genel fizik 1 - full ders notları (sunum)

8/10/2019 Genel Fizik 1 - Full Ders Notlar (Sunum)

1/568

5 AXL vf COF5.5 Vzugcul ltcf vf zeoeg steg`ertcer 5.: Oe``f vf od`fck

5.9 [d ugcul vf etdokl ltcf.5.6 Jkrkocfrkg fvrkcofsk5.1 [elce l `f frcfr vf jylclcfr

.

: PFL JD[VPPE BEZFLFP:.5 Ldguo, b z vf sret:.: Egc l b z vf sret

:.9 vof. erf f yemreo er :.6 Pfl jdyutte sejkt kvofck berflft:.1 Yfrjft ` fg ikskocfr

.5


2/568

9 QFLPZCFZ9.5 Lddr`kget skstfocfrk9.: Lertfzyfg lddr`kgetcer

9.9 Qfltrcfr .9.6 Qfltrcfrkg tdpcegoes 9.1 Qfltrcfrkg ler coes

.

0 L JD[VPPE BEZFLFP. , ,

0.: lk jdyutte sejkt kvofck berflft

0.9 F kl berflft/et

.0.6 Pf ftsfc vf ofrlfzikc kvof0.1 Mrfck b z vf mrfck kvof

:


3/568

6 Gfwtdg ug berflft yesecer .

6.: Gfwtdg ug jkrkgik yeses vf fycfoskzckl frfvfcfrk

6.9 Ltcf6.0 Gfwtdg ug klkgik eses 6.6 [frflkok luvvftk vf e rc l6.1 Gfwtdg ug gi yeses 6.= Gfwtdg yesecer g g jez uymuceoecer

6.2 Yrtgof luvvftcfrk

1 @ekrfsfc Berflft vf Gfwtdg [esecer g g @k fr V uceoecer 1.5 @zmg èkrfsfc berflftf Gfwtdg ug klkgik yeses g g uymucegoes 1.: @zmg dcoeyeg èkrfsfc berflft

.1.0 @krfg luvvftcfrkgkg dcùu drteocerè berflft1.6 êrei l `kgeok kg`f sey sec od`fccfofcfr

9


4/568

AXO5>6 Akzkl K fw dg ug erf f yese er

;.5 kzmksfc Odofgtuo vf Ldruguou;.: tof vf Odofgtuo;.9 Pfl Jdyutte erp oecer

;.0 lk-jdyutte erp

oecer .;.1 êrei lcerèg Dcueg Jkr Ykstfokg Berflftk;.= Zdlft tofsk

5> Yejkt Jkr Flsfg zfrg`f Let Ikskocfrkg @gof Berflftk5>.5 E sec ldguo, b z vf kvof5>.: @gof Lkgfoetk k8 Yejkt e sec kvof kcf `gof berflftk5>.9 E sec vf kzmksfc gkifcklcfr

.5>.6 Fycfoskzckl odogftkgkg bfsepcegoes 5>.1 Pdrl5>.= Pdrl vf e sec kvof eres gè je gt cer 5>.2 @gof berflftkg`f k , m vf fgfrhk 0


5/568

55 Gfwtdg ug berflft yesecer .

6.: Gfwtdg ug jkrkgik yeses vf fycfoskzckl frfvfcfrk

6.9 Ltcf6.0 Gfwtdg ug klkgik eses 6.6 [frflkok luvvftk vf e rc l6.1 Gfwtdg ug gi yeses 6.= Gfwtdg yesecer g g jez uymuceoecer

6.2 Yrtgof luvvftcfrk

5: @ekrfsfc Berflft vf Gfwtdg [esecer g g @k fr V uceoecer 1.5 @zmg èkrfsfc berflftf Gfwtdg ug klkgik yeses g g uymucegoes 1.: @zmg dcoeyeg èkrfsfc berflft

.1.0 @krfg luvvftcfrkgkg dcùu drteocerè berflft1.6 êrei l `kgeok kg`f sey sec od`fccfofcfr

6


6/568

5 AXL vf COF

5.5 Vzugcul, ltcf vf zeoeg steg`ertcer 5.: Oe``f vf od`fck

. d ug u vf e do f5.0 Jdyut egeckzk

.5.1 [elce l `f frcfr vf jylclcfr

.

Yeet 1


7/568

Akzkl, fvrfgk jeskt prfgskpcfrk kcf èbe kyk egceo o z . ,jkydcdhk, lkoye vf hfdcdhk mkjk fktck jkcko èccer g g ètfofckgk dcu turur. Akzkl kcf fvrfokz`f fck fgakzklsfc dceycer jeskt levreocer, tfdrkcfr vfoetfoetklsfc f ktcklcfrcf vfrkckr.

[egèlk rfsko`f :>>9 `f beveè petceyeg uzey oflk kgkg lecl eg

mrcofltf`kr.

=


8/568

5.Lceskl oflegkl, etdoe mrf dl jyl jdyutcerè vf l b z ge mrf dl yeve

berflft f`fg ikskocfrkg berflftk kcf kcmkcfgkr.:. Mrfckckl,bfrbegmk jkr yfrf mrf ikskocfrkg berflftkgk kgifcfr.

. , , ,èvreg cer g kgifcfr.

0. Fcfltrdoe gftkzoe fcfltrkl oe gftkzoe vf fcfltrdoe gftkl ecegcer kgifcfr.

6. Dptkl, g oeczfof kcf ftlkcf ofskgk kgifcfr.

1. Luegtuo oflegk k,ect oklrdsldjkl `zfy`fg oelrdsldpkl `zfyf leèroeczfofcfrkg èvreg cer g kgifcfr.

2


9/568

(5) gsegs z uy`u berflftcfrk, kgsegc eye kgk,

,

9 Jkckosfc ere t roe vf se c l eceg g`e leroe l rgtcfof tflgklcfrk,

(0) Mfgftkl obfg`ksckkg`f fc`f f`kcfg jez sdgucer,

;


10/568

. , Fldgdokl, mgcl, tkierk vs beyet o zè levme ftof`fg, egce oezc lcer

loeèg ec -vfrk yepejkcofokz kkg jez stegèrtcer lejuc ftoflzdrugèy z.

5;1> e ucuscereres jkr ldoktf terea gèg gkifcklcfr k kg stegèrtcer

bez rcego t r.

kfrkr. Jugcer uzugcul, ltcf vf zeoeg mkjk oftrf , lkcdmreo vf segkyf `kr.

fr s eg er er sf s ie g f v g , f f r e o g eopfr ,

k``ftk kkg (ieg`fce ) vf oe``f oklter kkg (odcf ).

5>


11/568

Vzugcul

OY 55:> `f gmkckz lrec uzugcul kkg jurgugug uiugèg ldcugug e l ùruoè klfgperoel ucer ge leèr dceg ofseafyk jkrko uzugcul dcerel yer` sfok tkr.

Aregse lrec 50gi Cduks ksf lfg`k eyel jylc g jkrko uzugcul dcerel sfok tkr.

.Flvetdrèg luzfy lutjuge kzkcfg vf êrkstfg kzmkgkg uzugcu ugug dg okydgè jkrkdcerel ec go t r. 5;1> c y ccerè lrkptdg-21 etdougug ècmejdyugug 5 16> =19.=9 let

.

@gyeye fg yel g luer g uzelc 5.0 x 5>:1 oftrfgyeye fg ye g me e s uze x of rf

Jkr l y c ;.01 x 5> 56 oftrf

@gyeg

g mgf ftrea

gèlk yrgmfskgkg yer

ep

5.6> x 5>55

oftrf .@gyeg g yer ep 1.9= x 5>1 oftrfVyùcer g yfr`fg ylsflck k : x 5>6

-5>

Etdo flkr`f kgkg ep 5>-50

oftrf^rdtdgug ep 5>-56 oftrf 55


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Ltcf

YK-jkrko skstfokg`f ltcfgkg jkrkok dcerel lkcdmreo (lm)

lucceg coelte` r. ^cetkgyuokrk`yuo ece o gèg skckg`krflckg`f

yep co vf Kgtfrgetkdgec Jurfeu da ]fkmbts eg` Ofesurfs Yvrfs,Aregse è selcegoelte` r. Ju ltcf jkrkok 522= `f lejuc f`kcok vf

zeoegce ltcfsk `f kofyfg lererc jkr ece oèg yep co t r. Ju

ltcfgkg `kfr jkr f k Getkdgec Kgstktutf da Ytegèr`s eg` Pfibgdcdmy(GKYP) Mektbfrsjurm, Oeryceg` è selcegoelte` r.

5:


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Ltcf

(e) Vcusec Lkcdmreo Ytegèr Yvrfs, Aregse Getkdgec Kgstktutf da Ytegèr`s eg`.

Getkdgec Kgstktutf da Ytegèr`s eg` Pfibgdcdmy cejdretuvercer

gè Jduc`fr,Idcdre`d è jucugoelte` r. Yeet :> okcydg y cè 5 segkyf kcfrk mk`fjkckr vfye mfrklecejkckr.

59


14/568

Fvrfgkg ye 6 x 5>5= gyeg g ye . x Ldcfh rfgikskgkg ye 1.9 x 5>2

= . 5 mg 2.1 x 5>0

Jkr frs seetk 9.> x 5> 9

lk lecp et eres gèlk zeoeg 2 x 5>-5

Yfs ecmecer eres gèlk zeoeg 5> -9

e yd e me er eres g e zeoeg -

Jkr let èlk etdo tktrf kocfrkgkg pfrkydù 5>-59

-56 Glcffr erp oecer eres srf 5> -::

K g jkr prdtdgu mfof srfsk 5> -:0

50


15/568

,5> -:0 yditd y5> -:5 zfptd z5> -52 ettd e5> -56 afotd a

-5: 5> -; gegd g5> -1 okird

-9

5> -: ifgtk i5> 5 `fik `

d5> 1 ofme O

5>;

mkme M5> 5: tfre P5> 56 pfte ^5> 52 fxe F5> :5 zftte X5> :0 ydtte [ 56


16/568

. Akzklkcfr jez levreocerce `d ruèg kcklk lureoezcerse

,

tfdrk mfcktkrkrcfr. rgfkg etdoèlk fcfltrdgcer vf

prdtdgcer kkg yept lcer mkjk. Mzcfgfjkcfg zfccklcfr`fgju tfdrkcfrkgk èbe se ceo tfofccfrf dturtoe e ec rcer.

flkc`flk mkjk ljkl ect g perecegoeye je ceg rse ju

pere eoe gfrfyf e er m f r

51


17/568

.Fcfltrdgkl ikbez seteg jkr oe ezeè ecuokgyuo vf

`fokr`fg rftkcok klk leofre jucugoelte`

r. Bfr klk(e) Ecuokgyuo leofre

(i) Bfr klk leofre è eyg jdyutcerè` r.

5=


18/568

[ugegc cerperecegeoeyeg fg l l oe``fyfetdods`fok cfr`k.52;= `f H.H.Pbdosdg ug`fgfycfrcfetdougfcfltrdgcer g gdc`uumstfrkc`k. @ebe

etdougflkr`f kperecegerel ectperei lcer(luerlcer)

.

52


19/568

. d ug u r o ei o f f o er d ere vfr r8

o -------Q

o-ltcfyk (oess),

-

Etdocer g aerlc d ugculcere sebk dcoes dgcer g akzklsfczfccklcfrkgk ey r` ftofl kkg lucceg cejkckr jkr zfcckltkr.rgf kg ecuokgyuo :.=> mr/io 9, lur ug 55.9 m/io 9

.5;


20/568

Lur ugug etdokl ltcfsk :>= jkrko vf ecuokgyuoug ksf :=.>

.

:>= jkrko /:=.> jkrko ? =.1= `f frk ju etdocer g

ydugculcer dreg dceg. . .

`f frkgf f kt `fkc`kr. Ju aerlc

c

l gfrf`fg mfckr4 Pejk lklrkstec yep `elk (let bec`flk) etdocer eres jd culcer`eg.

:>


21/568

Ecuokgyuoèg dcu ou let jkr lpg (yd ugcuu :.=> m/io ) beiok >.:>> io

dcerel vfrkcoktkr. :=.> mreo ecuokgyuo (etdokl ltcf jkrkok) 1.>: x 5> :9 leèr etdo

kfrofltf`kr. Lptf gf leèr etdo ver` r4 zo [d ugcul ltcfgkg beikof dreg flckg`f vfrkckydrse, ju lp kkg`flk etdocer g

tdpceo ltcfsk jucugur. Ltcfo ? Q ? (:.=> m/io 9)(>.:>> io 9) ? >.60> m vfye o ? lG flckg`f yez cejkckr.

@fglcfo`flk o rgf kg ltcfsk,G rgfltflk etdocer

g sey

s

vf l jkckgofyfg dregt

sejktk`kr.o ? lG o lG o :=.> m ? G :=.> m ju `fglcfocfr dregceg rse --------- ? -----------

jkckgofyfg l dregt sejktk se`fcf kr o:=.> m

lG :=.> m

>.60> G rgfl --------- ? -------------- jureèg G rgfl ? 5.::x5> :: etdo dcerel jucugur.:=.> 1.>:x5> :9

:5


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.@dru vfye yegc 8 Jdyut egeckzk kcf sejktcfrkg `ffrcfrkgkgerktoftkl kcfocfr sdguiug`e fc`f f`kcfg sey sec sdgucer

.

::


23/568

kzfcmf 5.5 dl lucceg ceg akzklsfc gkifcklcfr vf

gmkckzjkrkok

Vzugcul C C afft,at oftrf, kg

,

Xeoeg P P segkyf,s segkyf,s

kzmksfc b z v C/P at/s o/s

E sec b z w re`yeg/P re`yeg/s re`yeg/s

vof-kzmksfc e C/P: at/s : o/s :

vof-e sec re` eg/P : re` eg/s : re` eg/s : [d ugcul OC 9 scum/atlm/o 9 lm/o 9

Luvvft A O(C/P : ) pdug`, cj gfwtdg, G

Lkgfoetkl el legc l C : /P at : /s o : /sOdofgt (tdrl) O O(C : /P) at-cj G-o

: : l -o : -

Jes g ^ O/(C : P) Kj/at : G/o : :9


24/568

. Eceg Beiko Yret vof : 9 : YK o: o 9 o/s o/s :

EJ@ at:

at9

at/s at/s:

-P-zeoeg (Pkof)

Bfsepceoe k cfocfrkg`f sdguiug `d rucuugu dgeyceoel yegk se ceoeyepoel kkg jezfg jdyut egeckzk yep c r. Fktckkg jkr terea g`elk jdyutug

`kfr tereatelkgf f kt dcoes mfrflkr. rgfl dcerel x ? >.6et : sejkt kvofck

berflfttf ldguo `f frkgkg jd ut egeckzk u flkc`f e cejkckr8C

C ? ------ P: ? C:

:0


25/568

Jezfg jkr clfgkg lucceg` jkrko skstfokg`fg `k fr clfgkg

lucceg` jkrko skstfokgf mfk yepoel mfrflfjkckr8 o ? o ? . o 5 at ? >.9>0 2 o ? 9>.02 io o ? . g. ? . 5 kg. ? >.>:6 0 o ? :.60 io (teo dcerel)

rgfl 8 56.> kg. ? (56.> kg.) ( :.60 io / 5 kg.) ? 92.5 io

:6


26/568

.lk fbkr eres g`elk uzelc l 5> okc ksf

(e) fbkrcfr eres

uzelc

l 5>> lo `fg l

se`

r,(j) fbkrcfr eres uzelc l 5>> lo `fg jyltr,(i) Bfr klk jkrko`f eyg ` r.

:1


27/568

Okltercer vfye sey cer bell g`e ldgu urlfg vf jugcerce

.teo dcerel seyeoeyeie o z okltercer kkg yelce l

`f frcfr`fg jebsf`kckr. rgf kg jkr ozkl ldgsfrkg`flkvf e oktkg `flk kgsegcer g se s jkr droeg`elk

eecer g sey s , mg`f ec` o z gfafs sey s vfrkcfjkckr.

u tr ye e f fr fr ~ s omfs f mstfr r z.

>.>:9 ~ 5> -: vf e >.>>>5: ~5> -0 kjk.

:=


28/568

.Jkr segècyfgkg ldguou 5 oftrfckl jkr c ecftk kcfccofltf`kr. Yegècyfgkg drtes gèg ùvere dceg uzelc l

.yepoec ` r4.

:2


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.

.zug u u gf d ere frs g z(Ifvep kkg aerfyk t lcey g z)

bttp8//`jbs.wvus`.l5:.ie.us/wfj`dis/YkmAkms/YkmAkms.btoc:;


30/568

.

.(Ifvep kkg aerfyk t lcey g z)

.

bttp8//`jbs.wvus`.l5:.ie.us/wfj`dis/YkmAkms/YkmAkms.btoc9>


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.

Y v sfvkyfskgk oC dcerelcfrlfg gfrfyf jeleie z4

e) :=.6 oC , j) 6.>> oC

bttp8//`jbs.wvus`.l5:.ie.us/wfj`dis/YkmAkms/YkmAkms.btoc9:


33/568


34/568

rgfl 5.1 Dluoe betecer g g uvercet coes

Vymug bessesc l yelce o ge kbtkye ver r (kyk etoel mfrflkr)

Ju `f fr sujhfltka dcerel 51.== >.>: sfkcfjkckr.

90


35/568

.

51 5= 51 5=

Dluoe betes c cfg gfsgf f je c ` r.

[uler `elk se elk flkc`f iftvfc besses dcse jkcf bete

eze oez.

96


36/568

Bfrbegmk jkr co yep c rlfg jucugeg `f fr zfrkg`f f ktck betecer

flcfgfrfl sdgu yez c r. Mfgfc dcerel ju tr `f frcfrk egceoc sey cercekae`f f`frlfg sdc tereatelk s a rcer `klletf ecoey z. Y a r`eg aerlc

releocer g egceoc dc`uugu vf fg se elk s a rcer g eyg flkc`f jkr

egceo kfrof`k kgk lejuc f`frkz.

Ffr klk sey erp c ydrse fc`f f`kcfg sdgu fg ` l egceoc sey ye

se p f fr g re eo egfs e f e gere yez r. yg ure of

kkg`f mffrck`kr.

91


37/568

.

Ee `elk releocer g egceoc begf sey cer gf le`er` r4

.

(j) 9.=22 x 5> ; ? 0

(i) :.01 x 5> -1 ? 9

(`) >.>>69 ? :

9=


38/568

rgfl 5.; E e `elk sey cer g egceoc begfsey cer g jfckrcfykgkz.

Egceoc Egceoc begf sey s begf sey s

:.>9 ;1=>>>9 15.> 6.5>: 9

:.>> >.>>>>169 :

. .

5.>>9> >.>>61=>6 0

>.>>2=: =2>9 9

=2>>> =2>.>>>6 1

92


39/568

rgfl 5.5> E e `elk sey cer g egceoc begfsey cer g jfckrcfykgkz.

>.>::0 6>> >.555> >.>>0=5

9.>>> >.;> 60>>> >.>>2;

9>>> 0.69> =>2 :9>652

>.>>09>> >.>:9 =2>.>> 5>>>.5

>.>>2>> >.>>;1= =2>.> >.>>1>>=

;.1=>> =.>:>> >.>>>>6 >.>>>>>2

=>.510 >.>;> >.>>=1>>; >.;>2

>.0;>> 1=>>>0 5>.>6 6>>>>>>

9;


40/568

Peosey cer g vf fvrfgsfc sejktcfrkg egceoc begf sey cer jfckrskz`kr.

Ffr klk sey erp c ydrse fc`f f`kcfg sdgu fg ` l egceoc sey ye sebkp

.

mffrck`kr.

Ffr klk `f fr tdpceg ydrse fc`f f`kcfg sdgu fg ` l egceoc `f frkg

releo begfsk kcf vfrkckr. Eyg lurec leroe kkg`f mffrck`kr.

0>


41/568

.

Lfgercer e ? (6.6 >.5) io vf j ? (1.0 >.5) io dceg jkr `kl`rtmfgkg

fvrfsk gf dcoec ` r4fvrf ? :(e + j)

? . .

? :(55.; io) `kr.

Egceoc sey dcerel ju `f fr

fvrf ? :(5:) ? :0 io dcerel yez c r.

05


42/568

.

e e erp o g sdguiu gf d oe r 51.9061 (1 egceoc releo begfck sey )

. ---------------61.>160>2

vfye

61.5 Ydgu fg ez egceoc begfyf sebkp 9 egceoc begfyf

sebkp sey ye mrf yez c r.

0:


43/568

. .

Lfger uzugculcer e ? (6.6 >.5) io vf j ? (1.0 >.5) io dceg jkr `rtmfgkg

eceg gf dcoec ` r4@kl`rtmfg Eceg ? e j ? 6.6 io x 1.0 io? 96.: io : `kr.

Ydgu, lfger `f frcfrkg`flk co bete `f frcfrk lucceg cerel egceoc sey cer

f g f e e e m yez e r8

Eceg ? 96 io : dcerel yez c r.

Ydgu gf`fg ju flkc`f yez co t r (Ifvep kkg aerfyk t lcey g z)4

Lfger uzugculcer ccrlfg : (klk) egceoc begfyf le`er

ccfjkcokcfr`kr. Ydgu : (klk) begfck dcerel yez cejkckr. 09


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. .

@uverèg ùvere bec yfrcf tkrkcfifl dceg jkr dèg g uzugcu u

bfsepcey g z (Ifvep kkg aerfyk t lcey g z)4

Fg ` l egceoc begfyf sebkp sey 9.01 ` r. Juge mrf sdgu

yegk eceg 9 begfck dcoec ` r8 00.> 00


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.Jkr `rtmfg cfvbeg g lfger uzugculcer (:5.9 >.:) io vf (;.2 >.5) io dcerel

vfrkcofltf`kr. @rtmfg cfvbeg g eceg g vf fvrfskgk egceoc sey cerce jfckrtkgkz.

Eceg ? (:5.9 >.:) io x (;.2 >.5) io? :5.9 x ;.2 :5.9 x >.5 >.: x ;.2 >.5 x >.:

? . . . .

? :>2.=0 0.55 ? erpoe`e fg ` l egceoc begfyf sebkp sey (yegk ;.2)

? :>; 0 flckg`f teo sey dcerel yez coec ` r.

. . . . . . ?egceoc begfyf sebkp sey `klletf ec g r (yegk ;.2 klk begfsk egceoc dceg sey )

?

06


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.

\(;.=50 x 5> 6) (:.502: x 5> -; )_ \(0.5:5:) (9.==;: x 5> -6)_

.`f frcfrf `kllet f`kgkz.

Bfsepceoe sdguiug`e 5.99;2 x 5>5

fc`f f`kckr vf ju `f fr. .

0=


48/568

.

. x - . x . x - .sdguiugu yez g z.

Bfsepceoe sdguiug`e 0.1:6 x 5> -:: fc`f f`kckr. Ju `f fr 9

egceoc begfsk dceg 0.1: x 5> -:: f yuvercet c r.

02


49/568

.

615.> 90 ;>2 :9.> :5.222 =6.: 5:>.>>

sdguiugu yez g z.

. .

egceoc sey dcerel ::2> yuvercet c r vfye jkckosfc

mstfrkok :.:2x5> 9 dcerel yez cejkckr.

0;


50/568

. .uzugcul (io) mfgk ckl (io) eceg(io : )

e. :=.25 :>.0; 61;.2:1; ? 61;.2 (0 begfck)

?. . . . .

6>

rgfl 5 :5 E e `e vfrkcfg `f frcfrf mrf


51/568

rgfl 5.:5 E e e vfrkcfg f frcfrf mrf

beikocfrk io 9 ikgskg`fg yfgk`fg yez g z.Lec gc l (io) beiko (io 9)

e. >.=5> 0>0.6==>; ? 0>6 j. >.1;> 9;:.9=525 ? 9;:

Ljg vfye iksokg `k fr lfger `f frcfrk jure`e vfrkcofok . Eoe beiokg egceoc dcerel ez coes k kg lec gc ltelk begfsey cer kcf jfckrcfgoktkr.

65


52/568


53/568

, Betecer gf`fg gfock`kr4 ete t p fr resmf f vf s stfoet esses yft vf d ru u Betecer yuverceoel Ydgucer vf betecer Betecer g adroccftkrkcofsk Zesmfcf vf skstfoetkl betecer g jkrcftkrkcofsk Betecer g kstetklsfc `des

H ] Idiljurg, @fpertofgt da ^byskis eg` Estrdgdoy, Vgkvfrskty da Ybfaakfc`,

^b skis & Estrdgdo Cejdretdrkfs.

69


54/568

s ielc lcer ccydr8

92.: I vf 92.0 I

Y ielc l ert gfock ok`kr4 Ju `f frcfr betec o ` r4

. . . .

92.: >.6 I eg` 92.0 >.6 I ksf gfoskz`kr

60

Zesmfcf betecer


55/568

Zesmfcf betecer

cocfr`flk betecer g `f klfg dcoes g`eg leygelcegejkckr,

Beteg g ert vfye gfmetka tereate dcoes g`eg leygelcegejkckr,

Bfr zeoeg bete yep c r,

,

Bete, eyg gkifckl tflrer tflrer ccrsf ezect cejkckr vfye jkr

gkifckk `kfr jkr gkifckkg adglskydgu dcerel ccfjkckr vf

jucugejkckr,

Jezfg dlurlfg bete yep

c

r. 66


56/568

Ec geg cocfrkg eyg dcoes gèg,

,

ccfg f frcfrkg drteceoes g g `d ru `f fr`fg uzel

dcoes gèg, Jkr `fgfy`f skstfoetkl betecer g verc g g tfspktkgkg zdr

dcoes gèg leygelcegejkckr.

61


57/568

Ye`fif resmfcf bete

@dru `f fr

Zesmfcf + skstfoetkl

Jkr sdgu skstfoetkl betecer`eg er g` r co ksf `d ru`ur

Jkr sdgute resmfcf betecer ll ksf sdgu bessest r `fgkcfjkckr.

6=


58/568

Betey jkr jeseoelce jfckrtofl (jkr vfye klk jeseoel

lucceg cse jkcf . Ydguiu bete jeseoe kcf eyg ofrtfjf`f jfckrtofl.

@ffr vf betes

stfc sey

cerce lucceg

c

ydrse ju sey

cer

g.

62

rgfl 5 :: Lucceg cejkckr sdgu cer vf betecer


59/568

rgfl 5.:: Lucceg cejkckr sdgu cer vf betecer

@f fr 00 betes 6 006

@ffr 5:2, betes 9: 59>9>

@ffr 0.2x5> -9, betes =x5>-0 (0.2>.=)x5>-9

f fr , e es sf

@ffr 5>;:, betes 50 ksf 5>;: 50

@ffr 5:.906, betes >.96 ksf 5:.9 >.0

Ydguiu bete `f frkg`flk jeseoel sey s gèg èbe aezce sey èjeseoelce mstfrofykgkz 91.1=2;969=: >.6

6;


60/568

@kfr tereateg akzklsfc jkr `fgfy z`f ld uccerè zfgck vf `klletck jkr jkko`f tflrercegse jkcf

. , , ,

yer s g g lfstkrkcofskg`f dcù u mkjk `druèg `fgfyik`fg mfcfjkckr vfye `fgfy ld uccer gè

gif`fg jflcfgof fg rest fcf ec ecegoecer rgf kg fbkr frkckok kcf ec eg jkr cecftkgkg ju mfrkcko`flk dygeoecer gf`fgkycf aerlc `f frcfr cofsk, re`ydeltka perecegoeè

dcey g `d es gè jucugeg kstetkstklsfc ècmecegoecer vj) gf`fgkycf `f dcu ejkckr

MFCMXFC [EGKCMKCEZdcerel e`ceg` r ceg ju tr`fg yeg cm cer g gdroec ( Meuss)

è c o adglskydguge (jlz. flkc) uymug jkr è c o mstfr`k k vf ccfg gkifckkg teo `d ru

.

è c oe uyoeyeg jkr c tel o kkg erktoftkl drteceoe ecoeg g vf è c o bfsej yepoeg g

egceos z dcùu e lt r.

1>


61/568

15

Okckoftrf Jcofck Iftvfccf Vzugcul cocfrk


62/568

gg cocfr vf yeg cm bfsej kkg c ldgusu dcerel `zmg jkr oftecskckg`kr vfrkck dr. Ykckg`krkg C jd ugu oo jcofck jkr iftvfc e è frkt oftrf kcf

f ktck yfrcfrkg`fg cg. Ju iftvfc gf ùyerc lte jkr c vfrfjkckr4 oo ok4 ye

Jcofcfr oo'ck dcù uge mrf mzgz gfyk lfstkrfjkckydr4 Ju cy z`f

.

dcsug. Fg kyksk eyg `fgfy mrujugè ec egcer g jkrjkrcfrkgf sycfof`fg eyr eyr jkrle c ec p jkr yfrf yezoecer vf èbe sdgre sdgucer

jkrcftkrofsk`kr. Ck kcf mstfrfif kgkz ju ccfrkgkzk jkr kzfcmf`f tdpcey g

(jlz. kzfcmf 5.:). Ez dl `f kkl sey cer jucùguz ksf ju gfrf`fg

leygelceg ydr4 Ykz ok yegc ctgz, iksko ok `zmg `f kc, ydlse iftvfckgkz

ok lt4 [e è jugcer g bfpsk jkr`fg ok kkgkz jdzuydr41:


63/568

ko`k skckg`krkgC jdyu k kg fc`f fttkkgkz vfrkcfrk luccegerel flkc 5 `flkgf

jfgzfr jkr f rk kzkg. ccfrkgkzkg è c o ldgusugè gf sycfyfjkckrskgkz4

è c oe uyuydrse f rkgkg tfpf gdltes C gkg erktoftkl drteceoe `f frkgf

. drt

jucug. Eyr eyr cocfrcf C eres gèlk aerle k sey c cog e c o `fgkr.

19


64/568

e k ? C k C drt

ko`k e k cfrkg sect l (outcel) `f frcfrkgkg drteceoes g ec g.

G

k x x

G ?

10


65/568

Akzklsfc jkr gkifcklG lfz c csg. J cfcklcf x k ?5 : ...... G

tegf co sdguiu jucugeielt r. Ju ccfrkg drteceoes

ee `elk mkjk`kr8 G

k x x ??

16


66/568

,

uymugùr. Je c yeg cm , sect l yeg cm g g ccfg gkifckf dreg dcerel

. . ,C ? >.>5/ 9.6= ? >.>>:2 ? >.>>9

dcup cocfr`f >.>>9x 5>> ? %>.9 yeg cm ver `fofltkr vf

C ? (9.6= %>.9) io

kcf mstfrkckr. Je c yeg cm mfgfc dcerel cocfrkg gf leèr se c lc dcùugug

. .dcerel,

? - ? f ? . , ? . g if fr g fg

gkifckk èbe se c lc , J ksf èbe ùyerc lc ` r.11


67/568

x -----------

x kcl -x sdg

1=


68/568

Jureye `fl uzugcul mkjk `d ruèg ccfjkcfg gkifcklcfr zfrkg`flk

yeg cm cer g bfsepcegoes g kr`fcf`kl. Eoe akzkltf kcmkcfg`kkokz gkifcklcfrkg

jyl d ugcuu `d ruèg ccfofz< `d ruèg ccfrf èyegegoetfoetklsfc yez ocerce bfsepceg r. rgf kg skckg`krkg beiok zfrkg`flk

eg c e bfo @ e bfo `f C uzugcu u zfrkg`flk eg c cer juce r. D

bec`f beiko zfrkg`flk yeg cm y ec` o z cocfrf èyegerel. .

12

rgfl 5.:9 Ykckg`krkg uzugcuu vf ep cocfrk


69/568

cogd

C k (io) e k ? C k C drt @k (io) e k ? @k @ drt

5 9.6= >.>>6 5.:5 >.>5>: 9.62 >.>56 5.5; ->.>5>9 9.66 ->.>56 5.:> >.>>0 9.61 ->.>>6 5.52 ->.>:>6 9.61 ->.>>6 5.:> >>>1 9.6; >.>:6 5.5; ->.>5>= 9.66 ->.>56 5.:> >.>>>2 9.60 ->.>:6 5.:5 >.>5>; 9.6= >.>>6 5.:> >.>>>5> 9.62 >.>56 5.:: >.>:>

Cdrt ?9.616 >.>59 @drt ?5.:> >.>2>

C ? 9.616 vf C? >.>59 Egceoc se cerceC?9.6= >.>5 io dcerel vfrkckr.@drt ? 5.:> vf @?>.>2> Egceoc sey cerce@?5.:> >.>2 io dcerel vfrkckr.

1;

rgfl 5.:0


70/568

Oftec jkr lrfgkg ep aerlc c ecftcfrk lucceg cerel cco ee èlk

`f frcfr (io ikgskg`fg) fc`f f`kcok tkr. cocfrkg ùyerc c bell gè vf

begmk ecftcf ec go dcejkcfif kgk gf`fgcfrk kcf e lceyerel jfckrtkgkz.

:.90 :.96 :.9> :.996 :.0 :.90: :.99>

:.0> :.99 :.905 :.91 :.90> :.906 :.9

Oftec jkr skckg`krkg jdyu aerlc c ecftcfrk lucceg cerel jkrfr lfz cco tr.

Ju cocfr`fg begmksk 5/:>?>.>6 oo ùyerc lc ldopesce ec go t r4Gf`fg4

9.: io 9.:6 io 9.::> io 9.:: io=>

.


71/568

. Ee `elk kzfcmf`f ecuokgyuo, pkrkg (jel r+lur ug

vf jdyutcer vfrkcofltf`kr. Ikskocfrkg ydugculcer g egceoc

se cerce kae`f f`kgkz. Ltcfsk ep VzugcuuIksko (m) (io) (io)

Ecuokgyuo 65.6 :.6: 9.=6Jel r 61.9 5.:9 6.>1

r g . . .Pfgflf 1;.5 5.=6 9.=0

@fokr :51.5 5.2; ;.==

=5

.


72/568

.

f`kgkz.

e. ;.;= >.5:j. 62.0 5.:1i. . .

`. 5:2.6 :.2=. . .

a. 62.0 5.2m. :.>2= >.6b. 9.2:1 >.>:56k. ;=.9: >.52

=:


73/568


74/568

5. Jkckosfc jkr yese 8. z fgfg r d ey e eoeye e r.

J. Jkr `d ructuèg jel c gie `d eè cco `f frcfr I. Mzcfgfg èvreg cer g teoeo .

. .:. =2> >>> >>> sey s g jkckosfc sey dcerel mstfrkgkz.

E. =.2 x 5>-2 J. =2 x 5> = I. =2 x 5> -= @. =.2 x 5>2

9.5.>:> gkg l

e tegf egceoc releo begfsk ver4 E. 0 J. 9 I. : @. sdgsuz

0. >.>>>169 sey s gè egceoc begf sey s gf`kr4 E. = J. 9 I. 1 @. sdgsuz

2. =.;12 sey g egceoc sey dceiel flkc`f yuvercey g z. E. =.;1 J. 2.>> I. =.;= @. =.;>

. .=.9: x >.>>:96>

E. >.>5=: J. >.>5= I. >.>5=:> @. >.>:=0

^rdjcfocfr


75/568

5>. >.>:6>> + 9.> + 5.:5> ? 4 cfokgk mfrflcfykgkz vf egceoc sey cer beckg`f yez g z E. 0.: J. 0.:0 I. 0.:96 @. 0.>

55. >.>:5>5 x (99.6> - :9.1) ? 4 cfokgk mfrflcfykgkz vf egceoc sey flckg`f yez g z. E. >.:>2 J. >.:>2> I. >.:5 @. -::.;

5:. ::0 kgib k oftrfyf fvkrkp egceoc sey dcerel yez g z. E. >.22: o J. 6.1; o I. 22:> o @. 61;>> o

. . E. 5.>: x 5> 2 J. 5>: I. 5>:.56 @. 0;1

50. >.5:> o 9 le io 9 tr4 E. 5:.> J. 5.:> x 5> -9 I. 5.:> x 5> 6 @. 5.:> x 5>-=

56. 91.: mreo ltcfck vf 52.9 oC beikock jkr gfsgfgkg yd ugcuu ee `elkcfr`fg

. E. 5.;2 m/oC J. 5.;2 oC/m I. >.6>1 m/oC @. 11: m/oC

51. :62 mreo ltcfck vf >.;6 m/oC yd ugculcu iksokg beiok (oC) e e `elkcfr`fgbegmksk`kr4

E. :6> oC J. 9.= x 5> -9 I. >.:= oC @. :=> oC =6


76/568

* @fgf sfc jkr zcfo e co se, vfrkcfr lucceg c rlfg

skstfoetkl vf resmfcf (dluoe) betecer g g `klletf ec goes

mfrflofltf`kr Ju lfskgckl vf bessesc jfckrcfr,

* ,

* Dluoe betecer g g yuvercet coes egceoc dcoecer kkg mfrflck`kr,

* Jezfg betecer g lucceg o vf jkrcftkrkcofsk mfrflfjkckr,

e e e r g s e sf d es g ou e e e f e oe mfrf r .

@ebe aezce dluoe kkg 8 @diuofgt dg wfjsktf dr egy tfxt jddl dg preitkiec pbyskis

f.m. Fxpfrkofgtec Oftbd`s C Lkrlup dr ^reitkiec ^byskis M C Yqukrfs=1


77/568


78/568

Lceskl oflegk f mkrktf ikskocfrkg berflftkgkg uzeye vf

.lkgfoetkl `fgkr (lkgfoetkl skgfoe kcf eyg llfgck

lfckofcfr`kr4). Ju jco`f se`fif tfl jdyutte yegk `d ru

jkr kz k zfrkg`flk berflftcf kc kcfgkcfifltkr. gif ldguo

yfr`f ktkrof, b z vf kvof levreocer teg ocegeielt r.

e e sdgre u evreo er u eg ere gfsgf fr g se t vofkcf berflftcfrk kgifcfgfifltkr.


79/568


80/568

Mgcl beyetteg jkr gfsgfgkg berflftkgk srflck yfr

. tfcfof,

`gof vf rf o

berflftcfrk flckg`f s g aceg rejkckr.

. ,


81/568

Jkr perei gldguou sfkcfg

rfafregs ge yfrkgkgjfckrcfgofsk`kr.

e flkc`f erejecer g ldguou x-flsfgkjdyugie jkrje cegm vfye

jfckrcfgofltf`kr.


82/568


83/568


84/568

Ec gegydccer g

Pdpceo ydc

? --------------------tdpceo g gtdpceo Pdpceo srfsrfyfdreg ` r.

-


85/568

x ? xA - x E? 69 9> ? -29 o

-29 oDrteceoe b z ? ----------

? -5.= o/s5:= o

Drteceoe sret ? -----------6> s

? :.6 o/s

.


86/568

Jezfg drteceoeb z vfye sretyfrkgf èbe llzeoeg`kckocfrkg`flk egc lb z vf sret`f frcfrkgkgjkckgofsk èbeyererc dcur. [egk E

,gdltes gè vj.


87/568

(e) Erejeg g berflftk (j) J

eyr gt c dcerel vfrkcoktkr.

.


88/568

-mreakk x(t) ? -0t+:t:adglskydgu kcfvfrkcofltf`kr. P-segkyf

ikgskg`fg`kr.e) > t 5 vf 5 t 9zeoeg erec lcer g`elkyfr`f ktkrofykbfse ce g z.

j) > t 5 vf 5 t 9zeoeg erec lcer g`elkdrteceoe b z bfsepcey g z.

.


89/568

t ? :.6 segkyf`flk egc l b z ksfx .

.


90/568

Ffr iksokg b z `e zeoege je c dcerel `f kkydrse ju

.mstfrkcfjkckr. Jkrkok oftrf / s: `kr


91/568

@ebe ll zeoeg erec lcer g`elk b z `f kkocfrkgk jkcofl gfockksf ju e e `elk mkjk adroc kcf fc`f f`kcfjkckr8


92/568

Jkr gfsgf jkr kzmk jdyugie berflft f`kydrse

ju iksokg b

z

g

g vf kvofskgkg gcfrkbell g`e ugcer sycfgfjkckr8

sretk ert ydr`ur, Iksokg b z kcf kvofsk aerlc ygcfr`f ksf


93/568

-mreakkg`fg fc`ff`kcfjkckr.

e x kvofskgkgtz eoeg ge mrfmreakkg`fg

u ur.

(j) v x kgt yf mrfmreakkgkg

(e) `elk klkgdltey jkrcf tkrfgkzmkgkg teghegt`f frkg`fgbfsepceg r.

x, v x , vf e x Egc l b z x -t mreakkgkg teghegt

`f frcfrkg`fg bfsepceg r


94/568

f frcfrkg fg bfsepceg r.t ? > vf t ? t E, erec gè x -t

mreakkgkg fkok ertoelte` r.[egk b z è ertoelte` r.

t E vf t J , erec gè x -t mreakkgkgf kok sejkttkr vf b z sejktlecoelte` r.

t gdltes gè reak kg f kok x -tmreakkg`fg s a r` r, yegk egc l b z

s a r` r.t vf t erec gè x -t reak kgkg,

f kok ezecoelte` r yegk b zgfmetkatkr.

-F A,f kok gfmetkatkr vft A `f ju `f frs a r` r.

A, - mreakkgkg fkok s a r` r vf iksko

ùruydrùr.

.


95/568

- x -6t : ) o/s dcerel vfrkcofltf`kr. @fglcfo`flk t zeoeg

stfrofltf`kr.(e)> t : s erec g`e drteceoe kvofyk bfsepcey g z.v ? 0> - 6t : o/s ? 0> - 6 > : o/s?+0> o/s v x J

? (0> - 6t J

: ) o/s ? \0> - 6(:) : _o/s?+:> o/s

rgfl 5.: Drteceoe vf egc l kvof

(j) t ? : s `flk egc

l kvofyk bfsepcey

g

z


96/568

(j) t ? : s flk egc l kvofyk bfsepcey g z.


97/568

.


98/568

e) ldguo-zeoeg,j b z-zeoeg vfi) kvof-zeoeg mreaklcfrk


99/568


100/568


101/568

rgfl 5.9 Dtd dc treak kgf krofl

(E) ydlu -yuler dtdydce mkrfrlfg kvofgkzkg gf dceie g tebokg f`kgkz


102/568

(E) ydlu -yuler dtdydce mkrfrlfg kvofgkzkg gf dceie g tebokg f kgkz.

Ju prdjcfok zfrlfg e x kkg yelce l `f frcfr ecejkckrkz. @kfr `f klfgcfr ksf ldguo,

.mkrfjkcfifkokzk lejuc f`fcko., ju `f frkg OLY jkrko skstfokgf fvrkcofskmfrflofltf`kr8 (5 >>> o/5 lo) kcf lkcdoftrfyk oftrfyf vf (5 seet/9 1>> segkyf) kcf

. xaecec o. Je cegm b z o z è sdg b z g 5/9 dcerel ec rsel v xk ? 5> o/s.

Ydg dcerel 5> segkyfckl srf kkg`f treakf ler t o z ` gfcko. Jugu mgclbeyet g zè è tfirjf f`fjkckrskgkz. E e è drteceoe kvof vfrkcofltf`kr8

.


103/568

u vof vf zeoeg g yer s g e gf e er yd e r z vofo z g se tlec` g lejuc f`frfl ju sdruye ifvep jucejkckrkz.

rgfl 5.0 Jkr ue g uel mfokskgf kgkk


104/568

r ft ue mfo s gf o seet o s z f gof vf skkg`f ùroel kstfofltf`kr. @uroe fsges gèlk kvofsk gf dcur4Vel ju srf zera gè gf leèr ydc ec r4

rgfl 5.6

Jkr rflceo pegdsugug erles gè mkzcfgfg pdcks odtdsklcftk b z ckoktkgk mffg jkr erei


105/568

: .yeleceyejkcofsk kkg gf le`er srf mffr4

5.1 Yfrjfst ` fg ikskocfr Jtg ikskocfr f fr beve `krfgik kboec f`kckrsf

`gyeye `d ru yfrflko kvofsk kcf b zcegerel


106/568

gy y y gfr fr. u m r y ere e er e u

f`kcof`k. Jyl akcdzda Erkstdtcf (9209:: J.I.)

` tg sycfoktk. Ktecyeg Meckcfd Meckcfk(5610510:) jugug `d ru dcoe` g ^kseLucfsk g`fg aerlc e rc ltelk ikskocfrk yfrfj relerel eyg eg`e yfrf yfrf ver` lcer g mstfr`k. Eyr ie f kl zcfocfr zfrkg`f`fgfycfr yeperel ikskocfrkg kvofcfrkg`flk

.[frflko kvofsk `fgkz sfvkyfskgf yel g yfrcfr`f

:

tecyeg akzklk vf estrdgdo (5610-510:)

. .

.


107/568

f f mz pceyeg jkr tdpugldguougu, b z g vf kvofskgkzeoege mrf`f k ko reak kgkkzkgkz.

. .


108/568

rgfl 5.= [uler `d ru et ceg te6> o ylsflck kg`flk jkr jkgeg g tfpfskg`fg :>.> o/s kcl b zce jkr

te yuler

`d ru et

coelte`

r. t E ? > s lejuc f`frfl(E) Pdpug oelskouo ylsflck f uceoes kkg mffg srfyk,


109/568

,(I) Pe yfrf ` frlfg et c gdlteèg gf leèr srf sdgre

mffr4(@) Ju egè tdpug egc l b z gf`kr4

(F) Pe g t ?6 s `flk ldguou vf b z g jfckrcfykgkz.

. ,Jkr recck erei g g ldguou `f kkl zeoegcerè e e èlk kzfcmf`flk mkjkfc`f f`kcok tkr. Erejeg g drteceoe b z g


110/568

j g g g(e) Jkrkgik segkyf`f,(j) Ydg 9 s erec g`e vf t (s) > 5.> :.> 9.> 0.> 6.>

x (o) > :.9 ;.: :>.= 91.2 6=.6

:.9 >.>drt ---------- .

5 >.>

. .j) v drt ? ------------- ? 51.5 o/s

.

6=.6 >.>i) v drt ? ---------- ? 55.6 o/s

6 >.>

. ,

i f f d i f


111/568

r perei x f sfg dyugie yeg e mre tfmkjk berflft ftofltf`kr. ^erei g drteceoeb z g ee `elk zeoeg erec lcer kkg jfckrcfykgkz.

(e) > - : s, (j) > - 0 s, (i) : s - 0 s, (`) 0 s - = s, (f)> - 2 s.

.

- ? :


112/568

berflft ftofltf`kr. @fglcfo`f x -oftrf vf t -segkyf`kr. Ee èlkcfrk fc`f

.(e) t ? 9.>> s `flk ldguougu,

(j) 9.>> s+ t `flk ldguougu,

(i) t -7> ckokt ùruou kkg x / t b z g t?9 segkyf kkg bfsepcey g z.

(e) x(t?9) ? 9t : ?99: ? := oftrf

(j) x(t?9 + t) ? 9(t +t): ?9(t : + :t t + t : ).

i v ? o - ? x ? vf ? s g v ? o s r.

rgfl 5.55 Egk b z, sret

Jkr iksokg ùrmug bec`fg berflftf mfofsk flkc`flk mreakltflk mkjk vfrkcofltf`kr.(e) t ? 5> s vf t ?:> s cfrkg`f per ei g sretkgk bfsepcey g z,


113/568

(j) cl :> s kkg`f perei g ec` ydcu bfsepcey g z.

. Eifce (eb-YFCC-eb ]esbkgmtdg-Gfw [drl-


114/568

Eofrkleg trfgcfrkgkg ^drsibf sk`kr. lk cdldodtka

vf 1 ygftofgk ver` r. 9>0 ydciuyu 5=> ok/seet

b zce te r. [dciucer g sers gt cer ez bkssftofsk

kkg vemdgcer jkrjkrkgf gfrf`fysf yep lt r. Arfg

skstfok berflfttfg fc`f f`kcfg fcfltrkl fgfrhksk kcf

ec r. Ju trfgkg b z-zeoeg mreakk yegè

.

(e) Bfr zeoeg erec kkg trfgkg

berflftkgk egcet g z.

(j) Mreakltfg trfgkg kvofskgkg

fg j l dcù u frk jfckrcf kgkz.

(i) t ? > vf t ? :>> s erec gè trfgkg

yfr`f ktkrofskgk bfsepcey g z.

9 QFLPZCFZ9.5 Lddr`kget skstfocfrk9.: Lertfzyfg lddr`kgetcer 9 9 Qfl f


115/568

9.9 Qfltrcfr 9.0 Qfltrcfrkg jkcffgcfrk9.6 Qfltrcfrkg tdpcegoes 9.1 Qfltrcfrkg ler coes

. r o vf r

5

^kcdt ue g ldlpkt kg`fg beveeceg g ges c jucur4

.


116/568

:

.


117/568

9


118/568

0

Y `fif klt `ft f jk `f f f f


119/568

Ye fif oklter, e ft vfye sey sec jkr f fr vfrfg. ,

fgfrhk, sret, jkr yfr`flk iegc sey s vs.

[g, d ructusu vf jylc dceg gkifcklcfrfvfltr . , , .

6


120/568

1

.

Ee `elkcfr`fg begmkcfrk vfltr, begmkcfrk slecfr


121/568

Ee elkcfr fg begmkcfrk vfltr, begmkcfrk slecfrgkifcklcfr`kr4

e e g z(j) vofi z

(`) Yret(f) Ltcf

=

.


122/568

Z-jkcflf vfltr, E vf J -Z gkg jkcffgcfrk

2


123/568

;


124/568

5>


125/568

.J vfltr E vfltrgf flcfgkrsf, begmk `uruo`e jkcf lf vfltrE + J gkg `ffrk E + J yf f kttkr4


126/568

g g y(e) E vf J perecfc vf eyg `d ructcer`e dcugie,(j) E vf J perecfc vf z t ygcfr`f dcugie,(i) E vf J jkrjkrkgf `kl dcugie.

5:

.J vfltr E vfltrgf flcfgkrsf begmk ld uc`e jkcflf vfltrs a r dcejkckr4


127/568

j(e) E vf J jkrjkrkgf perecfc vf eyg ygcfr`f dcugie,

(j) E vf J perecfc vf z t ygcfr`f dcugie,(i) E vf J eyg jylcltf dcugie,(`) E vf J jkrjkrcfrkgf `kl dcugie.

59


128/568

Vymug jkr lddr`kget skstfok sfkgkz. Jkcffg sey s g ezecterel tdpceo ldceyie

yep ceiel becf mftkrkgkz. ^rdjcfo`flk teg oe uymug jkr flkc kzkgkz. fr vf rg x vf y f fg fr gf ey r g z vf f fg fr g if rsf dp eo g x vf y flsfgcfrk jdyugie yep g z.

flsfgcfr`fg gf le`er eyr c g `e trkmdgdoftrkl adglskydgcer luccegerel.

50

xy `zcfokg`f jucugeg E vf J vfltrcfrkgkg tdpceo g bfsepcey g z.? + ? -. . . .zo Qfltrcfrk jkcffgcfrk ikgskg`fg yez cejkckr.


129/568

E ? E k+ E jureè E ? :.> o vf E ? :.> o.

Jfgzfr flkc`f J x ? :.> o vf J y ? - 0.> o. Jkcf lf vfltr Z ee èlk mkjk dcur,

Z ? E + J ? (:.> + :.>) ko + (:.> - 0.>) ho ? (0.> k- :.> h) o

Qfye

Z x ? 0.> o Z y ? -:.> o

56

Jkr perei l e e èlk mkjk yfr`fktkrofcfrk yepo t r8` 5 ? (56 k+ 9> h + 5: l ) io, ` : ? (:9 k- 50 h - 6.>l ) io vf ` 9 ? (-59k+ 56 h) io. Jkcf lf


130/568

yfr`f ktkrofyk vf jylc g jucuguz.

51


131/568

.

Jkr vfltrg jkcf fgcfrkg`fg jkrk pdzktka `ffrf sebkpsf, juflt kk ` lk ld ` b k k `d ` 4


132/568

vfltr kkg ee èlk ld uccerèg begmksk `druùr4

e f fg fr g fg r gfme erf d eoez,(j) Y a r dceoez,i dyu u d eoez.

52

.

E + J ? > dcejkcofsk kkgE vf J gkg ges c dcoes mfrflkr4


133/568

(e) f kt

(j) pdzktka (i) gfmetka (`) X t kerftck.

5;

.

E e `elkcfr`fg begmkskg`f jkr vfltr jkcf fgcfrkg`fg jkrkgff kttk 4


134/568

f kttkr4

e ? + (j) J ? -9 hi ? +

:>

.


135/568

:5

.


136/568

::

E vfltrgg y-`d ructusug`eg jel gie x-flsfgk zfrkg`flk kz` o


137/568

flsfgk zfrkg flk kz o

:9


138/568

:0

.


139/568

:6


140/568

:1

.


141/568

Z?61 jkrko

E vfltrgg jylc :> jkrkoJ vfltrgg j lc 0> jkrko

I vfltrgg jylc 9> jkrko-

:;

j) Z-jkcf lf vfltrg yg4

ids06?skg06?>.=5

:=

.

E-J 4


142/568

E J 4

J-E E-:J

.skg9>?>.6>

:2

. Ee `e lutupsec lddr`kgetcer vfrkcfg gdltecer g ldguo vfltrcfrkgk yez g z8(e) 5:.2 o, 56>

(j) 9 9> io 1> >


143/568

(j) 9.9> io, 1>.>

(i) ::.> kg., :56.

:;

.

.

kcf yept e 5:> dcerel vfrkcofltf`kr. Ju vfltrg `kl jkcf fgkgk jucuguz (sdgu


144/568

y .

6>.> o

6>Zy ? 6> skg1> ? 09.9

:>

9>

Zy ? 6> ids9> ? 09.9

x

5>5:>

5> :> 9>

-5>

-5>-:>-9>

9>

-

-9>

.Jkr oe erei oe ereg g

Luzfy

mkrkkg`fg ktkjerfg oe ere kkg`f:>>6>.> o


145/568

gif =6.> o luzf f :6> o

`d uye, 5:6 o luzfy-`d uye

5>>

.

`d ructu`e) vf sdg dcerel 56> o@du

5>>-5>> :>> .

Oeerei g g oe ereg g mkrkkgf-5>>

mrf yfr f rofsgbfsepcey g z.

95Zx?962.9 o Z?962.6 oZy?-5:.6 o

.Jkr rdjdt ldcu gif yuler `d ru vf sdgre `d uye berflft f`kydr. Ydgre `d u-jet jdyugie ` fy `d ructu`e yer ep 0.2> io dceg fyrfl fojfr yey zfrkg`fberflft f`kydr. Zdjdt iksok ec p yuler vf 9.=> io ckl yer ep dceg fyrfl fojfr


146/568

yey zfr g f fy d ru tu e uzfyf d ru te rse8(e) tdpceo yfr`f ktkrofgkg jylcg bfsepcey g z.

dp eo yfr f rofg g fy f sfg fyepo dcùu e y bfsepcey g z.

9:

.

Jkr beve ldgtrdcr klk ue reèr flreg gè mrr. Jkrkgik uel yfr`fg2>> o ylsflckltf, yetey dcerel 5;.: lo vf :6.> mgfy-jet è


147/568

2>> o ylsflckltf, yetey dcerel 5;.: lo vf :6.> mgfy jet e

jucugoelte` r. lkgik uel ksf yfr`fg 55>> o ylsflckltf, lucf`fg 5=.1lo yetey `d ructuè :>.> mgfy-jet è jucugoelte` r. lk ueleres gèlk uzelc bfsepcey g z. ( x flsfgkgk jet , y flsfgkgk mgfy vf z

flsfgkgk f `d ructu dcerel ec g z .

Vel 5 kkg x5?5;:>>skg:6 ? 2550.: o, y 5?5;:>>ids:6 ?5=0>5.5 o, z 5?2>> o

e : g x : ? s g ? . o, y : ? ids ? . o, z : ? o

r ? ((2550.:-1>5;.9) : +(5=0>5.5-51692.1): +(2>>-55>>): )

99

. . .


148/568

- Jkr dl iksko klk

jdyutte berflftf`fr8uy`ugugberflftk fcfltrkl


149/568

berflftk, fcfltrkl

ylgg fcfltrkleceg kkg`fberflftk, suyzfykg`flk jkrmfokgkg

berflftk,vs. Ect kg`kscfr k-kgktkec, a-akgeclfckofcfrkgkg je

er fr r.

:


150/568

Jkrkozeoeg`e

of oklter

9


151/568

Jesfjecc e tdpevureg lkkje ce` yfrfld erel mfrk

gfr. r e eoeb z s a r` r.

0


152/568

dl llzeoeg

yfr`f ktkrof oklter .

6


153/568

Jkrkozeoegèb zèlk

`f k ko

1

Iksko Eèg J f


154/568

gmk`frlfg

`f ktkrkr.

flcf `kllet f`frsfgkz vfltrcfrkg tdpceo yep coelte` r.

B z g `f kkok `ebe llzeoeg erec lcer g`e dl

dcoelte` r8=

lk jd utte sejkt kvof kcf berflft f`fg jkr iksokg

ldguou zeoegce `f kkydrse b z


155/568

2


156/568


157/568

Yejkt kvofck berflfttf sdg ldguo `f frk


158/568

55


159/568

5:


160/568

. Jkr iksko t?> s eg g`e drkhkg`fg berflftf je c ydr. Iksokg je cegm b zcer g g x vf y

jkcffgcfrk :> o/s vf -56 o/s dcerel vfrkckydr. Iksko x-flsfgk jdyugie 0o/s : mkjk sejkt jkr.


161/568

50

.

Ydg b z `f frk


162/568

Iksokg t?6gik segkyf`flk b z vf yetey flsfg kcf b z vfltrgg yept e

56

.

Jkr tdpe vurucùugè beveèlk berflftk kgifcfg`k kg`f


163/568

5. Pdp berflftk fsges g`e b z ee ye ygfcok sejkt m-

yfrflkok kvofskgf je c dcerel `f kkr.

. .

Ju sdgucere mrf tdp beve kkg`f perejdc kzfrfl berflft

f`fr.

51

Fkl berflft


164/568

5=


165/568

[eg`elk rfsko`f oftecfrktfg jkr leygeli mrcofltf`kr.

52


166/568

[etey d ructu`e sejkt b zceberflft f`kckr, @fy `d ructu`e sejkt kvofckjkr berflft ver` r. 5;

Fkl berflft-rgfl 5.

Jkr iksokg ` fy vf yetey b z `f frcfrk 0> o/s vf :> o/s `kr. Iksokg

.


167/568

:>

V u ofgzkck


168/568

Ofgzkc:5

.


169/568

::

rgfl 0.9-Vzug etceoe


170/568

:9Oklf ^dwfcc, uzug etceoe rfldrugu l r` etcey 2.;6 o `kr.

. -


171/568

:0

-.


172/568

:6

. -


173/568

:1

-.

flkc`flk jkgeg g tfpfskg`fg

.yepeiel flkc`f :>.> o/sb z kcf a rcet coelte` r.Jkgeg g lsflck k 06.> oksf,

(E) P f f kk


174/568

(E) Pe g yfrf uce oes kkgmffg srf gf`kr4

(J) Pe g yfrf erpoe`egbfofg giflk b z gf`kr4

? .

:=

.

berflft iksokg sejkt jkr kvofsk ver` r.


175/568

e) fojfr zfrkg`f `dcegeg ereje, j) erejeg g ldguougug `f kko, i) erejeg gb z g g `f k kok

:2

.


176/568

:;

0.6 Pf ftsfc vf ofrlfzikc kvof

vofgkg tf ftsfc

b g` `f kk f


177/568

b z g e f kkof

gf`fg dcur.

yggg

`f kofskgf gf`fg

dcur.9>



178/568

95



179/568

e)Jkrko vfltrcfr teg ocegoelte` r, j) Pdpceo vfltr vf `d ructusu

9:

. -


180/568

Jkr ereje >.9>> o/s: kvof kcf flkc`flk mkjk berflft ftofltf`kr. [er ep 6>> o dceg jkr tfpf`fg

mffrlfg erejeg g yetey b z g g jylc 1.>> o/s `kr. Erejeye ftlk f`fg tdpceo kvof gf`kr4

99

.

Ju lfsko`f aerlc mzcfo frfvfskg`flk mzcfoikcfrkg

.

jkrjkrcfrkgf mrf ldguocer b zcer vf kvofcfrk ges c


181/568

jkrjkrcfrkgf mrf ldguocer , b zcer vf kvofcfrk ges c

dceielt r. [egk jkrjkrcfrkgf mrf mrfck berflft f`fg

zcfoikcfrkg sdgu cer aerlc dceielt r.

90

flkc`f jkrk yryfg

ofr`kvfg`f `k frk yfr`f

dceg klk mzcfoik yryfg


182/568

dceg klk mzcfoik yryfgofr`kvfg zfrkg`flk

eèo g (fg se elk) b z g

aerlc c fifltkr. [ryfg ydczfrkg`flk le` g eèo g

le` ge mrf èbe yeve .

96


183/568

(e) Leyley zfrkg`f berflft f`fg E lk ksk tdpug yuler `d ru berflft fttk kgkm r r,

(j) @ureg J mzcfoiksk ksf tdpug berflftkgk perejdc flckg`f mrr.91


184/568

gd es g e r i so g dguou r se fr erf f m z foi

terea

g`eg yuler

`elk flkc`flk mkjk mrcofltf`kr. @urmug frfvf Y vfsejkt v> b z dceg berflftck frfvf`f Y `r. r vfltr Y mzcfo

vfltrcfrk`kr.9=

,

Ldguo vfltrcfrkgkg trfvk ec g rse

mrfck b z jucugur


185/568

mrfck bz jucugur,B z vfltrcfrkgkg trfvk ec g rse

mrfck kvof `ffrcfrk fc`f f`kckr.Mrfck berflfttf kvof bfr mzcfo

frfvfskg`fg eyg `f fr`f

mzcfgkr.

92

rgfl 0.;-Gfbkr`f berflftf f m r dt, d uye dru yfrf

mrf) sejkt 6 lo/seet (ect skomf rF-rkvfr

Fertb) b zce eleg jkr gfbkr zfrkg`f gfbkrf

mrf 5>.> lo/seet (ect skomf jr-jdet rkvfr)

b zce luzfyf `d ru berflft ftofltf`kr.

Jd b lf ` lk j l f k `f


186/568

Jdtug b z g lfger`elk jegl zfrkg`f

jucugeg mzcfoikyf mrf (jF-jdet Fertb)

bfsepcey

g

z.

9;

. -Jkr giflk rgfltf berflftck mzcfo

frfvfsk (gfbkr-6 lo/seet) kkg`f ydc

eceg ley l (5> lo/seet) kgifcfgok tk.

Ley

l je ce`

gdlteg

g teol ` lk b l jk f k kk


187/568

y j g g gler s g`elk r bt oe lejkcofsk kkg

luzfy-jet ye `d ru luzfycf begmk e

kcf vf b zce berflftkgf je ceoec ` r4

0>

.

Jkr tfpf`f mdca tdpuge vurucoelte`

r. Mdca tdpugugx vf ylddr`kgetcer zeoege je c dcerel e e `elk mkjkvfrkcofltf`kr8

x ? (52.> o/s) t vf y ? (0.>> o/s) t - (0.;> o/s:)t

:


188/568

( ) y ( ) ( ; ) yez g z.

z vf r y zeoeg g dg s ydgu d ere yez g z.(i) vof vfltr e y zeoeg g adglskydgu dcerel yez g z.(`) 9 s sdgre mdca tdpugug ldguougu, b z g vf kvofskgk

bfsepcey g z.

05

. -

x ? (52.> o/s) t vf y ? (0.>> o/s) t - (0.;> o/s : )t:

r ? x k+y h


189/568

r ? x k+y h

? (52.> o/s) t k+ \(0.>> o/s) t - (0.;> o/s : )t: _ h

flckg`f yez cejkckr.

v ? (52.> o/s) k+ \(0.>> o/s) - (;.2> o/s : )t_ h

0:

. -

x ? (52.> o/s) t vf y ? (0.>> o/s) t - (0.;> o/s : )t:

- .

(`) t ? 9 s sdgre ldguo b z vf kvof `f frcfrk ee `elk mkjk`kr8


190/568

( ) t ? 9 s sdgre ldguo, b z vf kvof f frcfrk ee elk mkjk kr8

r ? (52.> o/s)9 k+ \(0.>> o/s)9 - (0.;> o/s : )9: _ h

? (60.> o/s) k (9:.5) h

? -. .

e ? - (;.2> o/s : ) h

09

. -Idrvfttf lk Eck v Eck? (9.>>k :.>> h) o/s : kcf kvofcfgofltf`kr. Hemuer`elk Ey f ksf

v Eyf ? (5.>>k + 9.>> h) o/s : kae`fsk kcf kvofcfgofltf`kr. Bfr klksk`f `zcfosfc xy

lddr`kget skstfokgkg drkhkgkg`fg `urmug bec`fg berflftf je ce` lcer ge mrf 6.>> s

sdgre e e e fr fsep ey g z8

(e) Eck gkg Eyfyf mrf b z g ,


191/568

f y f eres g e uze vf

(i) Eck gkg Eyfyf mrf kvofskgk bfsepcey g z.

00

.y

9 eEy f ?(5.>> k + 9.>> h) o/s:

5


192/568

x5 : 9-5-:-9

-5eEck?(9.>> k :.>> h) o/s

:

-:

-9

06

.y

56 vEy f ?(6.>> k + 56.>> ) o/s

6


193/568

x

6 5> 56-6-5>-56-6

vEck?(56.>> k 5>.>> h) o/s

-5>

-

01

.y

56 vEy f ?(6.>> k + 56.>> h) o/s

6

5>


194/568

6

x

vEck-vEy f ?(5>.>> k :6.>> h) o/s

-6

---

v ?(56.>> k 5>.>> ) o/s-5>

-0=

. -[fr-ley l-gfbkr `klletf ec gerel yfr-Eck-Eyf flckg`f ` gcfjkckr.

e Eck? (9.>>k :.>> h) o/s :

e Eyf ? (5.>>k + 9.>> h) o/s :

t ? 6.>> s

(e) Eck gkg Eyfyf mrf b z ,


195/568

( ) g g yy

v Eck? ((9.>>k :.>> h) o/s : )t ? 6(9.>>k :.>> h) o/s ? (56.>> k 5>.>> h) o/s

v Eyf

? ((5.>>k + 9.>> h) o/s : )t ? 6(5.>>k + 9.>> h) o/s ? (6.>> k + 56.>> h) o/s

v Eck v Eyf ? (56.>>k 5>.>> h) (6.>>k + 56.>> h) ? (5>.>>k :6.>> h) o/s

02

. -e Eck? (9.>>k :.>> h) o/s :

e Eyf ? (5.>>k + 9.>> h) o/s :

t ? 6.>> s

f y f eres g e uze vf

r Eck? ()((9.>> k :.>> h) o/s : )t: ? (:6/:)(9.>>k :.>> h) o ? (9=.6> k :6.>> h) o/s


196/568

r Eyf ? . . o s ? . . o ? . . o s

r Eck- r Eyf ? (9=.6>k :6.>> h) - (5:.6> k + 9=.6> h) ? (:6.>> k - 1:.6> h) o

.e Eck- e Eyf ? (9.>>k :.>> h) o/s : - (5.>>k + 9.>> h) o/s : ? (:.>> k - 6.>> h) o/s :

0;

.Jkr ereje `d uye `d ru 6>.> lo/seet sretcf kcfrcfofltf`kr.

lejuc f`kgkz. [eg ieoe ` fg jkr ye our `eoces g g` f cf 1>.> ckl jkr e e drse e our `eoces g g b z g

(e) erejeye mrf vf


197/568

( ) j y(j) yfrf mrf bfsepcey g z.

6>

.z (yfr`fg yuler `d ru)

v

1> d


198/568

x (`d u)

[e our[frfMrf ? v y o s

vEreje[frfMrf ?6> k o/s

65

.

(e)[fr-ley

l-gfbkr `klletf ec

gerel yfr-ereje-ye our flckg`f` gcfjkckr. [eourug erejeye mrf b z

[e our[frfMrf Ereje[frfMrf y . .

? -:2.; h + 6>.>ko/s dcerel jucugur.


199/568

(j) teg1> ? v y/v Ereje[frfMrf ? 5.=9 ? 6> / v y `fg v y ? :2.; o/s

? y .

6:

rgfl 0.50 Gfbkr`f yzoflJkr gfbkr sejkt >.6>> o/s sretcf eloelte` r. Jkr lkk ju gfbkr kkg`f gfbkr

el gt s ge ler 5.>> lo z èbe sdgre el gt gg`f je ceg gdltes ge `gydr. [zi 5.:> o/s ckl sejkt sretcf yzydrse je cegm

gf leèr dcurù4


200/568

69

rgfl 0.50 Gfbkr`f yzofl

? z i f r v[zi - vGfbkr ? 5.: >.6 ? >.= o/s `kr.

mffg srf ? 5>>> o / >.= o/s ? 50:2.1 sg f e g g f ? + fr gf


201/568

g f eyg y g f ? v [zi + vGfbkr yfr gf

v[zi + vGfbkr ? 5.: + >.6 ? 5.= o/s `kr.

[zi ju b zce 5 lo el gt kcf eyg yg`f yzfrsfmffg srf ? 5>>> o / 5.= o/s ? 622.: s

Pdpceo mffg srf ? :>51.2 s vfye 99.1 `elkle jucugur.

60


202/568

rgfl 0.51Jkr sebkc mvfgckl mrfvcksk luzfy-`du ygg`f 56.> e ect g`e :>.> lo uzelc lteteg ocegeoeyeg jkr mfok mro tr. Mfok luzfy-`d u ygg`f 0>.> e ect g`e

:1.> lo/seet sretcf berflft ftofltf`kr. Mvfgckl mrfvcksk ju mfokyf jkr sretjdtu ydcceyerel lkockkgk rfgofl kstfofltf`kr. Yret jdtu 6>.> lo/seet sretcfberflft fttk kgf mrf jdtug berflft `d ructusu begmk yg`f dcoec ` r4 Le tzfrkgf jkr pusuce luccegerel kzkgkz.

y (luzfy)


203/568

vJdtugB z

vMfokgkgB z

0> d

x (`d u)r MfokgkgLdguou

56 d

61


204/568

.Jkr ckjfrd autjdc tdpuge yeteyce 9>.> e yepeiel flkc`f :>.> o/s kcl sretcf

vuroelte` r. Ckjfrd`eg :>.> o uzelc ltelk adrvft begmk yg`f vf sejkt sretcf tdpe

`d ru berflft f`frsf tdpu yfr sfvkyfskg`f yeleceyejkckr4


205/568

dpug ofgz ? . o r. drvf gi of rf f fg dp e eres g e uze .o `kr. Pdpug beve`e lec` srf t?v kskg / (:m) ? >.65 segkyf`kr. Adrvft >.65 segkyf

. . . .

`fg v?9.69 o/s dcoec ` r.

62

. E truil cde`f` wktb ieggdgjecc wetfrofcdgs stdps su``fgcy td evdk` ruggkgm

dvfr tbf f`mf da e wesbf`-dut jrk`mf (Akm. ^0.10). Pbf qukil stdp ieusfs e

guojfr da ofcdgs td acy daa tbf truil. Dgf ofcdg rdccs dvfr tbf f`mf wktb egkgktkec spff vk ? 5>.> o/s kg tbf bdrkzdgtec `krfitkdg. E irdss-sfitkdg da tbfjegl bes tbf sbepf da tbf jdttdo beca da e perejdce wktb kts vfrtfx et tbf f`mfda tbf rde`, eg` wktb tbf fquetkdg y: ? 51 x, wbfrf x eg` y erf ofesurf` kg

oftfrs. ]bet erf tbf x eg` y iddr`kgetfs da tbf ofcdg wbfg kt spcettfrs dg tbfjegl4


206/568

6;

fw dg ug erf f yese er

.6.: Gfwtdg ug jkrkgik yeses vf fycfoskzckl frfvfcfrk6.9 Ltcf

.

6.6 [frflkok luvvftk vf e rc l6.1 Gfwtdg ug gi yeses fwtdg yese er g g ez uymu eoe er


207/568

. fwtdg yese er g g ez uymu eoe er 6.2 Yrtgof luvvftcfrk

5Ll jkr jdt jycf jyl jkryl mfokskgk ges c flfjkckr4

.

Luvvftcf kcmkck dcerel bfrlfskg mgcl yeeo g`eg jkr.

yfrf te goes , lktej yfrkg`fg le` r coes vfye autjdctdpuge vurucerel dgu berflftcfg`krofl mkjk eltkvktfcfr`kr


208/568

tdpuge vurucerel dgu berflftcfg krofl mkjk eltkvktfcfr kr.

Jugcer e erlfg ikskocfrf les luvvftk u ucer vf dgcer g

b zcer g `f ktkrkrkz. @fofl lk luvvft bfr zeoeg berflftfgf fg d ur. ezfg erf ft ftt rfof g z y tf

ikskocfrf`f luvvft uymucer z.

:

Jkr`fg aezce luvvft jkr iksof ftlk f`frsf iksko ges c

dge jkr ftlk (luvvft) f`kydr`ur. Gft luvvft tdpceo luvvftvfye jkcflf luvvft dcerel kskocfg`krkckr Jkr iksof ftlk


209/568

vfye jkcflf luvvft dcerel kskocfg krkckr. Jkr iksof ftlkf`fg luvvftcfr iksokg b z g `f k tkrfok drse iksof ftlk

f`fg tdpceo luvvft s a r` r. Iksko `fgmf`f`kr.

9


210/568

(5) Ikskocfr eres mrevktesydgfc luvvftcfr,

(:) Fcfltrkl ylcfrk eres g`elk fcfltrdoemgftkl luvvftcfr,

(9) Etdo ect perei lcer eres glcffr luvvftcfr, ,


211/568

Lceskl akzkl se`fif mrevktesydgfc vf fcfltrdoemgftkl luvvftcfrk kgifcfr.

6


212/568

6.: Gfwtdg ug jkrkgik yeses vf fycfoskzcklfrfvfcfrk

eve oeses g e oeseg gtejeg g`eg yuler `d ru beveacfg`k kg`f iksko beve`e es c mkjk lec r vf bfrbegmk jkrluvvft ftlk ftofzsf iksko

.


213/568

Ikskocfr eres g`e ftlkcf of dcoezse iksko kvofcfgofz.[egk iksof ftlk f`fg luvvftcfrkg tdpceo s a r ksf iksko fycfoskz ksf ycfif

lec

r, sejkt jkr b

ze sebkpsf eyg

b

zce ydcuge `fveo f`fr.

=


214/568


215/568

.

Ltcf gfsgfcfrkg eyr coez jkr peres ` r vf jfckrck jkrflckydltur. Ltcf flckg jdyutugu, oklter g , yegk sey s g jfckrtfg jkr gkifckltkr. [gfckok ydltur. Ltcf slecfr jkrgkifckltkr.


216/568

5>

.

Jkr iksof ftlk f`fg luvvftcfrkg tdpceo g g s a r`eg aerlc

.

luvvft, iksokg kvofsk vf ltcfsk kcf `d ru dregt c ` r . A ? o e


217/568

A ? o e

Ax ? o e , Ay ? o e , Az ? o e

55

YK jkrko skstfokg`f luvvftkg jkrkok Gfwtdg`ur. 5 l ltcf f 5 o/s : kvof

lezeg`

r

c

rse jycf jkr ltcfyf 5 Gfwtdg.


218/568

5 G ? 5 lm 5 o/s:

5:

,

f vof uvvfYK l o/s: G ? l o/s :

V.Y. scum at/s:

cj ? scum at/s:


219/568

5 G ? >.::6 cj.5 pdug` ? 5 scum 5 at/s:

59

. -

Ltcfsk >.9 lm dceg jkr bdlfy`kslk juz zfrkg`f srtgofskz

berflft ftofltf`kr. Ju bdlfy`kslkgf eyg eg`e klk bdlfy sdpe

kcf vurucoelte` r. A5 luvvftkgkg


220/568

jylc 6.> G vf A:luvvftkgkg jylc ksf 2.> G`ur. Bdlfy `kslkgkg kvofskgkgjylc g vf yggjfckrcfykgkz.

50

. -


221/568

56

Jtg ikskocfr gye terea gèg flkckrcfr. @gyeterea gèg dcuturuceg ju yfrflk luvvftk A m kcf mstfrkckr.Luvvft `gyeg g ofrlfzkgf `d ruùr vf gfsgfgkge rc dcerel kskocfg`krkckr.

@ebe gif sfrjfst ` fg ikskocfrkg kvofskgkg m vf


222/568

@ g j g g g g`g e ofrlfzkgf d ru dcù ugu jfckrtok tkl.

Gfwtdg ug klkgik yeses A ? o e k`k. Yfrjfst ` fg o? ? ? m , . m .

51

m , gkg `f klfg dcoes gèg `dcey jkr iksokg e rc `fgkz sfvkyfskg`fgylsflckf mrf `f kkr. [lsflck ertt le iksokg e rc ezec r. rgf kg

-

[drl telk Fopkrf Ytetf Jkges

g

g fg stg`f ;2>> G ùr.


223/568

Jkr rfgikgkg ltcfsk =>.> lm ksf e rc m ? ;.2> o/s : ec g gie A m ? om? 121 G (yelce l 56> cj). Jkr è g tfpfskg`f ksf m ? ;.== o/s : ,flckg`f cco tr. Ju ùruoè rfgikgkg e rc 120 G ùr. @kyft

.

5=


224/568

Ju fgfykok d uguz yeeo t r. Jkr esegsr`f yuler

dcurlfg, esegsr kcf e e `d ru mk`frlfg jugcer g jkrezbeakacf`kkgk bkssftokskgkz`kr.


225/568

5;

lk gfsgf jkrjkrk kcf ftlkcftkkg`f 5gik gfsgfgkg:gik gfsgf f u uce` luvvft A ksf :gik

gfsgf 5gik gfsgfyf eyg

jylcltf vf z

t:5 .

A ? A


226/568

A5: ? -A:5 Luvvft ikskocfr eres ftlkcfof`fg dcu ur. Pfl

.

:>


227/568

:5


228/568


229/568

`d ru) kcf `ei g g e rc ee d ru frs yg fr f r.

:9


230/568


231/568

^rdjcfokg rfsokgk kzkgkz.

Iksko zfrkgf ftlkyfg luvvftcfrkg iksokfgmf f u up ? u oe ge ? o e

lerer vfrkgkz.

^rdjcfokg luvvft k e reo g kzkgkz.

Luvvftcfrk sftkkgkz lddr`kget skstfokgf mrfyfgk`fg `zfgcfykgkz


232/568

yfgk fg zfgcfykgkz.

Flsfgcfr zfrkg`flk luvvftcfr kkg Gfwtdg ugklkgik yeses g uymucey g z.

.

Ydgucer g z ldgtrdc f`kgkz. Ydgucer oegt lc mfckydrse zo lejuc f`kgkz.

:1


233/568


234/568

:2


235/568

. -


236/568

9>


237/568

. -


238/568

9:


239/568

. -

lk iksko ltcfskz jkr kpcf jkrjkrcfrkgfsrtgofskz oelere`eg f krkcfrflje cego t r. Ju tr skstfocfrf Etwdd`

.cejdretuver drteo g`e sfrjfst ` of`f


240/568

.Ikskocfrkg kvofcfrkgkg jylcg vfkptflk mfrkcof bfsepceg r.

90

. -

(e) lk gfsgf ( o : + o 5)jkrjkrcfrkgf ltcfskz k cf vfoelere kcf kp eres g`e

f`kcfrfl flkc`flk mkjk


241/568

. (j) Yfrjfst-iksko

`kyemreocer .

96

. -

@fglcfocfrk yezerlfg `klletf`kcfifl fy kerft sfkokgkg

d ru yep oes r.[uler yg + (pdzktka),ee yg (gfmetka)d ere sf of r.


242/568

91

. -


243/568

Yrtgofskz oelere`eg mfkrkcfg kpkg jkr uiuge ltcfsk o5

vf `kfr uiugeltcfsk o dceg ikskocfr je cego t r. Jcdl srtgofskz f kl `zcfo zfrkg`f`kr.

9=lk iksokg kvofskgk bfsepcey g z.

. -


244/568

92

Jkr gfsgf jkr yzfy zfrkg`f vfye su,beve kjk el leg k kg`f berflftkfgmfccfgfifl flkc`f fvrfcfg`k k ju

.ftlkskgf srtgof luvvftk ftlksk `fgkr.


245/568

,ld oeo z, tflfrcflck erecer g berflftksrtgof luvvftk kcf se ceg r.

9;


246/568

Pfoes beckg`flk klk yzfy eres gèlk stetkl srtgof a s sgflckg`f`kr. @fglcfo`flk s-jdyutsuz stetkl srtgof letsey s vf g

. s s ,oex s

lk yzfy eres

gèlk lkgftkl srtgof a l ? l g flckg`f`kr.s l

gkifcklcfr`kr vf l letsey s s `fg èkoe lltr. Pkpkl `f frcfrkgd u >.>9 kcf 5.> eres gè `f kkr.


247/568

Yrtgof luvvftkgkg yg yzfyf perecfc vf berflft `d ructusugetfrs yg`f`kr.

Yrtgof dcey yzfycfrkg eceg ge je c `f kc`kr, se`fif e rc lcer ge

je c ` r.05

s l

fckl zfrkg`f fckl >.=0 >.6=

fckl zfrkg`f ecuokgyuo >.15 >.0=

fckl zfrkg`f jel r >.69 >.91

Jftdg zfrkg`f leuul 5.> >.2

Pebte zfrkg`f tebte >.:6>.6 >.:

Ieo zfrkg`f ieo >.;0 >.0


248/568

Kscel ler zfrkg`f ye c tebte >.50 >.5Luru ler zfrkg`f ye c tebte >.>0

Oftec stg`f oftec (ye c ) >.56 >.>1

Juz zfrkg`f juz >.5 >.>9

0:Pfacdg zfrkg`f Pfacdg >.>0 >.>0

Flcfo yfrcfrk >.>5 >.>>9


249/568

vofck berflft f`fjkckr ok4 e ze


250/568

00

Ytetkl srtgof letsey s g g `fgfysfcdcerel fc`f f`kcofsk

Jkr jcdl flkc`flk mkjk `zcfokgf klckkgkg `fk tkrkcfjkc`kk

f ko e s kcf `zcfo zfrkg`f

ley` r coeye ec c r. Jcdugteo leyoeye je ce` lrktklie s jucugoeye ec c r vf


251/568

letsey s s fc`f f`kckr.

06

rgfl 2-Lkgftkl srtgof letsey s g gbfsepcegoes Jcdl f kl `zcfo

zfrkg`f kvofck

sdgre (srtgof luvvftka l ? - l g) `zcfokgf klckkgk jfckrcfyfglrktkl

ie s

ezect coe e je ceg r.Jfckrck jkri e `f frkg`f jcdl f kl

z fo zfr g f er


252/568

gsejkt b zce berflftkgf`fveo f`fr (jcdlugkvofsk s a r` r).@fglcfo (5) vf (:) `f a

s

01

l lkgftkl srtgofletsey s fc`f f`kckr.


253/568

rgfl 6.;-Bdlfy `kslk


254/568

02

. - Yrtgofck yzfy zfrkg`f o 5 ltcfck jkr jcdl ltcfskz jkr kpkg oelere`eg mfkrkcofsk

f o : f r dpe e ego r. o 5 f d e uvvf e s f f f mftlkofltf`kr. l lkgftkl srtgof letsey s ksf klk iksokg kvofskgk bfsepcey g z.


255/568

0;

. -


256/568

6>

[dc zfrkg`f kcfrcfyfg jkr erejeg g tflfrk leyoeèg `gfrsf ydc kcftflfr eres gè oelskouo stetkl srtgof ( sg) dcuur. Ju fogkyftck

.leyoe dcey dcuoez. F fr tflfr ydc zfrkg`f leyoeye je cerselkgftkl srtgof ( g) dcu ur. Erejey fogkyftck jkr flkc`fùrùroeg g ydcu srtgofyk ert roel yegk tflfrkg `gfrlfgerejeg g yeveceoes ` r. Jycfcklcf erejeg g yg ldgtrdc`f

l f`k f k d f k`f f f dl l f k k flk `f


257/568

leyjf`kcofok dcur. Yricfr egk`fg arfgf dl luvvftck jkr flkc`fjeserel tflfrcfrkg lkcktcfgofskgf gf`fg dcurcer vf ereje leyoeye.

ju dcey zfrkg`f ec erel arfgcfrkg lkcktcfgofskgk fgmfccfyfg EgtkcdilJrelkgmYystfo k mfckstkrokcfr`kr.

65

Pdydte Idrdcce g g vfrkcfrkJe cegm sretk @uroe uzelc vof(ok/b) (o/s) (at) (o) (o/s : )

9> 59.0 90 5>.0 -2.19

1> :1.2 509 09.1 -2.:0

2> 96.2 :65 =1.6 -2.92


258/568

u z , 8 , .

6:

5>>

5:>leyoe ydl

leyoe ver

2> e a f s

k ( o

)

0>

1>

r o e o f

>

:> `

9> 1> 2>

b z (ok/b)

@ f f k


259/568

@uroe ofseafskJe cegm sretk leyoe ydl leyoe ver

9> 5>.0 59.;

1> 09.1 66.6

692> =1.6 ;2.;

Eutd]ffl oemezkgf, 028:::9, 5;;2.


260/568

60

Prfg kg ùvere ftlksk ùver g trfgfftlkskg`fg èbe jyl.


261/568

66

. -

Jkr A luvvftk o 5 ltcfskgf uymuceg gie dge 9.>>o/s : ckl kvof lezeg` roelte` r. Eyg luvvft oltcfskgf uymuceg gie ju ltcfyf 5.>> o/s :

.(e) o 5/o : ltcfcfr dreg gf`kr4

(j) 5 f : lt f f k jk ftk k k fA L ftk k j


262/568

(j) o 5 vf o : ltcfcfrk jkrcftkrkckrsfA Luvvftkgkg jultcfcfrf lezeg` r` kvof k bfse ce g z.

61

. -

A ? o 5e ? o 59 vf A ? o : e ? o : 5

o 5e ? o 59 ? o : e ? o : 5 jure`ego 5/ o : ? 5 / 9? ?

5

:

:

:


263/568

5 : : :? (0o : /9)e ? Ae ? 9A/(0o : ) ? 9o : 5/(0o : ) ? 9/0 o/s :

6=

. -

9.>>-lm c l jkr gfsgfyf e ? (:.>> k + 6.>> h)o/s : ckl jkr kvof lezeg` r coelte` r.Iksof ftlk f`fg luvvftk bfsepcey g z.

A ? o e ? 9.>> (:.>> k + 6.>> h) ? 1.>>k +56 >>hGf tdg


264/568

56.>> hGfwtdg: : .

62

rgfl 6.59-Ydru

A vf A luvvftcfrk 6.>>-l c l jkr gfsgf f ftlkofltf`kr. A ? :>.> G vf A ? 56.> G ksf (e) vf (j) `uruocer kkg kvofcfrk bfsepcey g z.

Ifvep 8

(e) e ? (A5 + A: )/o ? (:> k+56h) / 6 ? (0 k+9h) vf | e | ? (0:+9

:) ? :6 ? 6 o/s

:


265/568

(e) e ? (A + A )/o ? (:> k+56 h) / 6 ? (0 k+9 h) vf | e | ? (0 +9 ) ? :6 ? 6 o/s(j) e ? (A5 + A: )/o ? (:> k+(=.6k+59 h) / 6 ? (:=.6 k+59 h) vf | e | ? (:=.6 : +59: ) ? ;:6.:6 ?

.

6;

rgfl 6.50-Ydru flkc`flk skstfocfr `fgmf`f`kr. c ecftkGfwtdg e mrf slececeg` r co t r.Dlugeiel `f frcfr gfcfr dcejkckr4Oelerecer`e vf `zcfocfr`f srtgofgkgdcoe` g lejuc f`kgkz.

e) P - om ? > ksfP ? om ? 6 x 5>

? 6> G

om ? sf ? om ? vflegter`elk mfrkcof


266/568

legter elk mfrkcofP ? :P ? : x 6>

?

i) P omskg(9>) ? > ksf

1>

.? :6 G

. - [egèlk flckg sfrjfst

iksko k e reo g kzkgkz. Iksko kcf fkl`zcfo eres gèsrtgof dltur. F koe s ? 56.> `kr.

Iksko f kl `zcfokgùruoèg berflftfje cer vf :.>> o ckl

ee ye `d ru leyer e)ik k k f k k (j)


267/568

ee ye d ru leyer. e)iksokg kvofskgk, (j)

b z g bfsepcey g z.

15

. -

om skg56?oeG-omids56?>

Ykstfocf kcmkck `fglcfocfr yuler `elk mkjk ksf(e) e ? m skg56 ? :.1 o/s:

(j) v : sdg ? v : kcl+ : e ` ? > + : : 1 : ?5> 0


268/568

(j) v g ? v + : e ? > + : :.1 : ?5>.0vsdg ? 9.:: o/s

1:

Yrtgofskz jkr `zcfo zfrkg`flk

ltcfyf flkc`flk mkjk A ? 52G cul jkr luvvft o ltcfsk -terea g`eg ftlkofltf`kr. o 5 ?:.>> lm, o : ? 9.>> lm, o 9 ?0.>> l dcerel vfrkcofltf`kr.

(e) Ltcfcfrkg sebkp dc`uu kvofyk,(j) Bfr jcd e uymucegeg jkcflf

uvvf ,(i) Jcdlcer eres ldgtel luvvftcfrkgk

bfsepcey g z.

Ifvep 8e) A ? ko ke ? (o 5 + o : + o 9) e ? (: + 9 + 0) e ? 52 kae`fskg`fg e ? 52 / ; ? : o/s :ltcfcfr skstfokgkg kvofsk`kr.


269/568

j) o ltcfskgf ftlk f`fg luvvft eyg zeoegè o ltcfskgf `f ftlk f`fr. vofcfrk ksfjkrez gif bfsepcegeg `f fr`kr. Ju klk ltcfyf ftlk f`fg luvvft ksf A : ? (o : + o 9) e ?(9.>> + 0.>>) : ?50 G, oi ltcfyf ftlk f`fg luvvft ksf A

9? (o

9) e ? 0 : ? 2 G ùr.

19i) o 5 kcf o: ltcfcfrk eres gèlk luvvft 50 G, o : kcf o9 ltcfcfrk eres gèlk ftlkcf ofluvvftk 2 G ùr.

. -eour kkg`f leco ereje jkr flkik ere terea gèg :6>> G cul luvvft kcf

flkcofltf`kr. flof becet g g jkr uiu erejeye `k fr uiu flkikyf je cego t r.flof becet luvvftk E vf J ldccer ge è toelte` r. E vf J ujulcer zfrkg`flkluvvftcfrk bfsepcey g z. Luvvftcfr kkg sfrjfst iksko `kyemreo g kzkgkz.


270/568

10

. Jkr lkk eyel ucer zfrkg`f ùroeye ec rse `fgmf beckg`f e e èlkflkc`flk e ùruou drte e ler. j `flk flkc ksf e èlkgkg jfgzfrk`kr. A

yfrkg ktof luvvftk (yeè lk kgkg e rc ksf) ksf ekc tfg`dgugèlk P mfrkcofskgkvf eyel tejeg zfrkg`flk B vf Q luvvftcfrkgk bfsepcey g z.


271/568

16

rgfl 6.5= E kc tfg`dguP + B A ? > ?7 Pskg 9> + B - Askg 9> ? >

Py Q + Ay ? > ?7 Pids(9>) - Q + Aids(9>) ? >

Drte`elk gdlte zfrkg`flk `gof odofgtcfrkg`fgee `elk kae`fcfr yez cejkckr8

Py (C/0) ? Ay (9C/0)A ? => l ksf Py ? 9 => >.211 ? 525.2= lmJu `fglcfo`fg

P ? :5> lm:5> skg(9>) + B => skg(9>) ? >


272/568

:5> skg(9>) + B - => skg(9>) ? >

Ju `fglcfocfr`fg

B ? -5>6 + 96 ? -=> l11Q ? :0:.0; lm

dcerel bfsepceg r.

. Jkr lkk evuiugug kkg`f e rc :> G dceg jkr ltcf tutoelte` r. Ldc lescer ge ftlk f`fg

uvvf fr e e

e e vf f fr g f m s fr of f r. s fo fgmf f sfflckg`fg yerercegerel lestelk mfrkcofyk bfsepcey g z. l.o kcf jfckrtkcfg gdlte ldcug`krsfltfg e e `elk l so g g e rc l ofrlfzk`kr.


273/568

Ju (j) flckgf mrf `fgmf`flk skstfo kkg luvvft f ktcklcfrk(`gof `krsfltf dcoelte` r) ee èlk mkjk dcur8

1=Ples ids(:>)>.>96-16 >.5>-:>>.96?>

Ples ?05>6 Gfwtdgdcerel bfsepceg r.

1 @ekrfsfc Berflft vf Gfwtdgese er g g fr ymu eoe er

1.5 @zmg èkrfsfc berflftf Gfwtdg ug klkgikyeses g g uymucegoes 1.: @z g dcoe eg ekrfsfc berflft 1.9 vofck frfvfcfr`f berflft

1.0 @krfg luvvftcfrkgkg dcùu drteocerè1.6 êrei l `kgeok kg`f sey sec od`fccfofcfr


274/568

Cdg`re g g mz, Pbeofs gfbrkgkg5

lfger gèlk ` fy `d ructuèèkrfsfc berflft f`fg ju `gof`dcep kcffbkr sfyrf`kcfjkcofltf`kr.

@ekrfsfc Berflft vf Gfwtdg [esecer g g`kfr Vymuceoecer

giflk lfskocfr`f berflft f`fg ikskocfrf Gfwtdg

yepeg skstfocfrf uymuceoecer kgifcfg`k. Ju jco`f ksf

jkrez èbe leroe l berflftcfr rgf kg èkrfsfcrg f`f `dcegeg ikskocfrkg berflftcfrkgf kvofck

mzcfo frfvfcfrkgk vf el leg kkg`flk gfsgfcfrkg


275/568

g g g g g g

erf ft fr gf fwtdg yese er g g uymu e eoe er

egcet ceielt r.:

Gfwtdg ug klkgik yeses g g `zmg èkrfsfcberflftf uymucegoes

Jkr perei l sejkt jkr v sretkycfr yer epc èkrfsfc yrgmfzfrkg`f berflft f`kydrse kvofsk e e èlk mkjk`kr8


276/568

Ju kvof ofrlfzikc kvof ( ifgtrkpftec eiifcfretkdg ) dcerel kskocfg`krkckr. gl ei `ekrfgkgofrlfzkgf `d ru ygfcoktkr. Eyr ie e i bfr zeoeg v yf `kltkr. Ffr v yf perecfc jkr kvof

9

.

Gfwtdg ug klkgik yeses g g `zmg`ekrfsfc berflftf uymucegoes


277/568

0Frfa Epel :>>0 Etkgedckopkyetcer gè flk etoeè9gicl et g e erlfg.

Gfwtdg ug klkgik yeses g g `zmgèkrfsfc berflftf uymucegoes

Gfwtdg ug klkgik yeses

g

re`yec `d ructu kkg uymucersel ofrlfzikc kvofyk dcuturegluvvft e e èlk mkjk`kr 8


278/568

[egèlk flkc`flk kpf je c tdpe jelerseg z kpldper c gè tdp ert l kzmksfc betflftf yegk b z

èkrfsfc yrgmfyf bfr zeoeg tf ft dceg jkr6

berflftf je cer. Iksokg kp ldptulteg sdgrelkberflftk Gfwtdg ug jkrkgik yeses ge mrfe lcegejkckr.

tevege sejktcfgok Cuzugculcu jkr kpkguiuge je cego vf r yer epc èkrfsfcyrgmf zfrkg`f v sejkt b z kcf jkr `zcfo`zcfok kfrkskg`f`gofltf`kr (ldgklserle - idgkiec

pfgùcuo ). v

genel fizik 1 - full ders notları (sunum)

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