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:i~:I',, , Ui, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks, ".j, and, '. studymaterials, ', , ~, , /?___ ~___ ~A, ~, , I, , ", , l., 2., 3., 4., 5., 6., 7., , I, I, , 8., 9., 10., 1 l., , 12., , 13., , .~, , I, , ', , A, , .., , Physics' HandBook ~, , a, , ", , ~, , ., , 14., 15., 16., , 17., 18., 19., 20 ., 21., 22., 23., 24., 25., 26., , e:~~~~~~:,~tiCS_~~~~..PhY_S_iCS__._____ _ _ _ _, , ~, , ~ ~, , Unit. Dimension, Measurements and Practical Physics --13, Kinematics - ------ - - - - - - - - - - -----23, 33, Laws of Motion and Friction - - - - - - - - -- ...- 41, Work, Energy and Power - . - - - -- - - . - - - - . 47, Circular Motion ----------- - - - . -.. - - - - - 53, Collision and Centre of Mass --.-- - - -. -. - - . - Rotational Motion - - . - - -- .-.-.-.--.--.-.--.-.. 60, Gravitation -.-.------.-.-.--.---.---.--.- ..-.-., 65, 69-83, Properiies of Matter and Ruid Mechanics .-.--.-.-.--.-., (A) Elasticity -.-----.---.-...--.-... --.-.-.-..69, (B) Hydrostatics - - - - - - - . -...-----.-----.-.-., 73, 76, (C) Hydrodynamics - --.-- - - - - - . - -- ..- --., 78, (D) Surface Tension -.---.--.--- - - - -.----., 82, (E) Viscosity . - - - - - - -.-.--- - - - - - - -- - 8 4-101, Thermal Physics - . - - - - - - - - - - .---.---84, Temperature Scales and Thermal Expansion - - - -- .88, CalOrimetry ---~ ---------------­, 89, Heat Transfer . - - - 93, Kinetic Theory of Gases - - - - - - ., 97, Thermodynamics, ------Oscillations . - - -- - - - - - - -- - - - - - - - - -.- 10 2-11 2, 102, (A) Simple Harmonic Motion .- - - -- - - . - - - -.-..., (B) Free, Damped and Forced Oscillations & Resonance .110, Wave Theory and Doppler's Effect -.-.-.-.-.. --.-.- ......, Electrostatics - -.-.-.-.-.-.-.-.- .. -.-.-.--.--.-.-.-.-.-.-, , 'r, , m, , ~!~ ~1, , Capacitance and Capacitor -------------------------------Current electricity and Heating Effects of Current -.-.--Magnetic Effect of current and Magnetism --------------Electromagnetic Induction - . - - - - - - --- -------Alternating Current and EM Waves .------- - - - -., Ray Optics and Optical Instruments - - - -- - -- - - Wave Nature of Ught and Wave Optics - - - - - ---., Modern Physics, Semiconductor and Digital electronics . - - -- Communication Systems, , 133, 138, , 147, 155, , 161, 165, 178, • 18 2, 195, 201, -----.-- - - ---- 2 11-2 12, , Important Tables, (a) Some Fundamental Constants .-.- - - - - - -.. - - .(b) Conversions - -.--.---.-.-.--..--.- -_.--.-..., (c) Notations for units of measurements, , 27., , ~, , -------, , (d) Decimcal prefixes for units of measurements ----- -Dictio nary of Physics .-.-.-.------ - - - - .-.-.--, , 213, , I::, , I, , ,

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, •, , Maxima & Minima of a function y - fIx), dy, d'y, =0& - = -\Ie, dx, dx', , • For maximum value -, , • For minimum value, , •, , Average of a varying quantity, , If y = fIx) then, , ", Formulae for determination of area, , •, , Area of a square, , •, , Area of rectangle = length x breadth, , •, , 1, Area of a triangle = ,72 x base x height, , •, , Area of a Irapezoid, , •, , Area enclosed, , •, , Surface area of a sphere "" 4n r2, , •, , Area of a parallelogram, , =, , (side)', , =, , 21 x (distance between paraDeI sides) x (sum of parallel sides), , by a circle = 'It r2, , =, , (r = radiust, (r - radius), , base x height, , Area of curved surface of cylinder"" 2n rl, , ,, , (r = radius and t, , •, , Area of whole surface of cylinder = 2nr (r + t ) (i, , •, , Area of ellipse, , = 1t ab, , = length), , = length), , (a & b are semi major and semi minOT axis respectively), , ~_, , J, , Surface a rea of a cube = 6(siOO)', , •, , I, , ", Total surface area of a cone = nr2+1trl where nr! = nT .Jr2 + h2 = lateral area ;;•, , L-______________________________________________________, , 4, , ~, , ~, ", , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Phvslcs HandBook, , Formulae for determination of volume :, , •, , Volume of a rectangular slab = length x breadth x height = abt, , •, , Volume of a cube, , •, , Volume of a sphere =, , •, , Volume of a cylinder =, , •, , V ol ume of a cone, , =, , (side)', , =, , 4, , 3 1t r', , (r = radius), , r't, , (r, , = radius and e = length), , '31t r2h, , (r, , = radius and h = height), , 1t, , 1, , KEY POINTS:, , •, , •, , To convert an angle from degree to radian, we have to multiply it by 180', and to convert an angle from radian to degree, we have to multiply it, , 180', by-., 1t, , •, , By help of differentiation, if y is given, we can find, , if, , t •, , Ij, , ~~, , ~~, , and by help of integration,, , is given, we can find y., , The maximum and minimum values of function A cos8+Bsin9 are, , ,JA' + B', , and, , - ,J A', , + B' respectively., , i., , (a+b)' = a' + b' + 2ab, , (a-b)' = a' + b' - 2ab, , "ii, i, , (a+b) (a-b) = a' - b', , (a+b)' = a' + b' + 3ab (a+b), , (a-b)' = a' - b' - 3ab (a-b), , " L------------------c----------------~, 5, E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Vector Quantities, A physical quantity which requires magnitude and a particular direction, when it, , is expressed., , •, , Triangle law of Vector addition, , ::, IR=A+B~_, R, , -, , R=JA ' +B'+ 2ABcosG, , A, e, e, B.e, tan(l = A + BeosO if A = B then R = 2Acos:2 & a =:2, R ~., , •, , = A+B for 9=0' ;, , -, , B !Bsin9, .L.i, BeosS, , R"", = A-B for 9= 180', , Parallelogram Law of Addition of Two Vectors, , o .... -...--.----......., , ", , If two vectors are represented by two adjacent sides, of a parallelogram which are directed away from, their common point then their sum (j .e. resultant, , vector) is given by the diagonal of the parallelogram, passing away through that common point., AB + AD = AC =, , tan (l =, , ,, , ~ •, , i, t, ~, , i•, , Ror A +B = R ~ R = ~A ' + B', , ~-'--';-------+"I, , A, , +2AB cose, , B sinS, A sinS, 0, and tan ~ = ::---:---::A+Bcose, B + Acos e, , Vector subtraction, , l, , R = JA', /fA, , BsinS, + B' - 2ABcosO ' tan(l= A _ BeasS, , B then R = 2A sin!, 2, , ;;, , E, , 'i/, , 7, , :-, , IB, , _, , Bcose, , A, , -.S~ ....., , e

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , PhV.'e. HandBook, •, , Addition of More than Two Vectors (law of Polygon), If some vectors are represented by sides of a polygon in same order, then their, resultant vector is represented by the closing side of polygon in the opposite, order,, , ii, ii, , A Q, , -, , ~, , - R, , ', , C, , '_ _, , R=A+B+C+D, , B, , A, , •, , Rectangular component of a 3-D vector, , A, , A, , Angle made with x-axis, , cosa=.:......:.!..=, •, A v., IA 2+ A2+ A2, l, y, , Angle made with y-axis, , cosp=_Y, , A, , A, , =, , A, , II, , (, , m, , +A'I, VIA'+A', II, II, , Angle made with z-axis, , o, , t , m t n are called direction cosines, , ,, ~, , or sin 2 a + sin 2, , •, , General Vector In, , a, , p + sin2y =2, , x-v, , I, , plane, , 'CrT,"'b, 7, , r = xl + yj = r (cos 91 + sin Gil, , 9, , i, i, , x, , I, •, •,, , L-______________________________________________________-J, , ", , 8, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , Examples, 1. Construct a vector of magnitude 6 units making an angle of 60° with x·, axis., , Sol., , r = r(cos60i + sln 60j) = 6(~i + ~j) =3i +3./3j, , 2., , Construct an unit vector making an angle of 135 with x axis., , 0, , Sol. f = 1(cos 13soi +sin13So]) = ]z(-i+]), •, , Scalar product (Dot Product), , --, , o, , A.B = AB cos8 => Angle between two vectors 8 = cos', , o, , If A = A,i + A,] + A,k &, , l(A-B), As, , B= B,i + B,] + B,k then, , A.B = A,B, + A,B, + A,B,, , A, , and angle between, , &, , B is, , given by, , -AB AB, B, A.B _~~.~.-+~,~,~+-A~,~,=-~, coso=-=, AB, IA' +A'+A', l VIB'+ B'+B', Y, Y, , " J(, , [], , ", •, , Component of vector, , Component of, , b, , I, , It, , L, , b along vector a, b,,=(b . a)a, , perpendicular to, , a,, , b" i, , b.L = b - bll=b- (b .a)a, , Cross Product {Vector product), , o, , Ax B= AB sin 8 Ii where Ii is a vector perpendicular to A &, their plane and its direction given by right hand thumb rule., , B or, , A,it, , lW;z',~, , i, , I, , I,•, :;, , k, o, , A x B=, , A, A,, B,, , A, = i (A11B -AZB) - 'J' (A• Br-B A) + idA BY- B" A), I, , It, , •, , By B,, , o, AxB= -BxA, • L-______________________________________________________-J, , E, , 9

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Ph ysics HandBook, , Examples of dot products:, , •, , Work, W =, , F.Ci = Fdcos8, , where, , F -> force, d .... displacement, , •, , Power, P =, , F.ii = FvcosS, , where, , F ----. force, v --+ velocity, , •, , Electric flux , ~, =, , where, , E .... electric field, A .... Area, , •, , Magnetic flux, ~, = B.A, , where, , B .... magnetic field, A .... Area, , •, , Potential energy of dipole in, , whe re, , p ---tdipole moment,, , where, , E .... Electric field, , tA = EAcosS, , uniform field, U = -, , = BAcosS, , p.E, , Examples of cross products :, , t=f, , x, , F where r --+ position vector, F --+ force, , •, , T orque, , •, , Angular momentum j = f x p where r--+ JX)SitlonvectoT, p --+linearmomentum, , •, , Linear velocity, , •, , Torque on dipole placed in electric field 'i = P x E, , v=, , wx r, , where r --+ position vector, ro --+ angular velOcity, , where p .... dipole moment, E .... electric field, , KEYPOINTS :, Ten s o r : A quantity that has different values in differe nt directions is called, tensor,, , Ex. Moment of Inertia, ~, , In fact te nsors are merely a generalisation of scalars and vectors; a scalar is a, , 3, , zero rank tensor, and a vector is a first rank tensor., , ~, , Electric current is not a vector as it does not obey the law of vector addition., , ii, •, , I, , A unit vector has no unit., , •, , ,•, ", , •, , E, , To a vector only a vector of same type can be added and the resultant is a vector, of the same type., A scalar or a vector can never be divided by a vector., , 11

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'cr", , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , .Dimens~n'IMeasurement. s "., '3'l,f"" ,.~.'..Unjts,and, Practical Physics, , •, , j,,', , ';', , I, , ,." , ••, , ~ W·~t." t ,.'.•• ~ '~~r t r~.p '~~·it'!i~ fi1~~~~ ~r~tr.~ ", , Fundamental or base quantities :, The quantities which do not depend upon other quantities for their complete, deflnition are known as fundamental or base quantities., , e.g. : length, mass, time, etc., •, , Derived quantities :, The q~ntitles which can be expressed In terms of the fundamental quantities, are known as derived quantities .e.g., Speed (-distance/time), volume, acceleration, force, pressure, etc., , •, , Units of physical quantities, . The chosen reference standard of measurement in multiples of which, a physical, quantity is expressed is called the unit of that quantity., Physical Quantity = Numerical Value x Unit, , Systems of UnIts, (;), , MKS, , CGS, , fPS, , MKSQ, , MKSA, , l.enath 1m!, , Lenoth em, , l.enoth 1ft, , Lenoth 1m!, , l.enoth m!, , Moss 9), , Moss (pound), , (i), , Mas,, , (i;,, , TIme ~), , Ii,,), , -, , (kg), , TIme, , :,), , -, , nne(,), , -, , Moss, , (kg), , TIme ~), CharQe (Q), , Moss, , (kg), , TIme ~), , Current (A), , Fundamental Quantltleo In Sol. System and their units, ~, 3, , ?, , I, , I,, ~, , •, ;;, , S.N., 1, 2, , 3, 4, 5, 6, 7, , Ph~lcal Qty., Mass, Lenqth, TIme, Teml"'rature, Luminous intensity, Eiectric current, Amount of substance, , Name of Unit, kilogram, meter, second, kelvin, candela, ampere, mole, , Symbol, kg, m, s, K, Cd, A, , mol, , E ~-------------------1~3------------------~

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III.M., , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Ph ysics HandBook, SI Base Qua ntit ies and Units, , ,, .. ., ', ~'·'.I.t', ,', d· . 'i' ,.", I, ", I,,~~ ' , ~".Unlt., ", ,I'B_ Quant ity, ,, ,,;" Definition, ~' Name,! , ~ymbol, ,f' " ,., ", Length, The meter is the length of the path traveled, meter, m, by light in vacuum during a time interval of, , ., , 1/ 1299 792 458) of a second (1983), Mass, , kilogram, , kg, , The kilogram is equal, inte rnational prototype, platlnum-iridium alloy, International Bureau, ~~~res ,, , to the mass o f the, of the ki logram (a, cylinder) kept at, , of Weights and, at Sevres, near Paris. France., , Time, , second, , s, , The second is the duration o f 9. 192. 631,, 770 perkxls of the radiation corresponding, to the transition between the two hyperfine, levels o f lt ~e g;~und state o f the cesium-, , FJectric Current, , ampere, , A, , The ampere is that constant current which,, if maintained in two straight parallel, conductors of infinite length. o f negligible, circular cross-section, and placed 1 metre, apart in vacuum. would produce between, these condudors a force equal to 2 x 10-7, , Thennodynamk:, Tempera ture, , kelvin, , K, , Amount of, Substance, , mole, , mol, , The kelvin. is the fraction 1/27 3. 16 o f the, thermodynam~ (~em~rat ure of the triple, I ooint of water. 1967, The mole is the amount of substance of a, system,, which, contains, as many, elementary entities as J:he re are atoms in, , wminous, Intensity, , ctlndela, , Cd, , 133 atom 1967, , Newton oer metre of )enath. 119481, , 0.012 k;b,,,,,,, of ",roon-12. 11971\, The candela is the luminous intensity, in a, given direction, of a source that emits, monochromatic radiation of frequency 540, x 10 12 hertz and that has a radiant intensity, in tha t dire ction of 1/683 watt per, , sterad;'n 119791 ,, , •, , •, , SupplementaJy Units, , •, , Radian (rad), , •, , Steradia n (sr) - for measurement o f solid angle, , w, , for measurement of plane angle, , •, , Dbnen.ional Formula, , Relation w h ich express p h ysical quantities in tenns of appropriate powers, , of funda me ntal units,, , 14, , E

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. . . .e=.~~~t, , Physics HandBook, jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, ~, •, , •, , Use of dimensional analysis, , •, , To check the dimensional correctness of a given physical relation, , •, , To derive relationship between different physical quantities, , •, , To convert units of a physical quantity from one system to another, , Limitations of this method :, •, , In Mechanics the formula for a physical quantity depending on more than, three other physical quantities cannot be derived. lt can only be checked., , •, , This method can be used only if the dependency is of multiplication type., The formulae containing exponential, trigonometrical and logarithmic, functions can't, , be, , than, , t erm, , one, , derived using this method. Fonnulae containing more, which, , are - added, , or, , subtracted, , like, , 1, , s = ut + - at' also can't be derived., 2, •, , The relation derived from this methoo gives no information about the, dimensionless constants., , *, ~, , I, , f•, , •, , •, , If dimensions are given, physical quantity may not, , be, , unique, , !liS, , many, , physical quantities have the same dimensions., •, , It gives no infonnation whether a physical quantity is a scalar or a vector., , SIPREFIXES, , The magnitudes of physical quantities vary over a wide range. The CGPM, recommended standard prefixes for magnitude too large or too small to be, expressed more compactly for certain powers of 10., , I, " ~------------------------------------------~, E, 15

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , Prefixes used for different powers of 10, , ;Iii'''''' ., , ••.•, ' , iii., , .. ;, .,'~ ~~i:1 'j I;, "r, .k,', . ,i . POwer. of;:~,, ,,Ii:t~~Wef, "i ~:"' e~fl~~', ~ I I . ,. Symbol),' I,., 101, 'O'~, •, I .. ;;~;', .', ' 1". 1'(1'r,.~, "i'j, .•, " ."" I ' I'·, ., ',"t.,, ." (1;< . 'r,, .~;. ' ....'e..•• • ;, I I~l;'!,, .j !;, ~ ., Ir"/'1<, 'I;', t:':,,, ., ,', I., 10- 1, E, 10 18, exa, , .. , .', ; I I ' •. I• '-,, I""r'.·d.·, , ,I,., , 'e', , 1015, 10", 10', 10·, , tera, , T, , giga, , G, , mega, , M, , 10', 10', , kilo, , hecto, , 10, , P, , peta, , 1, , deca, , <I. .', , ; i,, , 'I p ·iI ·· .. · S ' bO! ', ~ JTe x. "fT~', ,'(IV, H: :, .i ., ,, , ., , ~',, , 10 ', 10-', 10";, , ded, , d, , centi, , c, , milll, , m, , micro, , ~, , nano, , n, , k, , 10'", 10 12, , pico, , P, , h, , IO- IS, , femto, , f, , da, , 10-18, , atto, , a, , Units of Important Physical Quantities, , ~ iilltt, ,, , .,, , ..., , :.':;":;!,'i.;:, i~if~1hI;li!~t~~, ~!Hi, , . ', , . :, , ., , ,,", , ,, , ., , i ' , ~ , , ',, , ,, , r., , ,, , .. :, 1,1,, , ., , ......, ': '.I l.:'iiIW'!~~~:i;li.[m:, ;;;,',.',, ':,': /1i', , ~gular, , rad s-2, , Frequency, , -, , Moment of inertia, , kg-m 2, , Resistance, , kg m 2 A-2, , Self inductance, , Henry, , Surface tension, , Magnetic flux, , Weber, , Pole strength, , A-m, , Dipole moment, , CouJomb-meter, , Viscosity, , Poise, , Stefan oonsiant, , watt m- 2 K-", , Reactance, , Ohm, , Specific heat, , J!1<g"C, , ":;f~~, , newton A -1 m, Parsec, , 1~, , ~~, free space ~, free space, , 1, , hertz, S- 3, , newton/m, joule K- 1 mort, , Coulomb'/N-m', Weber/A-m, , PlarK:k's constant, , louie-sec, , Entropy, , J/K, , ~, i, , I, , t, ;, •, , ", , ~------------------~1~6------------------~ E

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Dimensions of Important Physical Quantities, , _, , " -.ti;.~!:" P.bYsiC~:lj :);1 1 i' 'j ,,-,. ':', :r~, ; r:':I,;~ mw5iciill~' .j !:J, ~ :1'1:i .- fi I"'~ _ ~, ,llltilY ';:111 :.:· 'I,+ : ~I'~~-:WI9~if I I,J:·:", I . - ':1., i'~I'I~" ~I ' ,: I , '\::: 'l!ll ~~iO~ , f':,1, ",., tj" ~, I,, : ;" 11 ,'., ',I":1ii!~'ii", ~' . , ,.';!;::~;;L~:,~I ~_~ !,' l" '!ll~'! :"~.! I ~I ·1r.~W U~', , .»:'1, , qu, , .., , ' .", , ,., , ,, , ,, , .,',, , Capacitaoce, , M-'L-2T'N, , Calorie, , M' L' T-2, , Mooulus of, rigidity, , M' L-' T-2, , Latent heat, capacity, , MO L' T-2, , Magnetic, permeability, , M' L' T-2A-2, , Self inductance, , M' L'T-2A-2, , Pressure, , M' L-' T-2, , Coefficient of, thermal, conductivity, , M' L' T-2K-', , Plaock's ocnstant, , M'L' , ', , Pov..er, , M' L' T-2, , Solar constant, , M' Lo , ', , Impulse, , M'L',', , Magnetic flux, , M' L' T-2 A-', , M- ' LOT' A', , Current density, , MOL-2 T" A', , Bulk mooulus of, elasticity, , M'L- ' ~, , Young mooulJs, , M' L-' T-2, , Potential energy, , M' L' T-2, , Gravitational, , constant, , :, , t·, , M'L',', , semi cooductor, , I, , ,, , Momentum, , Hole mobility in a, , ~, , ', , 1, , Light year, Thermal, resistance, , Coefficient of, viscosity, , ~,, , L' T-2, , M" L' T", ~', , L-2T'K, , M'L-' , ', , Magnetic field, intensity, Magnetic, , MOL-' T"A', , Induction, , M'T-2A-', , Permittivity, , M-' L"""T'A', , Electric Reid, , M'L'T-2A-', , Resistance, , ML'I'A-2, , ;, , i•, , . ~----------------------------------~, E, 17

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,ru=, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , Sets of Quantities having same dimensions, , .., , S.N., l., , Dmensions, , Strain, refractive index, relative density, angle, solid, angle, phase, distance gradient, relative permeability,, relative, , permittivity, angle ot contact , Reynclds, , IMoLo~, , number, coefficient of friction, mechanical equivalent, of heat , electric susceptibility, etc., , 2., , Mass and Inertia, , IM'L°T"I, , 3., , Momentum and impulse., , 1M' L' " I, , 4., , Thrust, force. weight, tension, energy gradient., , IMI L' , 'I, , 5., , Pressure, stress, Young's modulus, bulk modulus,, shear modllus, modulus of rigidity, energy density., , 1M' L-', , ,~, , 6., , Angular manentum and Planck's constant (h)., , IM'L' ,II, , 7., , Acceleratic:o, g and gravitational field intensity., , I MOLl,.], , 8., , Surface tension , free surface energy (energy per unit, IM'Lo"l, , area), force gradient, spring constant., , 9., , Latent heat capacity and gravitational potential., , I MOL','], , 10., , Thermal capadty, Boltzmann constant. entropy., , I MLZJ'"""'K-I], , 1l., , Work,, , tOrqJe ,, , internal energy. potential energy,, , kinetic eI1f!rgy, moment of force , (q'/C), (U~. (qV),, , V', , (V'C), o'R~, 1ft, (VIt), (PV),, , 12., , (Rn. (mL), (me tJ. n, , Frequency, angular frequency, angular velocity,, , ,.2. ,k, , velocity gradient, radioactivity R, L RC, , 13., , 14., , IMI L' ' ' I, , (~r, , ,(:r, , ,(H (RC),(J[C). tUne, , (VI), O' R), (V'/ R). Power, , lM o Lo ,11, , LC, I MOLOT il, , 1M L' , 3), , 18, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, Some Fundamental Constants, Gravitational constant (G), , 6 .67 x 10-" N m' kg-', , Speed of light in varnum (c), , 3 x 108 ms- I, , Permea bility of vacuum (flo), , 41t x 10-' H m-', , Permittivity of vacuum (eo), , 8.85 x 10- 12 F m- ', , Planck constant (h), , 6.63 x 10-34 Js, , Atomic mass unit (amu), , 1. 66 x 10-27 kg, , Energy equivalent of 1 amu, , 931.5 MeV, , Electron rest mass (mJ, , 9.1 x 10-" kg = 0.511 MeV, , Avogadro constant (N",, , 6.02 x 10" mol- ', , Faraday constant, , 9.648 x 10' C mol - ', , (F), , Stefan- Boltzmann constant (cr), , 5.67 x 10-' W m-' K-', , Wi en constant (b), , 2.89 x 10-' mK, , Rydberg constant (R,,), , 1.097 x 10' m- ', , Triple point for water, , 273.16 K (0.01' 0, , Molar volume of ideal gas (NTP), , 22.4 L - 22.4, , X, , 10-3 m' mar', , KEY POINTS, 11, , •, , Fl, , ~, , J•, , i :., ~, , ;;, , j, , ", , Trigonometric functions sine, co59, tanS etc and their arrangements 9 are, , dimensionless., Dimensions of differential coefficients, Dimensions of integrals, , [~~] = [ :. ], , [f YdxJ = [yxI, , We can't add or subtract two physical quantities of different dimensions., Independent quantities may be taken as fundamental quantities in a new system, of units., , E ~------------------~1~9------------------~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, PRACTICAL PHYSICS, •, , Rules for Counting Significant Figures, For a number greater than 1, •, , All non-zero digits are significant., , •, , All zeros between two non-zero digits are significant. Location of decimal, does not matter., , •, , If the numbe is without decimal part, then the terminal or trailing zeros, are not significant., , •, •, , •, , •, , •, , •, •, , Trailing zeros in the decimal part are significant., , For a Number Less Than 1, Any zero to the right of a non-zero digit is significant. All zeros between decimal, point and first non-zero digit are not significant., Significant Figures, All accurately known digits in measurement plus the first uncertain digit together, form significant figure., 40.000 ..... 5SF,, Ex. 0.108 ..... 3SF,, l.23 x 10'" ..... 3SF., 0.0018 ..... 2SF, Rounding off, 6.87 ..... 6.9,, 6.84 ..... 6.8,, 6.85 ..... 6.8,, 6.65 --+ 6.6,, 6.95 ..... 7.0, 6.75 ..... 6.8,, Order of magnitude :, Power of 10 required to represent a quantity, 49 ~ 4.9 x 101 ,,10' ~ order of magnitude ~1, 51 = 5.1 x 101 " 10' ~ order of magnitude = 2, 0.051 ~ 5.1 xlO" " 10" ~ order of magnitude =-1, Propagation of combination of errors, Error in Summation and Difference : x ~ a + b then ru< = ± (6a+6b), Error In Product and Division A physical quantity X depend upon Y &, Z as X = ya Zbthen maximum possible fractional error in X., , ~:, , ~ = ±[ m(~) + n( ~b)], , •, , Error In Power ola Quantity: X =, , •, , Least count : lhe smallest value of a physical quantity which can be measured, accurately with an instrument is called the least count of the measuring, , then, , instrument., , •, , Vernier Callipers Least count - 1MSD - 1 VSD, (MSD ~ main scale division , VSD -.. Vernier scale division), , ?, , i, , i,, ";;, , L-__________________________~--------------------------~ ", , 20, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , Ex. A vernier scale has 10 parts, which are equal to 9 parts of main scale having, 9, each path equal to 1 mm then least count = I mm - 10 mm = 0 .1 mm, , •, , I': 9 MSD = 10 VSDJ, Screw Gauge :, Circular (Head) acaIe, , Least count, , =, , _....,.._-"p;.:itc",h.:....,.,..._, total no. of divisions, on circular scale, , Zero Error:, If there is no object between the jaws (i.e. jaws are in contact), the, screwgauge should give zero reading, But due to extra material on, jaws, even if there is no object, it gives some excess reading. This, excess reading is called Zero error,, , hgtYH 3 .07, , rTm, , I, , Exc.! .. rnding .. 0 .07 mn (zefo ""'><1, , In ... ,10;1'1 tIwnI II 0.07 ,...", ' - 10 be dltTacted., , ~"1'1'~, , 10 .....1~ .. 3.07 .. 0.07 .. :'1.00, , ~, , ~, , t, , I, •, , ;0, , 1, ;r;, , I, , ",hid., IT'011, , I, ~, , \, f~'""....d~lg, , IoWdIngI, , (:foro errorl, , I, , AclulII relld;og .. obMNeI:I .. n:c- ... ...tins, ., rudi--.g, ., (un. f rrl>fl, , Excess reading = 0.07 mm (zero error), Ex. The distance moved by spindle of a screw gauge for each turn of head is Imm., The edge of the humble is provided with a angular scale carrying 100 equal, Imm, divisions. The least count = 100, , R, , 0.01 mm, , E L-------------------~2-1------------------~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, •, , RElATIVE MOTION, , If reference is, not mentioned then we take the ground as a reference of motion. Generally, velocity or displacement of the particle w,r.t. ground is called actual velocity, or actual displacement of the body, If we describe the motion of a particle, w.r.t. and object which is also moving w,r,t. ground then velocity of particle, , There is no meaning of motion without reference or observer., , w,r,t. ground is its actual velocity (v~)and velocity of particle w,r,t. moving, , .l, , object is its relative velocity (v .. and the velocity of moving object (w.r.t., ground) is the reference velocity, , •, , (v m.), , then \im, , = vad - vm, , Relative velocity of Rain w.r.t. the MOving Man: A man walking west, , with velocity vm' represented by OA,, , Let the rain be falling vertically ·, , downwards with velocity ii,. represented by OB as shown in figure., :, , ...., , iI VertIcal." up, , ~., , ~"", , ", , e:, :, , v: (10 ~, w ......+.-..;....-¥----==---+., A, , v,, , D, , The relative velocity of rain w.r.t. man Vrm = Vr - Vm will be represented, by diagonal 00 of rectangle OBOe., , :. v nn =, , Jv, , 2, r, , v cos 90°, + vm2 + 2v rm, , = Jv2r + vm2, , If 6 is the angle which v= makes with the vertical direction then, , BOv, (vi, tanS = OB = v~ => S = tan-'l v~), , •, , }, , I?, j, , SwImmIng brto the RIver, , L-______________________________________________________-J, , !, ~, i, , 26, , E, , A man can swim with velocity V. i.e. It Is the velocity of man w.r,t. still, water, If water Is also flowing with velocity v. then velocity of man relative to, , "

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , MOTION UNDER GRAVITY, If a body is thrown vertically up with a velocity u in the uniform gravitational, field (neglecting air resistance) then, ",, , (i), , f ':, !,, :,,, :,, !,, H, ,, ,,, , u', , Maximum height attained H = 2g, , (ii) TIme of ascent. - time of descent =, (iii) Total time of flight =, , u, , 9, , u', , i, , 2u, , g, , (iv) Velocity of fall at the point of projection - u (downwards), Ga11l1eo's law of odd numbe... : For a freely falling body ratio of, successive distance covered in equal time intemval 't', S, : S, : S, : .... S, - 1: 3: 5 : .... : 2n-1, At any point on its path the body will have same speed, (··~~·i, for upward journey and downward journey., (v), , •, •, , If a body thrown upwards crosses a point in time, t, & t, respectively then height of point h _ 'h gt ,t,, Maximum height H, , •, , 1, , -"8 g(t,, , H, , tit, :, , 14, h, , + t,)', , A body is thrown upward, downward & horizontally, with same speed takes time t" t, & t, respectlvely, to reach the ground then t, =, , M, , & height from, , 1, where the particle was throw is H = 29t,t,, , •, , PROJECTIl£ MOTION, c Horizontal MotIon, u cos9 ,., , c, , t, , cose, , !, , U", , a, = 0, x - u,t - (u cose)!, Vertical Motion:, 1, 1, Vy - uy - gt where uy - u sinO; y - u,t -Zgt2. usJn9t -Zgt2, Net acceleration -, , o, , y, , i, , x, , J, , a= aJ + al'j =-gj, , At any Instant : v" - ue059,, , 28, , vr - usin9 - gt, , i, , u, , •i, , 0, , I, •

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"""'.=,, , Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , o, , •, , •, o, , For projectile motion :, A body crosses two points at same height in time t, and t, the points, are at distance x and y from starting point then, (a) x + y = R, (h) t, + t, = T, (c) h = 1/2 gt,t,, (d) Average velocity from A to B is ucosS, y, If a person can throw a ball to a maximum distance 'x' then the maximum, h,eight to which he can throw the ball will be (x/ 2), Velocity of particle at time t :, , v= v) + v,i = u,i + (u, , y, , -gt)] = ucossi +(usinS- gt)], , If angle of velocity ii from horizontal is a, then, , ta~a = v, = u, -gt = usinS-gt _ tanB - -.L, v~, , ucose, , Ux, , ucos9, , o, , At highest point :, , o, , Time of flight :, , T = 2u, = 2usinS, , o, , Horizontal range, , R=(ucosS)T= 2u'sinScosS, , Vy=0, v. =ucos9, , g, , 9, , u 2 sin 29, , g, , g, , 2u. uy, , =--, , g, , It is same for Sand (90· - S) and maximum for S = 45·, , o, , i •, , I, , I, , ,", , H, , 1, , o, , -=-tanS, R 4, , o, , Equation of trajectory, , y = x tanS -, , x, ~"g,,-x', -.-:= x tanS ( l- -R), 2, 2, 2u cos, , Horizontal projection from some height, , ~, , o, , Time of flight, , T=, , o, , Horizontal range, , R = uT =, , :;, , ", , Maximum height, , o, , u~, , e, , 1\, '--":"":R " ,, , Angle of velocity at any instant with horizontal S = tan- I, , (~), , E ~------------------~279------------------~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Ph ys ics HandBook, , KEY POINTS :, , •, , A positive acceleration can be associated with a "slowing down" of the body, because the origin and the positive cilrection of motion are a matter of choice., , •, , The x-t graph for a particle undergoing rectilinear motion, cannot be as shown, , in figure because infinitesimal changes in ve.locity are physically possible only, in infinitesimal time., , ~I, •, , In oblique projection of a projectile the speed gradually decreases up to the, highest point and then increases because the tangential acceleration opposes, , the motion till the particle reaches the highest point, and then it favours, the motion of the particle., In free fall , the initial velocity of a body may not be zero., A body can have acceleration even if its velOcity is zero at an instant., Average ve lOCity of a, •, , body may be equal to its instantaneous velocity., , The trajectory of an object moving under constant acceleration can, , be straight, , line or parabola., , •, , The path of one projectile as seen from another projectile is a straight line, as relative acceleration of one projectile w.r,t, another projectile is zero ., , ,, ~, , I, I, , ,•, ,f, , :;, , •, , E, , 31

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Force, A push or pull that one object exerts on another., , •, , Forces in nature, There are four fundamental forces in nature :, 2. Electromagnetic force, 1. Gravitational force, , 3. Strong nuclear force, •, , Types of forces on macroscopic objects, Field Forces or Range Forces:, ~, These are the forces in which contact between two objects is not, necessary., Ex. . (i) Gravitational force between two bodies., (ii) Electrostatic force between two charges., (b), , Contact Forces :, Contact forces exist only as long as the objects are touching each, other., Ex. (i) Normal force. (ii) Frictional force, , (q, , Attachment to Another Body :, Tension, , •, , 4 . Weak force, , min a string and spring force (F ... kx) comes in this group., , Newton's first law of motion (or GaB1eo's law of Inertia), Every body continues in its state of rest or unifonn motion in a straight line, unless compelled by an external unbalanced force to change that state., , Inertia : Inertia is the property of the body due to which body oppcses the, change of it's state. Inertia of a body is measured by mass of the body., , Iinertia oc mass I, , ~ •, , t, , dV _ dm, - dii d (_), F = Cit = dt mv = m Cit + v(it (Linear momentum p = mli ), , I, f, , ,•, ~, , Newton's second law, , [], , •, , For constant mass system, , Momentum, , F= rna, , : It Is the product of the mass and velocity of a body i.e., , momentum p = mv, SI Unit : kg m s ol, , DImensions: 1M L T-'I, , E ~------------------3-3------------------~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, •, , Impulse : Impulse, , a, , product of force with lime., F, , ,, , ., , impdse _ lrell under QJIVe, , ", , J, , For a finite interval of time from t, to t, then the impulse = Fdt, If constant force acts fOT an intetval .6t then : Impulse ="F6.t, Impulse- Momentum theorem, , Impulse of a force is equal to the change of momentum, •, , •, , IF At " AIlI, , Newton's third law of motion : Whenever a particle A exerts a force on, another particle S , S Simultaneously exerts a force on A with the same, magnitude in the opposite direction., ., Spring Force (According to Hooke'. law) :, In equilibrium F=kx (k is spring constant), , Note : Spring force is non impulsive in nature., , Ex. If the lower spring is cut, find acceleration of the blocks,, immediately after culling the spring ., 3mg, mg, Sol. Initial stretches x",,,,, = -k- and x"'- = k, On cutting the lower spring, by virtue of non-impulsive, nature o f spring the stretch in upper spring remains same, , immediately after culling the spring. Thus,, , Lower block :, , UP!-, , "i, 2mg=, , 2ma~, , a = g, , 2mg, , 3m g) - mg = ma~ a = 29, k ( -k-, , Upper block :, mg, , J, , i,•, ;;, , _, , ~------------~--------------------~, ., 34, E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, •, , Motion of bodies In contact, When two bodies of masses ro t and mt are kept on the frictionless surface, and a force F is applied on one body, then the force with which one body, presses the other at the point of contact is called force of contact. These, two bodies will move with same acceleration a., (i), When the force F acts on the body with mass m , as shown in fig.(i), F = (m , + m,la, , PIg.rl) : \.\/hen the forti! F (lets on mas.s In ,, , If the force exerted by m, on m , is f, (force of contactl then for body, m,' (F - f,l = m,a, , a-, , Hg. 1(11) : EB.D . representation of action and reaction forces., , •, , For body m 2 : (1=m 2a :::::) action of rn l on m 2: fl _ rnlF, PulJeysystem, m t + m2, , A single fixed pulley changes the direction of force only and in general,, assumed to be massless and frictionless ., , SOME CASES OF PUllEY, , Case-I, Let m] > rn 2, , ~, , (, , I, •1•, , now for mass mll rn 1 9 - T = mta, for mass m 2 ,T - m t 9 = m 2 a, , ·, (m, - m21, net pulling force, =aI t, g=, Acceeralon, (m , + m,1, total mass to be pulled, Tension, , =, , T, , 2 x Pr oduct of masses, Sum of two masses, , g, , Reaction at the suspension of pulley R = 2T, , • L-______________________________________________________, , E, , 35, , ~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, Case -II, For mass mJ, Formassm 2, , :, , :, , Acceleration a, , T = m} a, m2g-T=m 2 a, , =, , m 29, , (m, + m, ), , FRAME OF REFERENCE, Inertial frames of reference : A reference frame which Is either at rest, or in unifonn motion along the straight line. A non-accelerating frame of, reference is called an inertial frame of reference ., , All the fundamental laws of physics have been formulated in respect of, inertial frame of reference., , Non-inertial frame of reference: An accelerating frame of reference is, called a non-inertial frame of reference. Newton's laws of motion are not, direc~y applicable in such frames, before application we must add pseudo, force., , •, , Pseudo force : The force on a body due to acceleration of non-inertial, , frame is called fictitious or apparent or pseudo force and Is given by, , F = -mao', , where 30 is acceleration of non-inertial frame with respect to an inertial, frame and m is mass of the particle or body. The direction of pseudo force, , must be oPPosite to the direction of acceleration of the non-inertial frame., , •, , When we draw the free body diagram of a mass, with respect to an inertial, frame of reference we apply only the real forces (forces which are actually, acting on the mass). But when the free body diagram is drawn from a noninertial frame of reference a pseudo force (in addition to all real forces) has, to be applied to make the equation, , •, , F = ma, , to be valid in this frame alsc., , Man in a Lift, , If the lift moving with constant velocity v upwards or downwards. In, this case th ere is no accelerated motion hence no pseudo force, experienced by observer inside the lift., , i, , So apparent weight W' *Mg=Actual weight., , 0, , ~, , If the lift Is accelerated upward with constant acceleration a. lot, Then forces acting on the man w.r.t. observed inside the lift, are, (I) Weight W=Mg downward, , :0, , (ii) Fictitious force Fo=Ma downward., , iii, , So apparent weight W'=W+Fo-Mg+Ma=M(g+a), , ,, , L -_ _ _ _ _ _ _ _ _ _ _ _ _ _~--------------~ ", , ~6, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Phvsics HandBook, (c), , If the lift is acceierated downward with acceieration a<g., Then w.r.t. observer inside the lift fictitious force F,= Ma acts upward, while weight of man, W = Mg always acts downward., So apparent weight, , W' = W - Fa = Mg - Ma = M(g- a), , Special Case :, , if a=g then W' =0 (condition of weightlessness)., Thus, in a freeiy falling lift the man will experience weightlessness., (d), , If lift accelerates downward with acceleration a > 9 . Then as in Case, (e). Apparent weight W' =M(g-a} is negative, i.e., the man will be, acceierated upward and will stay at the ceiling o f the lift., , FRICTION, Friction is the force of two surfaces in contact, or the force of a medium, acting on a moving object. (Le. air on aircraft.), , Frictional forces arise due to molecular interactions. In some cases friction, acts as a supporting force and in some cases it acts as opposing force., •, , Cause of Friction: Friction is arises on account of strong atomic or molecular, forces of attraction between the two surfaces at the point of actual contact., , •, , Types of friction, Friction, , !, , 1, , l, , Dynamk fricti on, (Kinetic friction), (There is relative m otion, , Static friction, (No relative motion, betw"een objects), , betv..reen objects), , •, , ., ~, , (, , Graph between applied force and force of friction, Friction force (0, Umiting frkllon, , I-I, .., ,/, ..............•............., , i, , Dynamic friction, , ,J, •\, , Applied force F, , " L-__________________________~~------------------------~, , E, , 37

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Static friction coefficient ~., , (I ), , = .N~, , -, , • 0 ,;; I, ,;; ~.N. ~, , _, , = - F"""'"', , (I')m~ = ~.N = limiting friction, , •, , I, _, Sliding friction coefficient ~, = N' I,, , •, , Angle of Friction (l.), , = -(~ ,N, , Applied, , )., , v ........, , tan l., , Is, , ~.N, , =N =N, , =~ ,, , ~mmm'''~, , w, •, , Angle of repose : The maximum angle 01 an inclined plane lor which a, block remains stationary on the plane ., N, , tan ~- ~ •, , • For smooth surlace, •, , aR-, , 0, , Dependent MotIon of Connected Bodies, Method I : Method of constraint equations, , lUI = constant, , ;::::) 1: XI = 0 ;::::) E Xi =, , a, , For n moving bodies we have xl' x 2 .".x n, , o, , No. of constraint equations, , =, , 01, , no . of strings, , Method II : Method of virtual work: The sum 01 scalar products of lorces, applied by connecting links 01 constant length and displacement of corresponding contact pOints equal to zero., , ID',·lir, =0 => D',.ii, =o=> IF ,0, =01, 38, , ,1, ~, , ~, , I, , ,, f, , ", ;;, ;;, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , x,, , KEY POINTS, , Aeroplanes always fly at low altitudes because according to Newton's III law, of motion as aeroplane displaces air & at low altitude density of air is high., Rockets move by pushing the exhaust gases out so they can fly at low &, high altitude., Pulling a lawn roller is easier than pushing it because pushing increases the, apparent weight and hence friction., A moongphaliwala sells his moongphali using a weighing machine in an, elevator. He gain more profit, , if, , the elevator is accelerating up because the, , apparent weight of an object increases in an elevator while accelerating upward., , Pulling (figure I) is easier than pushing (figure II) on a rough horizontal surface, because normal reaction is less in pulling than in pushing., , ~F, m, , ~, , f, , 1, •, 1, , •, , ~, , .........., , -----, , Fig. I, , Fig. II, , While walking on ice, one should take small steps to avoid slipping . This, is because smaller step increases the normal reaction and that ensure smaller, friction ., , •, , A man in a closed cabin (lift) falling freely does not experience gravity as, inertial and gravitational mass have equivalence ., , ,, ~, , •, ", , m, , ilnmn,);i/IJ/1Hn, , j, , E, , --, , \\II\(\(\\k\\\\\\\~\\\, , 39

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, Conservative Forees, •, , Work done does not depend upon path., , •, , Work done in a round trip is zero., , •, , Central forces, spring forces etc. are conservative forces, , •, , When only a conservative force acts within a system, the kinetic energy, and potential energy can change into each other. However, their sum,, the mechanical energy of the system, doesn't change., , •, , Work done is .completely recoverable., , • If, , F, , is a conservative force then V x F = 6 (i.e. curl of, , F, , is zero), , Non-conservatlve F orees, , •, , Work done depends upon path., , •, , Work done in a round trip is not zero., , •, , Force are velocity-dependent & retarding in nature e.g. friction, viscous, , force etc ., •, , Work done against a non-conservative force may, , •, , Work done Is not recoverable ., , be dissipated as heat energy., , KInetic energy, , •, , The energy possessed by a body by virtue of its motion is called kinetic, energy., , K, •, , 1, , (- - ), , =21 mv =2 mv .v, 2, , Kinetic energy is a frame dependent quantity because velocity is a frame, , depends., Potential energy, , •, •, •, •, , The energy which a bcxfy has by virtue of its position or configuration in a, conservative force field., Potential energy is a relative quantity., Potential energy is defined omy for conservative force field., , Relationship between conservative force field and potential energy:, F- =-vu, , •, , :., , Ol/, aU =- grad(U) =- aU,, -1--) --k, ax, az, , i, , J, -i, , Oy, , If force varies only with one dimension (along x-axis) then, , dU, F2-dx", , ~, , f Fdx, , X2, , U=-, , ", , ~, , •, , i, -, , ~--------------------------~--------------------------~, F., A"

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,, _ """,., A"\HI, , Ph ysics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , •, , Potential e nergy curve and equilibrium, B, E, I, I, I, I, , C, , 11, , I, , ID, , I, I, I, I, I, , I, I, I, I, I, I, , A, , I, F~, , ~F, , G, , H, , I, I, I, I, I, I, , .- F, , positi on of partk le, , F~, , --+, , It is a curve which shows change in potential energy with postion of a particle., , •, , Stable Equilibrium :, When a particle is slightly displaced from eqUilibrium position and it tends to, come back ~owards equilibrium then it is said to, , be, , in stable equilibrium, , At point C : slope, , dU, is negative, dx, , so F is positive, , At point D : slope, , dU, is positive, dx, , so F is negative, , At point A : It is the point of stable equilibrium ., , U, , •, t, , E, , '"", , U, , dU = O, min, , ', , dx, , I, ,, , d' U, dx 2, , = positive, , Unstable equUibrlum :, , When a particle is slightly displaced from equilibrium and it tends to move, away from equilibrium position then it is said to be in unstable equilibrium, , (, , I, , and, , At point E : slope, , dU, , d;- is positive so F is negative, , At point G : slope dU is negative so F is postive, dx, At point B : It is the point of unstable equilibrium., , :;, , ~, i:, 1, , U=U, , ~K, , I, , dU, d2U, ., = 0 and - 2 = negative, dx, dx, , -, , • L-__________________________~--------------------------~, , E, , 43

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, •, , Neutral equilibrium:, When a particle is slightly displaced from equilibrium position and no force, acts on it then equilbirum is said to be neutral equilibrium. Point H is at, neutral equilibrium, , •, , ~ U = constant·,, , dU =0 d'U =0, dx, 'dx', , Work energy theorem: W = 6KE, Change in kinetic energy = work done by all force, , •, , dU, For conservative force F(x) =- d;, , change in potential energy 6U =, , •, , -I F(x)dx, , Law of conservation of Mechaoical energy, Total mechanical (kinetic + potential) energy of a system remains constant, if only conseJVative forces are acting on the system of particles or the work, done by all other forces is zero. From work energy theorem W = 6KE, Proof: For internal conservative forces, , => a(KE + U), , =, , 0 =>, , Wi~, , = -aU, , KE + U - constant, , •, , 1, Spring force Fa-kx, Elastic potential energy stored in spring U(x) = Zkx', , •, , Mass and energy are equivalent and are related by E = me', , •, , Power, • Power is a scalar quantity with dimension MlL'T-3, , • 51 unit of power is J/s or watt, , • 1 horsepower a 746 watt - 550 ft-lb/see., , •, , Average power P~ - Wit, , ~, , i, , I,, •, , ~--------------~--------------~, ., 44, E

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rr '."'. .'. .'·."., , Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , ~, , •, , C..i..~.. U"I..a..'r"M"'r.. ..t'i..:~..n":,,..ii'.., ~..,".,'~,:!'.!"".', C.., , O, .., ,, , I;.., , ,,, "',., ' I,, , Definition of Circular Motion, When a particle moves in a plane such that its distance from a fixed (or moving), , point remains constant then its motion is called as circular motion with respect, , to that fixed point. That fixed point is called centre and the distance is called, radius of circular path., , Radius Vector:, , The vector joining the centre of the circle and the center of the particle, performing circular motion is called radius vector. It has constant magnitude, and variable direction. It is directed outward, Frequency (n) ,, , No. of revolutions described by particle per sec. is its freque ncy. Its unit is, revolutions per second (r.p.s.) or revolutions per minute (r.p.m.), , Time Period, , m', , It is time taken by particle to complete one revolution ., , •, , "i, i, , I, , f, , •I•, , r, , •, , Average angular velocity, , 68, w = -;;;- (a scalar quantity), , •, , Instantaneous anguJar velocity, , d8, ro = ill (a vector quantity), , •, , For unifonn angular velOCity, , 2n, ro = - =211'f or 2n:n, T, , Angular displacement, , a = wt, , '0 --> Angular frequency, , n or f, , ~, , E, , n, , Angle 0 = arc length = ~, radius, , ~, , 1, , T=-, , 47, , = frequency, , •

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, B. Condition for pendulum motion (oscillating condition), u "J2gR (in between A to B), Velocity can be zero but T never be zero between A & B., mv', Because T is given by T = mg cos 8 + R, , C. Condition for leaving path, , J2gR < u < J5gR, , Particle crosses the point B but not complete the vertical circle., , Tension will be zero in between B to C & the angle where T = 0, u'-;:-...,2,!-g:.:R, cos 8 = .::, 3gR, 9 is from vertical line, , Note : After, , leavin~, , the circle, the particle will follow a parabolic path., , ~, , . KEYPOINTS, , .., , Average angular velocity is a scalar physical quanity whereas instantaneous, angular velocity is a vector physical quanity., , Small Angular displace ment de is a vector quantity, but large angula r ., displacement 8 is scalar quantity., , dO, + de, = de, + de, But, , i?, S, , j, , ,, •, i, c., , ~--------------------------~------------------~------~, ', 50, E

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , •, , Relative Angular Velocity, Relative angular velocity of a particle 'A' w.r,t. other moving particle B is the, angular velocity of the position vector of A, , W .T. t., , A.····S,, , B., , v,, , That means it is the rate at which position vector of 'A' w.r.t. B rotates at that, insta nt, (VA.),, , Relative velocity of A w.r.t. B perpendicular to line AB, , rAS, , seperation between A and B, , WAB=~=, , 1t, ~, , (, , i, , !, f, ~, , •, , I, •, E, , 51

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , HandBook, The centre of mass after removal of a part of a body, , Original mass (M) - mass of the removed part (m), - {original mass (M)) + I - mass o f the removed part (m)!, The formula changes to :, xc.. ~, , Mx-mx', My - my', M z- m z', M-m ;y"" = M-m ; yO! = M-m-, , CENTRE OF MASS OF SOME COMMON OBJECTS, , Uniform Ring, , Centre of ring, , Uniform Disc, , Centre of disc, , Uniform, , Roo, , Centre of n:xi, , eM, , ,, I, , Solid spherel, hollow sphere, , Triangular plane, , lamina, , Centre o f sphere, , ~, ~, , 1·,1, , , ,,, , Point of intersection of the medians, , of the triangle i. e. centroid, Point of intersection of diagonals, , Plane lamina in, the form of a, square or rectangle, or parallelogram, , .., ~, , i, , !, }, , Hollowl solid, cylinder, , Middle point of the axis of cylinder, , I., , •~, ;;, , ~~, , (

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Law of conservation of linear momentum, , I, , Unear momentum 01 a system 01 particles is equal to the product 01 mass 01 the, system with velocity 01 its centre 01 mass., From Newton's second law, , \I, , F~•. = 5 then, , FIX!., , M\iCM = constant, , If no external force acts on a system the velocity of its centre of mass remains, constant, i.e .• velocity of centre of mass is unaffected by internal forces., •, , ImpuJse- Momentum theorem, Impulse 01 a lorce is equal to the change 01 momentum, force time graph area gives change in momentum., , ", , fFdt = ~ii, '., , Collision of bodies, The event or the process, in which two bodies either coming in contact, with each other or due to mutual interaction at distance apart, affect each, others motion (velocity, momentum, energy or direction of motion) is defined, as a collision., InroDision, •, The particles come closer before collision and after collision they either, stick together or move away from each other., • The particles need not come in contact with each other for a collision., •, The law 01 conservation 01 linear momentum is necessarily applicable in a, collision, whereas the law of conservation of mechanical energy is not., I\PISOI, , (OIII~IO~, , !(, , I, , I·•, l, , 56, , •, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Coefficient of restitution (Newton's law), e=, , velocity of separation along line of impact, velocity of approach along line of impact, , v, - v,, u, - u,, , Value of e is 1 for elastic collision, 0 for perfectly inelastic collision and, < e < 1 for inelastic collision., ', Head. on collision, , o, , •, , ········,rlll,···i···~II,IJI~·~~!·--!, .:1, ,. ~, \".. ., rn l, , Ill:?, Before collision, , In J, , Collision, , m", , After collision, , Head on 1ne1astlc colHsion of two particles, Let the coefficient of restitution for collision is e, (i) Momentum is conserved m Ill! + mZu2 = mJv, + m 2v2, (ii) Kinetic energy is not conserved., , ..• (i}, , liii) According to Newton's law e= v,-v, ".Iii), ul -u2, By solving eq. Ii) and Iii) ,, , J, , - (m, - em, lll+, v}-, , [(1, , m,+~, , J _"m..!'c.u.!.,_+_m_,!Cu,-,--_m-<,e.::.o..(u",_--"u,'-1.), , + e) m, u, 2, , --, , ~+~, , m,+~, , ElastIc ColHsion (e-l), • If the two bodies are of equal masses: m, = m2 = m, vI = u2 and vl = u1, Thus, if two bodies of equal masses unde rgo elastic collision in one dimension,, then after the collision, the bodies will exchange their velocities., •, ~, ~, , ~, , J, ~, , ,, , !• •, , If the mass of a body is negligible as compared to other., , If m l » m 2 and u 2 = 0 then V I = u l ' v2 = 2u 1 when a heavy body A collides, against a light body B at rest, the body A sho uld keep on moving with same, velocity a nd the body B will move with velocity do uble that of A. If m,» m ,, , and, , Uz =, , 0 then Vz == 0, VI, , :I::, , -, , ul, , When light body A collides against a heavy body B at rest, the body A should, start moving with same velocity just in opposite direction while the body B, should practically remains at rest., , Loss in kinetic energy In ineIastic collision, , ;;, , •, E, , .1K =, , m,m,, , (1 - e' ) lu, - u, )', , 21m, + m, ), 57

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, Conserving the momentum of system in directions along normal (x axis in our, case) and tangential (y axis in our case), m1ujcosu, + m2ulcosCl z = m lvlcos~l + m2v2cosPz and, rn 2 L1 2sina z - m jll jsina \ = m l v l sinP2 - m1vjsinP t, , -f~~m~'~Q_,~~~, m~,~_u_', , ______, , ~~~~~, J_Y_~~,~_V_'___, , ,x, , ~, , u,, , AhH, , Before, collision, , eolli~on, , Since no force is acting on mt and., , ffi l, , along the tangent (Le. y-axis) the, , individual momentum of m I and m z remains conselVed., mtu,sina \ -= m1vIsinP 1 & m211 zsina z = m2v1sinP z, , By using Newton's experimental law along the line of impact, , e-, , v 2 cOSJ}Z-v 1 COSPt, , u t cosa l, , - U z casaz, , u, , v, , Rocket propulsion :, Thrust force on the rocket"'" vr ( -, , dd7), , At t-O, V=U, , Velocity of rocket at any instant, , v=u-gt+v,ln, , (:0), , m=mu, , At t- t, mx m, , V=V, , exhaust velocity =v,, , KEY POINTS, , Sum of mass moments about centre of mass is zero. Le. Lm i~/cm = 0, , •, , A quick collision between two bodies is more violent then s10w collision,, even when initial and final velocities are equal beca use the rate of change, of momentum determines that the impulsive force small or large ., , ~, , •, , Heavy water is used as moderator in nuclear reactors as energy transfer, is maximum if m\.:::: m2, , I, , •, , Impulse momentum theorem is equivalent to Newton's second law of, moti on., , •, , For a system, conservation of linear momentum is equivalent to Newton's, third law of motion., , t, , ~, , J, ", i", , L-__________________________~--------------------------~ ., , 58, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Rod, :, , M, (, , •, , Y, !(, , 0, , 1 = MI', 12, , ,, , ~, , MI', 1- 3, , M, , ,, , i, , i(, , R, , RectanguJar Lamina, , MR', 1- 2, , ~I =MR', M, , •, , Ring:, , C t Ry, , • Disc:, , j (Geometrical axis), , •, , Circular HoUow Disk : ~~~~~~~, , ~, , '-P 1- MR', , .~, , I, , r, , I, , I, :;;, , 1", , ", E, , :', , (, , •, , HoUow cylinder, , 1. . ... . ., , ==t::::=;\, , RJ \L., , +-- ( i, , ~, 61, , '

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , •, , Pure rolling motion on an Inclined plane, , o, , ., , gsin9, , Accelerahon a ~ 1 + k' / R', , [] . Minimum frictional coefficient, , 1..1 i1 =, m, , •, , Torque t~Ja~Jdffi ~ d(Iffi) ~ dLordJ, dt, dt, dt dt, , •, , Change In angular momentum 6L, , •, , Work done by, , 8, , torque W =, , ta~ 9, , l+R / k, , 2, , ~ t6t, , ft .dS, , KEY POINTS, • A ladder is more apt to slip, when you are high up on It than when you, just begin to climb because at the high up on a ladder the torque is large, and on climbing up the torque is small., • When a sphere is rolls on a horizontal table, it slows down and eventually, stops because when the sphere rolls on the table, both the sphere and the, surface deform near the contact. As a resuk the normal force does not pass, through the centre and provide an angular deceleration., The, spokes near the top of a rolling bicycle wheel are more blurred than, •, those near the bottom of the wheel because the spokes near the top of, wheel are moving faster than those near the bottom of the wheel., Instantaneous, angular velocity is a vector quantity because infinitesimal angular, •, displacement is a vector., The relative angular velocity between any two points of a rigid body Is zero, ~, at any instant ., (, All particles of a rigid body, which do not lie on an axis of rotation move, on circular paths with centres at an axis of rotation., Instantaneous axis of rotation is stationary w.r.t. ground., Many greater rivers flow toward the equator. The sediment that they carry, increases the time of rotation of the earth about its own axis because the, angular momentum of the earth about Its rotation axis is conserved., ;0, The hard boiled-egg and raw egg can be distinguished on the basis of spinning, • L -____________________________, of both ., , ., , I., , i:, ••, 1, , E, , --~, , 63

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Phvslcs HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , •, , Newton's law of gravitation, , m1, , III, , m2, Gmlrn2, , r, , •, , Force of attraction between two point masses F = - -, r, , Directed along the line joining of point masses ., ~, , • It is a conservative force fjeld, , mechanical energy is conserved ., , • It is a central force field => angular momentum is conserved., , •, , E, , Gravitational field due to spherical sheD, , GM, , where r > R, o Outside the shell E, = -,r, GM, , On the surface E, - R', , r-R, , ~-~~~~~..., , ~~, , where r=R, , V, , r, , ....I.. ... ....., , Inside the shell E, - 0, where r<R, [Note : Direction always towards the centre of the sphere], •, , E, , Gravltatlana1 field due to solid sphen!, , GM, , Outside the sphere E, - - r ,- , where r > R, On the surface Eg, , GM, , &, , Inside the sphere E, -, , R2 ' where, GMr, , R", , where r< R, , ""t, , ., j, , Acceleration due to gravitv g _ G~, R, , i, , o, , J, •i•, , r-R, , GM, At height h ' g, - (R+h)', , At depth d g,o, , GM(R-d), R', , If h«, , -g., , (, , R; g,, , "'9.(1-~), , I-Ii:d), , Effect of rotation on g : g' - g--<o'Rcos'l. where l. is angle of latitude ., , • L-__________________________~---------------------------', , E, , 65

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, •, , Gravitational potential, Due to a point mass at a, , •, , GM, V - --, , dista~ce, , r, , Gravitational potential due to spherical shell, GM, o Outside the shell, V - - - . r>R, r, , 0, , V=, , Inside/on the surface the shell, , GM, , -R, - • rS R, , V, R, , 0, , _ GM, R, , •, , Potential due to so Id sphere, GM, , 0, , Outside the sphere, , V - -r- • r>R, , [], , On the surface, , GM, V-- R, , 0, , Inside the sphere, , V--, , , r - R, , GM(3R' - r'), 2R', , I, , r <R, , V, R, , 0, , r, , ~, _GM, R, , ---, , r'--, , _3GM, 2R, , GM, , •, , Potential on the __ of a, thin ring at a dlstanm x, , V-- JR' +x', , •, , &cape veIodIy from a pIanot of, _ M and radius R, , v• -, , •, , Orbital velocity of satellite, , v. -, , 66, , l~M, , ~~, -r-= (R+h), , ~, ~, , I, ~, , 1, ~, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , PhysIcs HandBook, , o, , JGM _ v,, , For nearby satellite, , -"12, , R, , Here V. = escape velocity on earth surface., , •, •, , •, , 21(T, , 2nr 3 / 2, , T - ~ = JGM, , Time period ofsatellite, Energies of a satellite, 0, , Potential energy, , GMm, u = - -r, , 0, , Kinetic energy, , K =-mv = - -, , 0, , Mechanical energy, , GMm, E = U + K =--2r, , 0, , Binding energy, , BE=- E =, , 1, 2, , ,, , GMm, 2r, , GMm, 2r, , Kepler's laws, , o I" Law of orbitals, Path of a planet is elliptical with the sun at a focus., dA, , dt =, , L, constant - 2m, , o, , II'" Law of areas Areal velocity, , o, , III" - Law of periods T' oc a' or T' oc (r.., ; rmil ) ' oc (mean radiUS)', For circular orblts 1"2 oc R3, , KEY POINTS, , •, •, ~, , ~, , •, , ( •, , I•, , i,•, , •, , ", •, E, , •, , At the centre of earth, a body has centre of mass, but no centre of gravity., body coincide if gravitation, field Is uniform., You does not experience gravitational force in daily life due to objects of, The centre of mass and centre of gravity of a, , same size as value of G is very small., , Moon travellers lie heavy weight at their back before landing on Moon due, to smaller value of g at Moon., Space rockets are usually launched in equatorial line from West to East because, 9 is minimum at equator and earth rotates from W est to East about its axis., Angular momentum in gravitational field is conseIVed because gravitational, force is a central force ., , Kepler's second law or constancy of areal velocity is a corlsequence of, conselVation of angular momentum., , 67

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, lateral strain, longitudinal straln, , •, , Poisson's ratio (al, , •, , Work done In stretching wire, , W-, , 1·, , 2 x stress, , x strain x volume :, , 1Flll, 1, Wa - x - x - x A x l - - F x I!.l, 2 A, 2, l, •, , Rod Is rigidly ftxed between walls, Thermal Strain =, , •, •, •, , <lAO, , Thermal stress - Y<lAO, Thermal tension = YaAJ!.O, , Effect of Temperature on elasticity, , When temperature is increased then due to weakness of inter molecular force, the elastic properties in general decreases i.e. elastic constant decreases., Plasticity increases with temperature. For example, at ordinary room, , temperature, carbon is elastic but at high temperature, carbon becomes plastic., , Lead is not much elastic at room temperature but when cooled in liquid nitrogen, exhibit highly elastic behaviour., For a special kind of steel, elastic constants do not vary appreciably temperature., This steel is called 1NVAR steel'., , •, , ~, , t, , Effect of Impurity on elasticity, , it, , Y is slightly increase by impUrity. The inter molecular attraction force inside, , ,, , i•, , wire effectively increase by impurity due to this external force can be easily ;, L-__, , ____________________, opposed., , __________________________, , 72, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , HandBook, , (B) HYDROSTATICS, , mass, , •, , Density = - volume, , •, , Specific weight, , •, , R e Iatve, I d ensty=, I, , •, , Density of a Mixture of substance In the proportion of mass, , weight, , = -- -, , volwne, , pg, , _ _ d_ens_lty,,-o_f.:9_ive_n_liqu'-id----,density of pure water at 4°C, , the density of the mixture is, , •, , Density of a mixture of substance In the proportion of volume, , •, , Pressure = nanna] force, area, , •, , Variation of pressure with depth, Pressure is same at two pOints in the same horizontal level PI, , =, , P2, , The difference of pressure between two points separated by a depth h, (P,-P,) - hpg, , !, i, , •, , Pressure In case of accelerating fluid, , 01 Uquid placed In elevator: When elevator accelerates upward with acceleration, , I, , " then pressure In the fluid, at depth h may be given by, P=hp[9+a,[, , ,, f•, , •, ", , E, , 73

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , (II) Free surface of liquid in case of horizontal ac:c:eleration :, tanS = mao =~, mg, g, If P, and P, are pressures at point 1 & 2 then, , P,-P, - pg (h,- h,) = pgetan6 = peao, (Iii) Free surface of liquid in case of rotating cylinder, , '", ....!"_._ B, , A, , •, , Pascal's Law, • The pressure in a fluid at rest is same at all the points if gravity is ignored., • A liquid exerts equal pressures in all directions., • If the pressure in an enclosed fluid is changed at a particular point. the, change is transmitted to every point of the fluid and to the walis of the, container without being diminished in magn~ude. [for ideal fluids/, , •, , Types of Pressure : Pressure is of three types, (i) Atmospheric pressure (PJ, , (ii) Gauge pressure (P...,), , J, , (iii) Absolute pressure (P•••, , •, , Atmospheric pressure : Force exerted by air column on unit crc>ss--sec:tic.c1, area of sea level called atmospheric pressure (P), , ....... _.... ., .._-- .. -_ ...., , F, , P, - A = 101.3 kN/m', X, , ~, , air, , sea, , :. P, = 1.013, , up to top of, atmosphere, , level, , 10' N/ m', , Barometer is used to measure atmospheric pressure., , Which was discovered by Torrlcelli., , column, , /, , I, , ,, f, , Atmospheric pressure varies from place to place and at a particular place from ", ii, time to time., , ---------------------------J", , L-____________________________, , 74, , E

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Gauge Pressure, Excess Pressure ( P- P...) measured with the help of pressure measuring Instru, ment called Gauge pressure. Pgo... hpg Dr p..... a: h, &, , Gauge pressure Is always measured with help of "manometer", , Absolute Pressure :, Sum of atmospheric and Gauge pressure Is called absolute pressure., , The pressure which we measure In our automobile tyres Is gauge pressure., , ~, (, , I, , •, , Buoyant force - Weight of displaced fluid - Vog, , •, , Apparent weight - Weight - Upthrust, , ., , t., ~, , ii, , I, , Rotatory - Equilibrium In floatation: for rotational equilibrium of floating, body the meta-centre must always be higher than the centre of gravity of, the body., Relative density of body _ c:Den=si::.;;ty:<...::o;.-fbodv=:<.., Density of water, , .~------------~=---------------~, 75, E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , (C) HYDRODYNAMICS, , •, , Steady and Unsteady Flow : Steady flow Is defined as that type of flow in, which the fluid characteristics like velocity, pressure and density at a point do, not change with .time., , •, , StreamUne Flow : In steady flow aD the particles passing through a given point, follow the same path and hence a unique line of flow. This line or path Is caDed, a streamline., , •, , LamInar and Turbulent Flow: Laminar flow Is the flow In whlch the fluid, , particles move along well-defined streamlines which are straight and parallel., , •, , Compiesslble and IncompJasIbIe Flow : In compressible flow the density of, fluid varies from point to point i.e. the density Is not constant for the fluid, whereas in incompressible flow the density of the fluid remains constant, throughout., , •, , Rotational and Irrotatlonal Flow : Rotational flow Is the flow In whlch the, fluid particles while flowing along path-lir.es also rotate about their own axis., In irrotationai flow particles do not roI2Ite about their axis., , •, , Equation of continuity, , •, , BemouIII's theorem :, , Al VI •, , A,v, Based on conservation of mass, , Ip + ~pv2 + pgh . constant I, , Based on energy conservation, , ~, t, , I, , h,, , ~, iii, , i, , 76, , ", E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Kinetic Energy, kinetic energy per unit volume, , •, , Kinetic Energy, , 1m, 2V, , 2, , 1, 2, , =-- v =-pv, , Potential Energy = m gh = pgh, volume, V, , Pressure Energy, , Pressure energy per unit volume =, , Pressure energy, volume, , •, , For horizontal flow In venturlmeter, , •, , Rate of flow :, , Volume of water flowing per second, , Q = A,v,, , =, , - P, , A,A,JA;~A2, ,, , •, , Velocity of efflux v = J2gh, , ~, , ;, , I, I" •, , Horizontal range R = 2 ,Jh(H - h), , ;;, , i, ", E, , 2, , Potential Energy, Potential energy per unit volume, , •, , volume, , 77, , 2

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, Phvslcs HandBook, , (0) SURFACE TENSION, Surface tension is basica\Jy a property of liquid. The liquid surface behaves like a, stretched elastic membrane which has a natural tendency to contract and tends to, have a minimum surface area. This property of liquid is called surface tension ., .Intermolecular forces, (a) Cohesive force, , The force acting between the molecules of one type of molecules of same, substance is ca\Jed cohesive force., (b) Adhesive force, , The force acting between different types of molecules or molecules of different, substance Is ca\Jed adhesive force ., r:J, , Intermolecular forces are different from the gravitational forces and do not, obey the Inverse-square law, , r:J, , The distance upto which these forces effective, is ca\Jed.molecuiar range., This distance is nearly 10" m. Within this limit this Increases very rapidly, as the distance decreases., , r:J, , Molecular range depends on the nature of the substance, , Properties of surface tension, , •, , Surface tension Is a scalar quantity., , •, , It acts tangential to liquid surface., , •, , Surface tension is always produced due to cohesive force., , •, , More is the cohesive force, more is the surface tension., , •, , When surface area of liquid is Increased, molecules from the interior of the ~, liquid rise to the surface. For this, work.!. done agalnsi the downward cohestve, force., , I, , Dependency of Surface Tension, , •, , On Cohesive Force: lbose factors which Increase the cohesive force between, molecules Increase the surface tension and those which decrease the cohesive i~, force between molecules decrease the surface tension., , I, , L-____________________~~--------------------~., , 78, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Phvslcs HandBook, , •, , On Impurities : If the impurity is completely soluble then on mixing it in the, liquid, its surface tension increases. e.g., on dissolving ionic salts in small quantities, in a liquid, its surface tension increases. If the impurity is partially soluble in a, liquid then its surface tension decreases because adhesive force between insoluble, impurity molecules and liquid molecules decreases cohesive force effectively,, e .g ., .(a) On mixing detergent in water its surface tension decreases., (b) Surface tension of water is more than (alcohol + water) mixture., , •, , On Temperature, , On increasing temperature surface tension decreases. At critical temperature, and ooiling point it becomes zero., , Note : Surface tension o f water is maximum at 4 OC, , •, , On Contamination, The dust particles or lubricating materials on the liquid surface decreases its, surface tension., , •, , On ElectrIficatIon, The surface tension of a liquid decreases due to electrification because a force, starts acting due to it in the outward direction normal to the free surface of liquid., , DeflnHion of surface tension, The force acting per unit length of an imaginary line drawn on the free liquid, surface at right angles to the line and in the plane of liquid surface, is defined, as surface tension., , ~, , ~, , i, , 1, , I, ;, :i, , ", , E, , o, , •, , For floating needle 2T I sinS = mg, , Required excess force for lift, F" = 2Tt, , o, , Wire, , o, , For ring, , o, , Square frame, , Fex, , =, , 4rcrT, FQ = BaT, , 79, , o, , Hollow disc FQ = 2nT (r, + r,), , o, , Circular disc, , o, , Square plate F" = 4aT, , Fex - 27t'rT

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, •, , •, , Work = surface energy - T IIA, rl, , Uquid drop W = 4nr'T, , rl, , Soap bubble W = 8nr'T, , Splitting of bigger drop Into smaller droples R _, Work done- Change in surface energy =, , •, , Excess pressure, In liquid drop, rl, , Pa = P • - P, , P, a, , =, , n1/3, , r, , 41tR'T(~-k) = 41tR'T (n ' 13-1), , ~, , 2T, , R, , 4T, In soap bubble P a = If, , ANGLE OF CONTACT (9 c), , The angle enclosed between the tangent plane at the liquid surface and the, tangent plane at the solid surface at the point of contact inside the liquid is, defined as the angle of contact., The angle of contact depends the nature of the solid and liquid in contact., , •, , Angle of contact 9 < 90· => concave shape, Uquid rise up, Angle of contact 9 > 90· => convex shape, Uquid falls, Angle of contact 9 = 90· => plane shape, Uquid neither rise nor falls, , •, , Effect of Temperature on angle of contact, On increasing temperature surface tension decreases, thus cosO( increases, , [.: cos9,, , •, , <£, , t], , and 9, decrease. So on increasing temperature, 9, decreases., , Effect of impurities on angle of rontact, (a), , Solute impurities increase surface tension, so cosSc decreases and angle, increases., o f contact, , e(:, , (b), , Partially solute Impurities decrease surface tension, so angle of contact, ec decreases., , ~, , t, , I, 'l, , ", 1, ;;, , ~------------------~80~------------------~ E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , Effect of Water Proofing Agent, Angle of contact increases due to water proofing agent. It gets converted acute, to obtuse angle., , •, , Capillary rise, , h, , =, , 2T cos 9, rpg, , 1, , •, , Zurin's law h a: r, , •, , Jeager's method T = r: (Hp - hd), , •, , The height 'h' is measured from the bottom of the meniscus. However,, there exist some liquid above this line also. If correction of this is applied, , then the formula will be, , •, , When two soap bubbles are in contact then, radius of curvature of the common SUlface, , •, , When two soap bubbles are combining to, form a new bubble then radius of new bWbIe, , ~, ~, , i •, , I, , Force required to separate two plates, , I, ~, , IE, , 81, , F = 2AT, d

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, IE) VISCOSITY, , •, , Newton's law of viscosity, , Nxs, , ·51 UNITS: - 2 - or deca poise, , m, , • CGS UNITS : dyne-./cm' or poise (1 decapoise - 10 poise), •, , Dependency of viscosity of Hulda, On Temperature of Fluid, (a) Since cohesive forces decrease with increase in temperature as increase in, K.E .. Therefore with the rise in temperature, the viscosity of Iiqulds de-, , creases., (b), , The viscosity of gases is the resuk 01 diffusion of gas molecules from one, moving layer to other moving layer. Now with increase in temperature, the, rate of diffusion increases. So, the Viscosity also increases. Thus, the viscosity, of gases increases with the rise of temperature., , On Pressure of Fluid, (a) The viscosity of liquids increases with the increase of pressure., (b) The viscosity of gases is practically independent of pressure., On Nature of Fluid, , •, , PolseulUel'a formula, , iN Itpr4, Q - -=S"L, dt, , •, , Viscous force, , F,, , ~, , -, , ,, , 67tT]fV, , ~, , 2 r'(p-o)g, , •, , Terminal velocity, , vT, , •, , Reynolds number, , R., , R. < 1000 laminar flow,, , R. > 2000 turbulent flow, , 9, , ~, , =>vToc r, , pvd, ~, , 82, , ~, , I, , I••, i, , •, , E, , •

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , THERMAL EXPANSION, It is due to asymme try in potential energy curve., , u, , \, , To, , e~, , In solids -> Linear expansion, , ~'====~~C, ~O~======:j11, Before heating, , Tl., , (l+aLlD, , .~,====~;I=o+=LI~(:;(::==::j, T+Ll.TL, , ~, , In solids -> Areal expansion, , 10, , After heating, Ao (l+Pt.D, , A~, , T+t.T, T, , [}c$, , A, , (, , Co, (, , In solids, liquids and gases -> volume expansion, , V~Vo (l+ yIlD, , ~, , i, , I, , i,, •, , ;;, , IFor isotropic solids , a , P , y ~ 1 , 2 , 31, Thermal expansion of an isotropic object may be imagined as a photographic, enlargement., Fo r anisotropic materials, P = u + o'y a nd y ax + a " + u ,, L, , XY, , T,, , If a is variable, , M~, , f CoadT, T,, , " L-______________________________________________________, , E, , 85

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , Application of Thermal expansion In solids, Bi-metallic strlp(used as /hennoslat or auto-cut in electric healing circuits}, , 1, , I., , Simple pendulum: T =2n, , II => T '", , ~g, , (112, , => 6.T, T, , =.!. M, 2 e, , 6T 1, Fractional change in time period ~ T = Za69, , .. Scale reading : Due to linear expansion / contraction, scale reading will, be lesser I more than actual value., If temperature t then actual value - scale reading (1+a69), IV, Thermal Stress, , Cooling ITensile Stress), , Heating ICompressive Stress), , M, , Thermal strain _ -- = a69, C, , As Young's modulus Y = F I A ; So thermal stress, , Ml c, , =, , YAM9, , t, Thennal expansion in liquids (Only volume expansion), Apparent Increase In volume, , Y. = Initial volume x Temperature rise, reallncrese In volume, Y = _...c..::.:=..=.:.:c..:=..;"'-'.:..=:.:.:..._, r, Y,, , Inttlal volume x temperature rise, , ="f., , + Y..-.., , Change in volume of liquid w.r.t. vessel 6V = V. (y, -3a)6T, , ~, , ~, , }, , I, :;;, , ;;, , ,, , ~--------------------------~--------------------------~, ., 86, E

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Phvslcs HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Expansion in enclosed volume, , Initially, , Finally, , 10--+ vessel; y,--+ liquid], Increase in height of liquid level in tube when bulb was initially completely, filled., h = apparent change in volume of liquid, area of tube, , VO(YL -3(l)~T, Ao(l +20)~T, , Anomalous expansion of water :, In the range QOC to 4 "C water contract on heating and expands on cooling., At 4°C -+ density is maximum., Aquatic life is able to survive in very cold countries as the lake bcttom remains, unfrozen at the temperature around 4°C., Thennal expansion of gases :, , Coefficient of volume expansion, IPV, , •, , =, , KEY POINTS:, , ~, , •, , J•, -_, , ;, :;;, , i• ., ", , ~T, , T ], , Coefficient of pressure expansion, , ;, o, , ~V, , nRT at constant pressure Va: T => I i =, , Uquids usually expand more than solids because the intermolecular forces, in liquids are weaker than in solids., Rubber contract on heating because in rubber as temperature increases, the, amplitude of transverse vibrations increases more than the amplitude of, longitudinal vibrations., Water expands both when heated or cooled from 4"C because volume of, water at 4°C is minimum ., In cold countries, water pipes sometimes burst, because water expands on, freezing., , E ~--~~----------------------------~, 87

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , PhysIcs HandBook, CALORIMETRY, , 11 cal, , =, , 4.186 J ; 4.2 JI, , Q, Thennal capacity of a body = f!. T, , Amount of heat required to raise the temp. of a given body by 1"C (or 1K)., Q, Specific heat capacity = mf!.T (m, , =, , mass), , Amount of heat required to raise the temperature of unit mass of a, , body, , through 1'C (or lK), , Molar heat capacity=, , Q, , nf!.T, , (n=number of males), , Water equivalent: If thennal capacity of a body is expressed in terms af, mass of water, it is called water equivalent . Water equivalent of a body is, the mass of water which when given same amount of heat as to the body,, changes the temperature of water through same range as that of the body., Therefore water equivalent of a body is the quantity of water, whose heat, , capacity is the same as the heat capacity of the body., Water equivalent of the body,, specific heat of body ), W - mass af body x ( specific heat of water, Unit of water equivalent is 9 or kg., , Latent Heat (Hidden heat) : The amount of heat that has to supplied ta, (or removed from) a body for its camplete change af state (from solid to ;, liquid, liquid to gas etc) is called latent heat of the body. Remember that ~, phase transfonnation is an isothermal (Le. temperature = constant) change., , !, l, , PrInciple of calorimetry : Heat lost = heat gained, For temperature change Q = ms.6.T. For phase change Q ,. mL, , Heating curve : If to a given mass (m) of a solid, heat is supplied at constant, rate (Q) and a graph is plotted between temperature and lime, the graph, ~, , is called heating curve., , ________________, , ~, , 88, , ________________, , ~, , I", , •, I, N, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , Temperature, , E, , C, D, BP. . ..................................r--,--"(, boiling, M.P., , A, , B, , ! melting:, , .1i, , !.i, , tl, , t2, , Ii~, , 0 " - - - - - ' - -.......---'---"-------+, t~, , ~, , J, Specific heat (or thermal capacity) oc -,---";-slope of curve, , Latent heat a: length of horizontal line., KEY POINTS, Specific heat of a body may be greater than its thermal capacity as mass, of the body may be less than unity., •, The steam at lOOoe causes more severe burn to human body than the water, at l OQoe because steam has greater internal energy than water due to latent, heat of vaporization,, , •, , Heat is energy in transit which is transferred from hot body to cold body., , •, , One calorie is the amount of heat required to raise the temperature of one, , •, , Clausins & clapeyron equation (effect of pressure on boiling point of liquids, , gram of water through J"e (more precisely from 14.5 "C to lS.S"C)., , dP, &, , melting pOint of solids related with latent heat), , L, , dT = T(V, _ V,), , ,, ~, , I, , I•, •, ~, , ", , C<J,ndluclion Convection, In conduction, heat is transferred from .one point to another without the, actual motion of heated particles., In the process of convection, the heated particles of matter actually move ., In radiation, intervening medium is not affected and heat is transferred without, any material medium., , E ~------------------~879------------------~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , PhIlS/CS HandBook, , RADIATION, Spectral, emissIYe, absorptive and transmIttIve power of a gillen body suriace, : Due to incident radiations on the surface of a body following phenomena, , occur by which the radialion is divided into three parts,, (b) Absorption, (a) Reflection, (c) Transmission, amount of indden, radiation, , amount of reflected, radiation Q,, , !, " lImount of, _.... ··~·-·-·----------·----\--abSorlie(f-••••••••••, , '.pdialion, , From energy conservation, , Q, , • Reflective Coefficient : r •, , Q, , Reflection power (r) =, , Absorpllon power (a) =, , ~, , (, , i, , i••, , ~, , Q, , Q, , • Transmittive Coefficient: t =, r ~ 1 and a - 0 , t = 0, a · ' 1 and r - 0, t = 0, t ~ 1 and a = 0, r = 0, , • Absorptive Coefficient : a =, , =>, =>, =>, , Perfect reflector, Ideal absorber (ideal black body), Perfect transmitter (daithennanons), , [~ x 100] %, [~ x 100] %, , Transmission power (t) =, , [~' x 100] %, , Stefan's Boltzmann law :, Radiated energy emitted by a perfect black body per unit area/sec E= aT', For a general body E=ae,T', [where 0 ~ e, ~ IJ, , Prevost's theory of heat exchange : A body is simultaneously emilling radiations, , to its surrounding and absorbing radiations from the surroundings., If surrounding has temperature T o then E~, . e,arr'-To'), KJrchhoff's law: The ratio of emissive power to absorptive power is same, for all surfaces at the same temperature and is equal to the emissive pO\..VeT, . L-__________________________________, , i, , E, , ~, , 91

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , of a perfectly black body at that temperature., e, , E, , E, , e, , = - ;::) = E::) e oc a, a A 1 a, Therefore a good absorber is a good emitter., , - =-, , Perfectly Black Body : A body which absorbs all the radiations incident on, it is called a perfectly black body., AbsorptIve Power (a) : Absorptive power of a surface is defined as the ratio, of the radiant energy absorbed by it in a given time to the total radiant energy, incident on it in the same time., For ideal black body, absorptive power =1, EmIssIve power(e): For a given surface it is defined as the radiant energy, emitted per second pei unit area of the surface., , o, , Newton's law of cooling:, If temperature difference is small, , 0,, , dO, , Rate of cooling dt '" (0 - 00 ), , 9" .-•.. -------......... --..........., , => 0 = 00 +(0, .- Oo)e-", Iwhere k - constantl, when a body cools from 01 to 0, In time'\, In a surrounding of temperatur, 0, then, , 0-0., , - t - = k[OI+O', -2- 1, , 0], 0, , Iwhere k- constantl, , Wlen's DIsplacement Law : Product of the wavelength Amof most intense, radiation emitted by a black body and absolute temperature of the black body, is a constant A. T =b = 2.89 x 10-3 mK - Wein's constant, , e,, T,, , ~, , Area under e,. - A graph-fe,dA = e = aT', o, , !, ii•, , i, , L-______________________________________________________-J", , 92, , E

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IiIA""-':1, , Physics HandBook, , CAREER lNSlTTiJii, jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Solar constant, The Sun emits radiant energy continuously in, space of which an insignificant part reaches, the Earth. The solar radiant energy received, per unit area per unit time by a black surface, , held at right angles to the Sun's rays and placed, at the mean distance of the Earth (in the, absence of atmosphere) is called solar constant., , ~ 4rrR~"T', , 5 = 4rrr' =, , 4m', , =, , :.. ········r·····_:, , ~, , d, , ( Rs )' T', r, , where, , Rs, , Note :-, , r = average distance between sun and earth., 5 = 2 cal cm-'min=1.4 kWm-', T = temperature of sun ~ 5800 K, , =, , i, , radius of sun, , KEY POINTS:, Stainless steel cooking pans are preferred with extra copper bottom because, thermal conductivity of copper is more than steel., Two layers of cloth of same thickness provide warmer covering than a single, layer of cloth of double the thickness because air (which is better insulator, of heat) is trapped between them., Animals curl into a ball when they feel very cold to reduce the surface area, of the body., •, Water cannot be boiled inside a satellite by convection because in lAIeightlessness, conditions, natural movement of heated fluid is not possible., •, Metals have high thermal conductivity because metals have free electrons., KINETIC THEORY OF GASES, It related the macroscopic properties of gases to the microscopic properties, of gas molecules., , I-, , Basic postulates of KInetic theory of gases, Every gas consists of extremely small particles known as molecules. The, molecules of a given gas are all identical but are different than those another, gas., The molecules of a gas are identical, spherical, rigid and perfectly elastic, point masses., The size is negligible in comparision to inter molecular distance (10--9 m), , 1, .:, ::., :;, 2, , 1, , AsswnptIons regarding motion :, •, Molecules of a gas keep on moving randomly in all possible direction UJith all, possible velocities., • The speed of gas molecules lie between zero and infinity (very high speed)., • The number of molecules moving with most probable speed is maximum., , • L-______________________________________________________, , E, , 93, , ~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , HandBook, , Assumptions regarding collision:, • The gas molecules keep colliding among themselves as well as with the walls, of containing vessel. These collision are perfectly elastic . (ie., the total, energy before collision = total energy after the collisions.), Assumptions regarding foroe:, No attractive or repulsive force acts between gas molecuJes., , Gravitational attraction among the molecules is ineffective due to extremely, small masses and very high speed of molecules., AssumpIIons regarding pressure:, , Molecules constantly collide with the walls of container due to which their, the walls of, the container. Consequently pressure is exerted by gas molecules on the, , momentum changes. This change in momentum is transferred to, , walls of container., , Assumptions Jeganllug density:, The density of gas is constant at all points of the container., , KInetic interpretation of pressure :, [ m = mass of a molecule, N = no. of moleculesJ, , ~RT, , ~NAkT, , Idealgasequatlon PV - ~RT => P - V = - V - -, , (N), , V kT, , nkT, , Gaslaws, CI, CI, CI, , 1, Boyle's law :For a given mass at constant temperature.' V ox; p, Charles' law : For a given mass at constant pressure V a:: T, Gay-Lussac's law For a given mass at constant volume P oc T, Avogadro's law:lf P,V & T are same then no. of molecules N,sN,, , CI, , Graham's law : At constant P and T, Rate of diffusion oc, , CI, , Dalton's law : P - P, + P, + ....., Total pressure =Stim of partial pressures, , CI, , (, , l, , 1P1, , ~2a ~, , Real gas equation (Vander Waal's equationJ P + 7) ry - ~b} - ~RT, , J, , I, ,, , where a & b are vander waal's constant and depend on the nature oj ,!las. ~, L-______________________________________________________-J, , 94, , ~, E, "

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , KEY POINTS :, , •, , Kinetic energy per unit volume, , •, , At absolute zero, the motion of all molecules of the gas stops., , •, , At higher temperature and low pressure or at higher temperature and low, density, a real gas behaves as an ideal gas ., , •, , For any general process, , (a), , Internal energy change AU = nCvdT, , (b), , Heat supplied to a gas AQ = nCdT, where C for any polytropic process PV', , (c), , a, , constant is C = C + ~, v 1- x, , Work done for any process AW = PAV, It can be calculated as area under p·v curve, , (d), , Work done - AQ - AU, , =, , nR, , --dT, , I -x, , For any polytropic process PV', , =, , constant, , THERMODYNAMICS, , Zeroth law of thennodynamlcs : If two systems are each in thermal equilibrium, with a third, they are also in thermal equilibrium with each other., , First law of thermodynamics : Heat supplied (Q) to a system is equal to, , ~, ~, , I, J, ••, , I, , algebraic sum of change in internal energy (A U) of the system and mechanical, work (W) done by the system, Q - W + AU (Here W = JPdV ; AU, , For differential change, , =, , nCvAT], , 6Q - 6W + dU, \ ';;:(J, 1, depo ..... nc, , ...., , ndtpmdont, , E ~------------~--------------------~, 97

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , Sign Convention, Heat absorbed by the system ... positive, Heat rejected by the system -+ negative, Increase in internal energy (i.e. rise in temperature)-tpositive, , Decrease in internal energy (i.e. fall In temperature)-+ negative, Work done by the system -+positive, Work done on the system .... negatlve, , For cyclic process, , W, , For Isochorlc process, , v = constant => P a:; T & W - 0, Q = 6U = ~Cv6T, P = I'onstant => V a:; T, Q = ~C,AT, 6U a ~Cv6T, W = P(V, - V,) - ~R6T, , •, , Fodsobark: process, , •, , For adiabatic process, , =, , 0 => Q-W, , PV' = constant, or Tr p I-J "" constant, or, , lVT- 1, , _, , constant, , In this process Q = 0 and, W = -6U - ~Cv, •, , For Isothermal Pli oc::ess, , T, , rr, - T,), , =P,V,-P,V,, , y-l, , = constant, , or 6T - 0 => PV - constant, In this process 6U - ~C,6T = 0, , (y:"l, , l, , So, Q = W = ~RT tn V.J = ~RTtn, , (!'Ll, , lp,), ~, , . For any general polytropic process PV' = constant, , •, , Molar heat capacity, , R, C=C v +-I-x, , •, , Work done by gas, , W = nR(T, - T,), x-I, , •, , Slope of P-V diagram, , t, , =, , (P,V, -P,V,), x-I, , dP, (also known as indicator diagram at any point dV, , =, , P, -x V ), , I, , i•, •, , 1, , ~--------------~--------------~, ", 98, E

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Efficiency of a cycle, , ~=, , Work done by workingsubstance, Heat sup plied, , For carnot cycle, , Q,, Q,, , -, , T,, T,, , = -50, , w = Q, -Q, = 1 - Q,, Q,, , ~=1- 9z., Q,, , Q,, =, , Q,, , 1 - T,, T,, , For refrigerator, , Coefficient of performance, , Bulk modulus of gases :, , p=, , ~ = Q,~'Q,, , ~, T,- T,, , B=~, IN, V, , Isothermal bulk modulus of elasticity., Adiabatic bulk modulus of elasticity., , ~, , t, , I, , i, ~, , ;•, , ., , KEY POINTS, Work done is least for monoatomic gas (adiabatic process) in shown expansion., p, , ".---....- - - isobariC, , Isothermal, Diatomic, , J, , Adiabatic, , Monoatomic, L-~---------------------+V, , E ~------------------~9~9------------------~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Phvsics HandBook, , SIMPl£ HARMONIC MOTIONS, •, , Periodic Motion, , Any motion which repeats itself after regular interval of time (i.e. time period) is, called periodic motion or harmonic motion., Ex. (i) Motion of planets around the sun., (ii) Motion of the pendulum of wall clock., .•, , OsclUatory Motion, , The motion of body is said to be oscillatory or vibratory motion If It moves back, and forth (to and fro) about a fixed point after regular interval of time., The fixed point about which the body oscUlates is called mean position or, equilibrium position., , Ex.: (i) Vibration of the wire of 'Sitar'., (il) Oscillation of the mass suspended from spring., Note : Every oscillatory motion is periodic but every periodic motion is not, , oscillatory ., •, , Simple Harmonic Motion (S.H.M.), , Simple harmonic motion is the simplest form of vibratory or oscillatory motion., •, , Some Basic Terms In SAM, Mean Position, , The point at which the restoring force on the particle is zero and potential, energy is minimum, is knovro as its mean position., Restoring Force, , The force acting-on the particle which tends to bring the particle towards, its mean position, is known as restoring force ., Restoring force always acts in a direction opposite to that of displacement., Displacement is measured from, • Amplitude, , the me~n position., , ~, , i, , I, t-~, , The maximum (positive or negative) value of displacement of particle from, mean position is defined as amplitude., , • TIme period, , m, , L -__________________________________, , 102, , .b, , 1", E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , The minimum time after which the particle keeps on repeating its motion is, , known as time period., The smallest time taken to complete one oscillation or vibration is also defined, as time period., , 2n, It is given by T = (j), , 1, , = -n, , where co is angular frequency and n is frequency., , One oscillation or One vibration, When a particle goes on one side from mean position and returns back and, then it goes to other side and again returns back to mean position, then, , this process is known as one oscillation., one, , one, , t -_. oscillation - -C-' oscillation ••..•:, i:, i:, , _w_, , ~f---~r---~:----t----i;L----r--~~, ~, , ~, .0, , ", , Frequency (n or f), , The number of oscillations per second is defined as frequency., , '", It is given by n = -1 = -T 2n, Phase, , Phase of a vibrating particle at any Instant is the state of the vibrating, particle regarding its displacement and direction of vibration at that particular, , ~, , instant., ((j)t+~), , i, , In the equation x = A sin (rot + +),, , I, , The phase angle at time t = 0 is known as initial phase or epoch., , ~, ~, , ., 1, , is the phase of the particle., , The difference of total phase angles of two particles executing SHM with, respect to the mean position is known as phase difference., Two vibrating particles are said to be in same phase if the phase difference, between them is an even multiple of n, I.e. ,,~= 2nn where n = 0, 1,2,3, ...., Two vibrating particle are said to be in opposite phase, , if the phase difference, , 103, E~------------------------~~~------------------------~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , TE, , displacement, , Physics HandBook, , t=_, time, , Note:, , •, , (i), , Total energy of a particle in S.H.M. is same at all instant and at all, displacement., , (Ii), , Total energy depends upon mass, amplitude and frequency of vibration, of the particle executing S.H.M., , Average energy in SHM, , (I) The time average of P.E. and K.E. over one cycle is, (a) <K>, -, , 1 2, 4kA, , (b) <PE>, -, , 1 2, 4kA, , (c) < TE>, - lkA' + U0, , 2", , (II) The position average of P.E. and K.E. between x - - A to x=A, , i, , (a) <K>, , ;, , t, , J•, , f, •"\, ", , E, , 1, , • = -kA, 3, , ,, , Differential equation of SHM, , d'x, , [], , Unear SHM: cit' +ro'x-O, , [], , d' S, Angular SHM: cit' +ro'S = 0, , 105

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , PhysIcs HandBook, , If length of simple pendulum is comparable to the radius of the earth R, then, T, , ~ 2n, , If t », , •, , ., , 1, , gG+~), , . If t «, , R then T = 2nJf, 9, , {R, , R then T = 2nfii '" 84 minutes, , Second penduhun, Time period = 2 seconds, Length '" 1 meter (on earth's surface), , •, , Time period of Physical pendulum, 2, , ~, -, , +C, , T = 211J I = 211 _i__, mgt, g, , •, , where lern, , OK, , mk2, , TIme period of Conical pendulum, , .., ~, , i, , J, , i., , Time period of Torsional pendulum T-2n, , ;;;, , where k, , ,•, ~, , ;:;, , =, , I ~moment, , Jf, , torsional constant of the wire, , of Inertia of the body about the vertical axis, , E ~------------------1~O~7~----------------~

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Physics HandBook, •, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , SliM of a particle In a tunnel inside the earth., , In accelet"lltlng cage, , j., gel! - g-a, , 9.1I =g+a, , T=, •, , 2"Jg+aI, , T=, , 2"Jg-a£, , SHM of gas-piston system, , Here elastic force is developed due to bulk elasticity of the gas, , A, , •, , . SHM of Floating Body, , Restoring force -+ ThUTSt, mg, , E, , pAhg -+ Equilibrium, , Restoring force F= - {pAg)x, , 2"J%, , ~, , i, , I, , I•, , ", I•, ~----------------~1~O~8~----------------~ E, T=

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Phvslcs HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , SHM In U-tube, , T=2n~, , h, , KEY POINTS, •, , SHM is the projection of uniform circular motion along one of the diameters of, , the circle., •, , The periodic time of a hard spring is less as compared to that o f a soft spring, , because the spring constant is large for hard spring., , •, , For a system executing SHM, the mechanical energy remains constant., , •, , Maximum kinetic energy of a particle in SHM may be greater than mechanical, energy as potential energy of a system may be negative., , •, , The frequency of oscillation of potential energy and kinetic energy is twice as, that of displacement or velocity or acceleration of a particle executing S.H.M., , •, , Spring cut Into two parts :, , ~, , ~, , i, , j, , :;, , I,, , =(~), c, m+n', , I,, , =(~I, e, m+~, , ~ k, = (m + n) k; k = (m + n) k, m, , ', , n, , •, 1, " ~------------------1~O~9~~--------------~, E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Phvs1cs HondBoo!c, , FREE. DAMPED. FORCED OSCIllATIONS AND RESONANCE, , Free oscillation, •, , The oscillations of a particle with fundamental frequency under the influence, of restoring force are defined as free oscillations., , Damped oscillations, •, •, , The oscillations of a body whose amplitude goes on decreasing with time are, defined as damped oscillations., In these osci1lations the amplitude of oscillations decreases exponentially due, to damping forces like frictional force, viscous force etc., , •, , If initial amplitude is Xmthen amplitude after lime I will be x =, , xme-" where, , y - Damping coefficient, , FORCED OSCIllATIONS, •, , The oscillations in which a body oscillates under Ihe influence of an external, periodic force (driver) are known as forced oscUlations., , •, , The driven body does not oscUlate with its natural frequency rather it oscillates ~, with the frequency of the driver., , •, , The amplitude of oscillator decreases due to damping forces but on account, of the energy gained from the external source (driver) it remains constant., , RESONANCE, , •, , <;, , I,, , When the frequency of external force (driver) Is equal to the natural frequency, of the osci1lator (driven), then this state of the driver and the driven is known, ;;, as the state of resonance., , •, , ", , ~------------------------------------------~, E, 110

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , •, , In the state of resonance, there occurs maximum transfer of energy from the, driver to the driven. Hence the amplitude of motion becomes maximum., , •, , In the state of resonance the frequency of the driver (Ol) is known as the, resonant frequency., , Damped Oscillations :, Damping force F. = -bv, where v = velocity,, b - damping constant, Restoring force on block F = -kx, So net force on block, , F =-kx - bv, ~,, , ma = - kx-bv, , d'x, , m, +kx+bv=O, dt, , It is the differential equation of damped oscillation., , Solution of this equation is given by, x=, , t, , I, , A) -;';;1 sin(ro'! + ~), , where, , A(!) = A)-,':l, , =>, , A(t) = A, e-T', , so, , Iy = 2m, b I, , and, , ro' =, , J, , k _ b', , m, , 4m', , Energy in damped oscillation, , ,, J, •, , ;;, , . L-____________~~--------~----~, , E, , 111

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Phvsfcs HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , A wave is a disturbance that propagates In space, transports energy and momentum, from one point to another without the transport of matler., ClASSIFICATION OF WAVES, , Mechanical (Elastic) waves, Non-mechanical waves (EM waves), ~:I!:J:rm:J:':C Progressive waves, , 'I', , ~"'i'~', , ;0 . ~ ., , Statlonary (standing) waves, , Transverse waves, longitudinal waves, I-D rJJaves on strings), _~2-D, _~3 -D, , ~, , t, , J, , •, , A mechanical wave will be transverse or longitudinal depending on the nature, of medium and mode of excitation., , •, •, , In strings, mechanical waves are always transverse., , ., , ~, , ,•, f;;, , •, , (Surface waves or ripples on water), (Sound or light waves), , In gases and liquids, mechanical waves are always longitudinal because fluids, cannot sustain shear., Partially transverse waves are possible on a liquid surface because surface, tension provide some rigidity on a liquid surface. These waves are called, as ripples as they are combination of transverse & longitudinal., In solids mechanical waves (may be sound) can be either transverse or, longitudinal depending on the mode of excitation., , In longitudinal wave motion, oocUlatory mollon of the medium particles produce, regions of compression (hIgh pressure) and rarefaction Oow pressure) ., , E ~------------------1~1~3~----------------~

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Intensity : J, , Power, = 1. pro' A'v, area of cross-section 2, , Speed of transverse wave on string :, , v=, , If, , where, , ~=, , mass/length and T = tension in the string., , KEY POINTS, • A wave can be represented by function y = f(kx ± rot) because it satisfy the, , a'y = v21 (f)'at?v), , differential equation iJx?, , •, , where v .., , ro, , k', , A pulse whose wave function is given by y-4 / [(2x +5t)'+2J propagates in, -x direction as this wave function is of the form y-f (kx + rot) which represent, a wave travelling in -x direction., , •, , longitudinal waves can be produced in solids, liquids and gases because bulk, modulus of elasticity is present in all three., , WAVEFRONT, , •, , ", , Spherical wave front (source -+point source), , , .. :t. . ./, , ¢;z, / (""tl~'x*, ...., ...., , •, , Cylindrical wave front (source, , ---t linear, , source), , '", , .................., , :=rD, "::':::::', !=:, ,, :::J, , ~, , ! '"'''', , ~"" M •••••, , •, , (/ 1, I, , Plane wave front (source --> point / linear, , I, , f--·1---+, , !., , (I, , i~ i I, Ie I), , source at very large distance), , I, , ...-, , I, , INTENSITY OF WAVE, , ;;; •, 2, , Due to point source I oc, , r~, , y(r,t)- Asin(rot-k.f), , 1, , r, , y(r, t) = ~r sin (rot- k· f), , Due to cylindrical source I oc -, , vT, , r, , 1" L-______________________________________________________, . Due to plane source I - constant, y(r,t)=Asin(rot-k.f), E, , 115, , ~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Phvslcs HandBook, , •, , The frequency of the wave remain unchanged., , •, , V, Amplitude of refleeted wave-> A, = ( =-..:.L, A,, , •, , Amplitude of transmitted wave ->A, =(~)AI, , -v ), , VI +V2, , VI +V2, , •, •, •, , If V2 > VI i.e. medium-2 is rarer, A, > 0 => no phase change in refleeted wave, If V z < vJ i.e. medium-! is rarer, A, < 0 => There is a phase change of n in reflected wave, As Al is always positive whatever be v I & v2 the phase of transmitted wave, always remains unchanged., , •, , In case of reflection from a denser medium or rigid support or fixed end,, there is inversion of reflected wave i.e. phase difference of 7t between reflected, and Incident wave., , •, , the transmitted wave is never inverted ., Denser, , •, , ~, ~, , I, , Den.er, , y,-A,sln(rot-k,x), , i., t, , • L-______________________________________________________, , E, , 117, , ~

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, HandBook, , Beats, When two sound waves of nearly equal (but not exactly equal) frequencies travel, in same direction, at a given point due to their super poSition, intensity, alternatively increases and decreases periodically. This periodic waxing and, waning of sound at a given position is called beats., :. -_I, , Stationary waves or standing waves : When two waves of same frequency, and amplitude travel in opposite direction at same speed, their superstition, gives rise to a new type of wave, called stationary waves or standing waves., Formation of standing wave is possible only in bounded medium., •, , Let two waves are y, = Asin(Olt-kx) ; y, =ASIn(Olt+kx)by principle of, superposition, , y = y, +y, = 2Acoskxsinoot <- Equation of stationary wave, , ~~ , it represent a wave., , •, , As this equation satisfies the wave equation : ; = : ', , •, , Its amplitude is not constant but varies periodically with poSition., , •, , ). 3), 5),, Nodes -> amplitude is minimum: coskx = 0 ~ x = 4'4 '4 '......, , •, , ). 3)., Antlnode. -> amplitude Is maximum: coskx = 1 ~ x = 0'2.1.'2' ......, , •, •, , The nodes divide the medium into segments Ooops). All the particles in a, segment vibrate in same phase but in opposite phase with the particles in, the adjacent segment., As nodes are permanently at rest, so no energy can, , be, , transmitted across, , them, i.e . energy of one region (segment) is confjned in that region., Transverse stationary waves In stretched string, [Fixed at both ends), [fixed end ->Node & free end->Antinode), , l•, , <, , Fundamental or, first harmonic, , >, , <, .1:.., 2, , >, , second hannonic, first overtone, , f=~, 2t, , j, , I, ;;, , ;;, , ~, , L -__________________________________--J ", , 118, , E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Sound Waves, Velocity of sound in a medium of elasticity E and density p Is, , Solids, """"'........., , v~, !, , !, , vI, ~v=~, , •, , Newton's formula : Sound propagation is Isothermal B = P, , •, , Laplace correction : Sound propagation is adiabatic B = yP ~ v = ~, , KEY POINTS, , tRT, , •, , With rise in temperature, velocity of sound in a gas increases as v =, , •, , With rise in humidity velocity of sound increases due to presence of water in, , Mw, , air., , •, , Pressure has no effeet on velocity of sound in a gas as long as temperature, remains 'Constant., , Displacement and pressure wave, A sound wave can be described either in terms of the longitudinal displacement, suffered by the particles of the medium (called displacement wave) or in terms, of the excess pressure generated due to compression and rarefaction (called, pressure wave),, Displacement wave, , y-Asin(mt-kx), , Pressure wave, , p - pocos(mt-kx), , i, Po - ABk - pAvm, ~, ~, Note : As sound-sensors (e.g., ear or mike) detect pressure changes, description, of sound as pressure wave is preferred over displacement wave., , where, , KEYPOINTS, •, , The pressure wave is 90° out of phase w.r.t. displacement wave, i.e., , displacement will be maximum when pressure is minimum and vlce-versa., 2, , •, , Intensity In terms of pressure amplitude 1=1'2.., 2pv, , 120, , I;, •, , ", , E, , ~

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~, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , PhllSlcs HandBook, , Vibrations of organ pipes, , Stationary longitudinal waves closed end -+ displacement node, open end-+, displacement antlnode, Closed end organ pipe, , Rx, , KXX, 51., 4, , 5v, 4C, , ( =-~f=-, , • Only odd harmonics are present, • Maximum possible waveiength - 4l, • Frequency of m'" overtone = (2m + l)~, 4l, Open end organ pipe, , cx:x, 2v, , ( = A ~f=-, , 2t, , 31., 2, , 3v, 2l, , ( =-~f=-, , • AU hannonics are present, , • Maximum possible wavelength is 2(., • Frequency of m'" overtone = (m + l)~, , 2t, , ;, , End colTection :, , i, , not exactly, , t, , ,f, , ,, , 1•, , E, , Due to finite momentum of air molecules in organ pipes reflection takes place, , at open end bUt some what above it, so antinode is not formed, , exactly at free end but slightly above it., In closed organ pipe f, =, , v, , 4((+e), , In open organ pipe f, = (v, , 2 ( +2e, , where e - 0.6 R (R- radius of pipe), , ), , 121

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Physics HandBook, , jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Resonance Tube, , ---{'---, , ., , .., , -{------.;;;:::;:.~, :. :. :. :, ::::::::, ...... b, b, , -{, , ~, , A, , A, , f~ )./4, f, , I,, , !, , 1, , 5, , I, , I,, , 3)./4, , 11, 'W, , Wavelen'gth, , 1.-2(C,- t ,1, , End correction, , t,-3e,, e-, 2-, , Intensity of sound In decibels, Sound level, SL=10Iog,.(t), Where I, - threshold of human ear = 10-12 W/m', , Characteristics of sound, •, , Loudness --> Sensation received by the ear due to Intensity of sound., , •, , Pitch --> Sensation received by the ear .due to frequency of sound., , •, , Quality (or l1mbrel--> Sensation received by the ear due to waveform of sound., , Doppler'. effect In sound :, , ~, , i, !, , A stationary source emits wave fronts that propagate with constant velocity, with constant separation between them and a stationary observer encounters, them at regular constant Intervals at whlch they were emitted by the source., A moving observer will encounter more or lesser number of wavefronts, , depending on whether he is approachlng or receding the __________, source ., _J, , L-__________________________________________, , 122, , ~, , j, ", , ;;•, , j", E

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jOin Our telegram Channel Cleariitjee fOr mOre bOOks and studymaterials, , Physics HandBook, , A source in motion wiD emit different wave fronl at different places and therefore, alter wavelength i.e. separation between the wavefronts., The apparent change in frequency or pitch due to relative motion of source, and observer along the line of sight is called Doppler Effect., Sourcel.~-.', , ~, , v,, , n, , v,.•'--4•• observer, , Sound Wave, , , speed of sound wave W.f.t. obsetver, observed wavelength, , Observed frequency n = ., , ,_ v+vo -_(v+vo, ), --n, , n-, , If, , VOt, , (v~v, ), , v-v,, , v+v) n, v, «<v then n' ,. ( 1 + ~, , • Mach Number= speed of source, speed of sound, , Doppler's effect In light :, , Case I :, , Observer, , •o, , Frequency, , v', , Wavelength, , ~, , i, , CaseD, , -, , Light Source, , v, , S, , =W:~]V ~(l+~)V, , A' = (J~:~)A ~ (l-~)A, , Observer, , •o, , -, , Violet Shift, , Light Source, v, , S, , Frequency, , I, , Wavelength, , A' = (J~ :~)A * ( 1 +~)A, , . ~----------------~----------------~, E, 123