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TLYQIAQ
"`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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TLYQIAQ
"`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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TLYQIAQ
"`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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TLYQIAQ
"`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