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"`kjislmu`krplysias.ij" ;

J SEJQ B ^ EO @ESIEJ;. OEWAH

K pubb er pusl wlial alkjnhs er thjcs te alkjnh tlh stkth eo rhst er eo ujioer` `etiej er cirhatiej eo `etiej

eo kjy egfhat is akbbhc oerah. Oerah is tlh ijthrkatiej ghtwhhj tlh egfhat kjc tlh seurah (previcijn tlh pubber pusl). It is k vhater qukjtity.

Hoohat eo rhsubtkjt oerah 6(;) `ky alkjnh ejby sphhc

(7) `ky alkjnh ejby cirhatiej eo `etiej.

(1) `ky alkjnh getl tlh sphhc kjc cirhatiej eo `etiej.

(3) `ky alkjnh sizh kjc slkph eo k gecy

Xjit eo oerah 6 Jhwtej kjc 7s

`mn (@MQ Qysth`)

cyjh kjc 7s

a`n(ANQ Qysth`)

; Jhwtej 0 ;48 cyjh

Mibenrk` oerah (mno)

Slh oerah witl wlial hkrtl kttrkats k ;mn gecy tewkrcs its ahjtrh is akbbhc mibenrk` oerah, tlus

mno 0n

jhwtejijOerhah

Ci`hjsiejkb Oer`ubk eo oerah 6 ]@BS7 P;.; Oujck`hjtkb OerahsKbb tlh oerahs egshrvhc ij jkturh sual ks `usaubkr oerah, thjsiej, rhkatiej, oriatiej, hbkstia, whinlt,

hbhatria, `knjhtia, juabhkr, hta., akj gh hxpbkijhc ij thr s eo ejby oebbewijn oeur gksia ijthrkatiejs6

] K P Nrkv i tkt iejkb OerahSlh oerah eo ijthrkatiej wlial hxists ghtwhhj twe pkrtiabhs eo `ksshs `

;kjc `

7, cuh te tlhir

`ksshs is akbbhc nrkvitktiejkb oerah.

rr

``NO

1

7;

r

0 pesitiej vhater eo thst pkrtiabh S witl rhsphat te seurah pkrtiabh Q. kjc N 0 uji vh rs kb

nrkvitktiejkb aejstkjt

0 ?.?> ;4;; J`7/mn7.

(i) It is tlh whkmhst oerah kjc is kbwkys kttrkativh.

(ii) It is k bejn rkjnh oerah ks it kats ghtwhhj kjy twe pkrtiabhs situkthc kt kjy cistkjah ij tlh

ujivhrsh.

(iii) It is ijchphjchjt eo tlh jkturh eo hciu` ghtwhhj tlh pkrtiabhs.

Kj kppbh is orhhby okbbijn ks slewj ij oinurh, ^lhj it is kt k lhinlt l, oerah ghtwhhj hkrtl kjc kppbh

is nivhj gy

O 0 7h

h

)lW(

`N@

wlhrh hkrtleorkciusWhkrtl,eo`kss@ hh

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TLYQIAQ

"`kjislmu`krplysias.ij" 7

It kats tewkrcs hkrtls ahjtrh. Jew rhkrrkjnijn kgevh rhsubt,

O 0 ` . 7h

h

W

N@.

7

h

h

lW

W

O 0 `n

7

h

h

lW

W

7

h

h

W

N@n

Lhrh l 22 Wh, se

lW

W

h

h

;

O 0 `nSlis is tlh oerah hxhrthc gy hkrtl ej kjy pkrtiabh eo `kss ` jhkr tlh hkrtl surokah. Slh vkbuh eo

n 0 9.6;4-1. QTWIJN OEWAH 6Hvhry sprijn rhsists kjy ktth`pt te alkjnh its bhjntl= wlhj it is ae`prhsshc er hxthjchc, it hxhrts oerah kt

its hjcs. Slh oerah hxhrthc gy k sprijn is nivhj gy O 0 -mx, wlhrh x is tlh alkjnh ij bhjntl kjc m is tlh

stioojhss aejstkjt er sprijn aejstkjt (ujit J` -;).

^lhj sprijn is ij its jkturkb bhjntl, sprijn oerah is zhre.

O 0 4

O 0 mx

Hxk`pbh ;>. Swe gbeams krh aejjhathc gy k sprijn eo jkturkb bhjntl 7 `.

Slh oerah aejstkjt eo sprijn is 744 J/`.

Oijc sprijn oerah ij oebbewijn situktiejs 6

(k) Io gbeam K kjc G getl krh cispbkahc gy 4.8 ` ij sk`h cirhatiej.

(g) Io gbeam K kjc G getl krh cispbkahc gy 4.8 ` ij eppesith cirhatiej.

Qebutiej 6 (k) Qijah getl gbeams krh cispbkahc gy 4.8 ` ij sk`h cirhatiej, se alkjnh ij bhjntl eo sprijn is

zhre. Lhjah, sprijn oerah is zhre.

(g) Ij tlis aksh, alkjnh ij bhjntl eo sprijn is ; `. Ij aksh eo hxthjsiej er ae`prhssiej eo sprijn,

sprijn oerah is O 0 Mx 0 (744) . (;)

O 0 744 J

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"`kjislmu`krplysias.ij" ;8

Hxk`pbh ;.; Qprijn Gkbkjah 6It cehs jet `hksurh tlh whinlt.t `hksurhs tlh oerah hxhrthc gy

tlh egfhat kt tlh leem.

Qy`gebiakbby, it is rhprhshjthc ks slewj ij oinurh.

K gbeam eo `kss ` is susphjchc kt leem.

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TLYQIAQ

"`kjislmu`krplysias.ij" ;?

^lhj sprijn gkbkjah is ij hquibigriu`, wh crkw tlh O.G.C. eo `kss ` oer akbaubktijn tlh rhkcijn eo

gkbkjah.

O.G.C. eo `.

`n S 0 4

S 0 `n

@knjituch eo S nivhs tlh rhkcijn eo sprijn gkbkjah.

Hxk`pbh 74. K gbeam eo `kss 74 mn is susphjchc tlreunl twe binlt sprijn gkbkjahs ks

slewj ij oinurh. Akbaubkth tlh 6

(;) rhkcijn eo sprijn gkbkjah (;).

(7) rhkcijn eo sprijn gkbkjah (7).

Qebutiej6 Oer akbaubktijn tlh rhkcijn, oirst wh crkw O.G.C. eo 74 mn gbeam.

O.G.C eo 74 mn.

`n S 0 4

S 0 74 n 0 744 J

Qijah getl gkbkjahs krh binlt se, getl tlh sakbhs wibb rhkc 74 mn.

< . AEJQSWKIJHC @ESIEJ6

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"`kjislmu`krplysias.ij" ;>

egfhat se tkmh tlh vhbeaity eo tlh egfhat kbejn tlh bhjntl eo tlh strijn 7;; __

ct

c

Skmh pesitivh sinj io it thjcs te ijarhksh tlh bhjntl kjc jhnktivh sinj io it thjcs te charhksh tlh

bhjntl. Lhrh +_;

rhprhshjts tlkt upphr hjc is thjcijn te ijarhksh tlh bhjntl kt rkth _;

kjc bewhr hjc

is thjcijn te ijarhksh tlh bhjntl kt rkth _7.

Qthp 8. Whphkt kbb kgevh sthps oer cioohrhjt-cioohrhjt strijns.

Bht us aejsichr k pregbh` nivhj ghbew

_T

_7_;

_T

;7

Lhrh ;+

70 aejstkjt

ct

c ;+ 4

ct

c 7

(_; _

T) + (_

T _

7) 0 4

_p

0 ; 7_ _

7

Qi`ibkrby,

kT

0 ; 7k k

7

Wh`h`ghr tlis rhsubt

Hxk`pbh 7;. Swe gbeams eo `ksshs `;

kjc `7

krh kttkalhc kt tlh hjcs eo kj ijhxthjsigbh

strijn wlial pksshs evhr k s`eetl `kssbhss pubbhy. Io `;: `

7, oijc 6

(i) tlh kaahbhrktiej eo hkal gbeam

(ii) tlh thjsiej ij tlh strijn.

`7

`;

Qebutiej 6 Slh gbeam `; is kssu`hc te gh `evijn cewjwkrc kjc tlh gbeam ` 7 is kssu`hc te gh `evijnupwkrc. It is `hrhby kj kssu`ptiej kjc it cehs jet i`pby tlh rhkb cirhatiej. Io tlh vkbuhs eo k;

kjc k7

ae`h eut te gh pesitivh tlhj ejby tlh kssu`hc cirhatiejs krh aerrhat= etlhrwish tlh gecy `evhs ij

tlh eppesith cirhatiej. Qijah tlh pubbhy is s`eetl kjc `kssbhss, tlhrhoerh, tlh thjsiej ej hkal

sich eo tlh pubbhy is sk`h.

Slh orhh gecy ciknrk` eo hkal gbeam is slewj ij tlh oinurh.

O.G.C. eo `7

O.G.C. eo `;

Kppbyijn Jhwtejs shaejc Bkw ej gbeams `;kjc `

7

Gbeam `;

`;n S 0 `

;k

; .............(;)

Gbeam `7

`7n + S 0 `

7k

7 .............(7)

Ju`ghr eo ujmjewjs 6 S, k;

kjc k7

(tlrhh)

Ju`ghr eo hquktiejs6 ejby tweEgvieusby, wh rhquirh ejh `erh hquktiej te sebvh tlh pregbh`. Jeth tlkt wlhjhvhr ejh oijcs tlh

ju`ghr eo hquktiejs bhss tlkj tlh ju`ghr eo ujmjewjs, ejh `ust tlijm kgeut tlh aejstrkijt rhbk-

tiej. Jew wh krh neijn te hxpbkij tlh `ktlh`ktiakb preahcurh oer tlis.

Lew te chthr`ijh Aejstrkijt Whbktiej 5

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TLYQIAQ

"`kjislmu`krplysias.ij" ;. K biot lkvijn k si`pbh phjcubu` kttkalhc witl its ahibijn is `evijn upwkrc witl aejstkjt kaahbhrktiej

k. ^lkt wibb gh tlh thjsiej ij tlh strijn eo phjcubu` witl rhsphat te k gey ijsich tlh biot kjc k geystkjcijn ej hkrtl, `kss eo geg eo si`pbh phjcubu` is `.

Qebutiej 6 O.G.C. eo geg (witl rhsphat te nreujc)

S `n 0 `kS 0 `n + `k ........(i)

^itl rhsphat te gey ijsich tlh biot, tlh kaahbhrktiej eo geg is zhre.

Qe lh wibb writh kgevh hquktiej ij tlis kjjhr.

S `n 0 `. (4) .

S 0 `n

Lh wibb thbb tlh vkbuh eo thjsiej ij strijn is `n. Gut tlis is wrejn . Se aerrhat lis rhsubt, lh `kmhs k

orhh gecy ciknrk` ij tlis `kjjhr, kjc ushs Jhwtejs shaejc bkw.

S 0 `n + `k ..................(ii)

Gy usijn tlishxtrk oerah, hquktiejs (i) kjc (ii) nivh tlh sk`h rhsubt . Slishxtrk oerah is akbbhc

pshuce oerah. Slis pshuce oerah is ushc wlhj k pregbh` is sebvhc witl k kaahbhrktijn ork`h (Jej-

ijhrtikb)

Jeth 6 @knjituch eo Tshuce oerah0 `kss eo systh` kaahbhrktiej eo ork`h eo rhohrhjah .

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"`kjislmu`krplysias.ij" 71

Cirhatiej eo oerah 6

Eppesith te tlh cirhatiej eo kaahbhrktiej eo ork`h eo rhohrhjah, (jet ij tlh cirhatiej eo `etiej eo ork`h eo

rhohrhjah)

Hxk`pbh 7

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"`kjislmu`krplysias.ij" 73

Tregbh` ;. Crkw jer kb oerahs ej tlh kssivh rec kt peijt ; kjc 7 ks slewj ij oinurh.

Qebutiej 6 Jer kb oerah kats phrphjciaubkr te hxthjchc surokah kt peijt eo aejtkat.

Tregbh` 7. Slrhh trikjnubkr gbeamsK,G kjc A eo hqukb `ksshs ` krh krrkjnhc ks slewj ij oinurh. Crkw O.G.C.

eo gbeams K,G kjc A. Ijciakth katiejrhkatiej pkir ghtwhhj K,G kjc G,A.

Qebutiej 6

Tregbh` 1. Slh systh` slewj ij oinurh is ij hquibigriu`, oijc tlh thjsiej

ij hkal strijn =

S;,S

7,S

1, S

3kjc S

8.

Kjswhr 6 S;0 S

70

1

744J, S

30 S

80 744 J, S

10

1

744J.

Qebutiej 6 OGC eo 74 mn gbeam

S

74n

74 mn

Qe, S 0 74 n 0 744 J ............ (;)

Ore` oinurh

S aes147

S

S aes14;S sij147 S sij147

S 0 S;aes14 + S

7aes14 .......... (7)

S;sij14 0 S

7sij14

S;

0 S7

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

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"`kjislmu`krplysias.ij" 78

se ore` hquktiej (1) S 0 7S;aes14

S;

01

7440 S

7 .......... (3)

Ore` oinurh OGC eo peijt G

S sij?43

S aes?43

S aes14;

S sij14;S1

GIj vhrtiakb cirhatiej

Qe, S3aes?4 0 S

;aes14

S3

7

;0

7

1

1

744 0 744 J

Qe, S30 744 J

OGC eo peijt A

S sij147

S aes?48

S aes147

S sij?48

S1

A

Hquktijn oerahs Ij vhrtiakb cirhatiej -

S8aes?40 S

7aes14

S8

7

;0

1

744

7

1

S80 744 J

Oer S1

Hquktijn oerahs ij lerizejtkb cirhatiej -

S1

+ S7sij14 0 S

8sij?4

S10 744 7

1

1

744

7

;

S10 J1

7

Tregbh` 3. Slh grhkmijn strhjntl eo tlh strijn aejjhatijn wkbb kjc gbeam

G is ;>8 J, oijc tlh `knjituch eo whinlt eo gbeam K oer wlial

tlh systh` wibb gh stktiejkry. Slh gbeam G whinls >44 J.

(n 0 ;4 `/s7)

Qebutiej 6 OGC eo gbeam G

@n

;>8J ;>8JG

J

OGC eo peijt ij oinurh

S'

;>8J Saes14

Ssij14

Hquktijn oerahs ij lerizejtkb cirhatiej

Saes14 0 ;>8

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TLYQIAQ

"`kjislmu`krplysias.ij" 7?

S 01

7;>8 J

Ij vhrtiakb cirhatiej Ssij14 0 S

Qe, S01

;>8

7

;

1

7;>8

J

OGC eo gbeam K

^

S'

K

Qe, S0 ^ 0 1>8

J

Tregbh` 8. Ij tlh krrkjnh`hjt slewj ij oinurh, wlkt sleubc gh tlh

`kss eo gbeam K se tlkt tlh systh` rh`kijs kt rhst. Kbse

oijc oerah hxhrthc gy strijn ej tlh pubbhy [. (n 0 ;4 /s7)

Kjs. ` 0 1 mn, 114 J.

Qebutiej 6 Ore` oinurh

OGC eo 7 mn gbeam lkjnijn vhrtiakbby

7n

7mn

S

S 0 74 J ............. (;)

OGC eo 7mn gbeam ej ijabijh pbkjh

J

7n

7naes147n

sij14

S'

S

14

Kbejn tlh pbkjhS + 7nsij14 0 S

S 0 74 +7

;74 0 14 J

OGC eo gbeam K

@ nK

K

S'

Qe S0 @K

n

@K0 n

'S

0 ;4

14

0 1 mn

@K

0 1 mn

OGC eo pubbhy [

?4

S'

W S'

[

Qe, W 0 7Saes7

W 0 714aes14

W 0 7 14 7

1

W 0 1 J

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TLYQIAQ

"`kjislmu`krplysias.ij" 7. K gbeam eo `kss 7 mn is mhpt kt rhst ej k gin gex `evijn witl vhbeaity

i7 kjc lkvijn kaahbhrktiej f3i1 `/s7. Oijc tlh vkbuh eo Tshuce

oerah katijn ej gbeam witl rhsphat te gex

Kjswhr 6 ork`hpshuce k`O

0 )f3i1(7

O 0 f