficial expansionora:b:γ 1:2:3γ 2β 3aSpecific Heat T Qcalorimetrys Q n n TV0 TdVV0 dTγ V V – V0V0(T – T0)Increase in volume of a solid on heating.Coefficient of cubical expansion. F l Y , Y Young’s modulusA l Heat lost Heat GainMolar specific heat capacity, c Heat capacity s sQSpecific heat capacity C m m TA form of energy, transferred betweentwo systems by virtue of temperaturedifference.t5For water, latent heat of fusion, L f 3.33 10 J / kg5Latent heat of vapourisation, Lv 22.6 10 J / kgCubicalor volume expanRelatsioionnteaHChapter - 11Heat required to change the state of unit mass substancewithout changing its temperature , L QmQ. x(K) A( T2 T1 ) tFor small temperature difference betweena body and its surroundings, the loss ofdQheat is given by k ( T2 T1 )dtIncrease of length of a solid on heating.Coefficient of linear expansionTC 0T 32TK 273.15–0 F – R100 0 212 32 373.15 273.15 80 – 0Relation among different temperature scalesDegree of hotness or coldness of a bodymeasuring device Thermometer(i) Conduction : heat transfer through molecular collisionswithout any actual motion of matter.(ii) Convection : heat transfer by actual motion of matterwithin the medium. Land breeze, sea breeze, tradewinds based on natural convection are some examples.(iii) Radiation : method of heat transfer requiringno material medium.E σ T T0(For a perfectly black bodyσ 5.672 Js 1 m 2 k 4E T 4 ; E σ T 4TT 3b(wine’s constant) 2.9 10 mKλmlawThermExpan alsioneλaλ Eλ constantalermTh awsLSuperficialor areaExpansionit ytivucf ’sLatentHeaAt any given temperatureMind map : learning made simpleOSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI11

Two systems are in thermalequilibrium with each otherif they have the sametemperature.Heat EngineV1 V2nRTdvVWQTEfficiency η 1– 2 1– 2QT1QT1Converts continuously heat intomechanical energy in cyclic process.W PγTn- γ Constant;PV Constantγ 1TV Constantγ γCvCpRefrigerator and heat pumpV1 V2 T1 T2 ConstantP1 P2 T1 T2VCP γCVMayer’s EquationCP C Rv Vβ WQ2 Q1 - Q 2Q22T1 - TT2Refrigerator is a heat engine working in thereverse direction. Coefficient of performance,The pressure (P) & temperature (T) of theenvironment can differ from those of thesystem only infinitesimally.In this process, systemreturns to initial statefor a cyclic process U 0 (zero)Pressure ConstantTIsochoricProcessVolume ConstantP ConstantT Infinity slow process such that systems remainin thermal & mechanical equilibrium withthe surroundings throughout.processi-staticQuasCyclic ProcesscessProciarobA thermally insulatedsystem neither gainsnor loses heatIsBranch of Science which deals with concepts ofheat & temperature and their interconversion bythermodynamic processThermodynamicscapacity Relationific heatSpecPropertyTemperature ConstantPV Constant n RTEfficiency of Carnot’s engineQTη 1 – 2 1 – 2Q1T2An Ideal engine works on a reversiblecycle of four operations in succession.(i) isothermal expansion ,(ii) adiabatic expansion,(iii) isothermal compression,(iv)adiabatic compression.It is the statement of law of conservation ofIt is impossible for an engine working betweenEnergy; Q U W U P U (Here, U P U) a cyclic process to extract heat from a reservoirand convert completely into work.Chapter - 12If two systems A&B are in thermal equilibriumicswith a third system C, then A&B are in thermalamnequilibrium with each other.wyodt la yrmZerirsedFhoothMeasure of molecular disorder of a system.ftTheLawrmwoδQofrmothe econd laChange in entropy δ S dynaSmicsLawsTThermodynamicstate variablen ofamics(i) Extensive – indicate the size of thesystem. e.g. U, volume, total mass.(ii) Intensive – do not indicate size of thesystem. e.g. , pressure & temperatureot’ EngineCarnersible & IrreversiblReve ProceAny process made to proceed in thessreverse direction by changing itsconditions is called ReversibleProcess.Any process which cannotbe retraced in the reverse directionexactly is called Irreversible Process.quilibriumrmal ETheMind map : learning made simplepy (S)EntroIsothermalProcessAdiabaticProcess12OSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI

3PV3P3 RT ρMMCvCp53 γ (4 f)(3 f )De greEnergy associated with each degree of freedom per molecule 1kT2Pathd omFreefre eMeane of(f)and Ki ne ti c EneyergEnHence, f is the degree of freedomfor polyatomic gases,for diatomic γ 7 γ Cv5CpCvTheory of GasesCpbrtedλ )2πnd 21ssure (Prgy (E)Re l ati on be twee n Presxeeeursy ga 32PV1 2P ρV rms3Total pressure of a mixtureof non - reacting gases,P P1 P2 . Pn2 π d2 PkBTFor polyatomic gas:(i)at room temperature, f 6(ii)at high temperature, f 8For monoatomic gas: f 3For diatomic gas :(i) at room temperature, f 5(ii) at high temperature, f 7E eDal ton’s Law of Parti al Pre ssur1VChapter - 13(If T constant)PV constantor P1V1 P2V2P esPrionrtitaipqufor monoatomicKinetic TheoryAssumption of Kinetic All the molecules of a gas are identical. The molecules of different gases are different. The molecules of gases are in a state of randommotion. The collisions of gases molecules are ecific Heat Capacityfor an ideal gas, Cp– Cv Rvmp areSpbl eob arpts qusMoRootme anwLa2 RT 2 0.816 vrms 3 vrmsM va v 8 RT 8 vrms 0.92 v rmsπ M 3π v v2 v3 . vNva v 1NrmsvwLae’slyBoAn ideal gas satisfies equation PV nRT atall pressure and temperature n no. ofmoles, R NAkB universal gas constantBehaviourUnder the same condition of temperatureand pressure equal volumes of all gasescontain equal no. of molecules.i.e. N1 N2GuyLussac’sLawV T (If P constant)V constantTV1 V 2or T1T2Charles’sLawof GasesP T (If V constant)P constantT P Por 1 2T1T2Mind map : learning made simpleOSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI13

FrequencyF spring constantxDamping force Fd –bv, b damping constant-(b/2m)tx xmeAmplitude decreases with time asx xme-bt/2m sin(ωt φ)mlaceDispegsprinto aeuns datiollicOsnsioatnSHOscillations22Fo2 2d2 2d{m (ω ω ) ω b } votanφ ωd xoAmplitude, A Displacement, x (t) Acos (ωd φ)12Every oscillatory motion is periodic,but every periodic motion need not beoscillatory.To and fro motion repeatedly abouta fixed point in a definite interval of time.Driving force, F (t) Fo cosωd t OscillationsintEVelocity in SHMA Amplitude i.e.,maximum displacement of particles.dDisplacement of damped oscillatorPhaseSimple Harmonic Motion isThe smallest interval of time T)im ethe simplest form ofp eri o d ( Tafter which the motionoscillatory motionis repeatedTime varyingquantity ( ωt φ )ceOscillation of a body whose amplitude goes on decreasing with time.Here, k mkIl 2 πmglgTime period T 2 πTime period T 2 πThe number of oscillationsper secondi.e.,1ωf T 2π x(t) A(cosωt φ)Chapter - 14(a)MPhase constant or Phase angle (φ)It depends upon velocity ( v) anddisplacement of particle at t 0Mind map : learning made simpleFo rDampeda dv ω 2A cos (ωt φ)dta max ω 2 Adx – ωA sin(ωt φ )d (t )vmax ωAv When frequency of external forceis equal to natural frequencyof oscillator. ω kmF k ( x) , k mω2Force law equation for SHM1kA2 cos 2 ( ωt φ) sin2 ( ωt φ) 2Potential Energy1P.E mω 2 A2 cos2 (ωt φ)2Total energy, T.E. K.E. P.E.Kinetic Energy1K.E mω2A2 sin2 (ωt ϕ)2HMin SyrgneOscillSHM14OSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI

2lmv2latio n(iii) In open organ pipe, higher harmonics, bothodd & even. In closed organ pipe, higher harmonics, oddonly.4l(b) Closed at one end ν vFundamental freq. or I harmonic ν (ii) In organ pipe:(a) Open at both ends,(i) In string: Fundamental Frequency, ν 1 TStationary wavesWaves associated with particleslike-electrons, protons, neutrons,atoms, molecules etc.tterMapoWhen two or more waves arePrinciple of superpropagating with differentsdisplacements then the neto f w a vedisplacement of collective waveis given as Y y1 y2 y3 . ynvesWaonsitiar y Waves1FrequencyWave number, v TypesDo not require any materialmedium for their propagatione.g., light wavesMechanical WavesWaves1λ)V ersin ait u dLongswavel Individual particles ofthe medium oscillatealong the direction ofpropagation of wave.Individual particles of themedium oscillate perpendicularto the direction of propagationof waveT tension & M mass/length Speed of a longitudinal wave speed of sound, V BρYPγP for air, γ 7/5ρ ρ ρRequire material mediumfor their propagationvnsTra mT ,Speed of transverse wave in a stretched stringDifference in frequencies of twosuperposing waves, νbeat ν1 ν2(( t)) A sin (–kx t) ωφy (x,y (x,t) Asin 2 π t – xT λ( ) amplitudeVelocityv0 Aω2Acceleration Amplitude a0 Aω2Essential propertiesfor propagation Elasticity Inertia Minimum frictionlare etivenm ressceaglotsspprDiBeawavelength1 1 νAngular Frequency (ω) 2 πνv νλTime period (T) tnio lengtal eRe wavν νs νm n1 n ν ν0 νm Here, v speed ofsound,v0 observer speedvs source speedvm medium speedGeneral Formula,Apparent FrequencyElectromagnetic Wavesela ntiow n inavapePropertiesb/wh wa(λ ve)& v elofrec it yque n c ( v),y (ν)Chapter - 14(b)eStespoavDoctfeEfrlewMind map : learning made simpleOSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XI15

sin ( δmin A ) / 2Ray OpticsMP –fo& L fo fefeWhen image is at Df f MP o 1 e fe– D f & L f o e fD e Magnifying Power (MP)When image is at TelescopeD v D L MP 1 1 fe u fe fo ntTotal InternalReflectAstronomicalMagnifying Power (MP)When image is at v D MP & L u feu fe When image is at DP 1f1 1 1 f f1 f2P P1 P2sin A / 2δ A (µ 1)µ δ i e AA r1 r2 Compound microscope Astronomical microscope Newtonian TelescopeThe complete reflection of a lightray reaching an interface with aless dense medium when theangle of incidence exceeds thecritical angle.&wsLaR2 1 n2 1 f n1 11 RR2 1Mirror formula 1 1 1 f v uI vff v(2) Linear magnification, m O uf uf(1) Focal length f The separation of visible light into its differentcolours.δred δviolet because ηred ηviolet(ii) Angular dispersion : θ δv – δr (ηv – ηr )Aδ δr(iii) Dispersive power : ω vδrWhen beam of light goes from one medium to anothermedium, it deviates from its path, such deviation oflight in called refraction of light.Laws :(i) Incident ray, refracted ray & normal lie in the sameplane.sin i(ii) Snell’s Law, refractive index (η) sin rSphericalMirrorsFormulaChapter - 15When beam of incident light bounces in the samemedium.Laws :(i) Incident ray, reflected ray and normal lie inthe same plane.(ii) Angle of incidence ( i) Angle of reflection ( r)Dispersion of lightnioctarfReflection&LawsMind map : learning made ioRe16OSWAAL CBSE Chapterwise Mind Maps, PHYSICS, Class - XIerakMsn’Le

OSWAAL CBSE Chapterwise Mind Maps, PHYSICS , Class - XI 1 Mind map : learning made simple Chapter - 1 S P h y s i c s E x c i t e m e n t o f c o p e a n d Fundamental Forces of Nature Physical World Study of the basic laws of nature and manifestation in different natural phenomenon Technology gives rise to new physics; similarly physics gives rise to new technologies.