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bdkbZµ14% cksey ,oa Vksfcu dk ;ksxnku
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2- udnh 'ks"k blfy, j[ks tkrs gSa fd ,d lkFk ugha gksrsA uksV
lehdj.k (2) ls Li"V gS fd ;fn nykyh c<+ tk,xh] rks fudklksa dh la[;k de gks tk,xhA nwljs 'kCnksa esa]
b"Vre udnh 'ks"k c<+ tk,xk] D;ksafd iQeZ ckaMksa esa de fuos'k djsxhA nwljh vksj] ;fn ckaMksa ij C;kt dh nj
c<+ tk,xh] rks iQeZ osQ fy, ckaMksa esa fuos'k djuk vfèkd ykHknk;d gksxk vkSj b"Vre udnh 'ks"k vis{kkÑr de
gks tk,¡xs vkSj foykse'k% HkhA
cksey dk fo'ys"k.k ysu&nsu 'ks"kksa dh ek¡x osQ O;ogkj osQ izfr ,d vkSj egÙoiw.kZ rF; dks y{; djrk gSA tc
dksbZ iQeZ ;k O;fDr cM+h la[;k esa ckaM [kjhnrk gS] rks mlosQ ikl ysu&nsu 'ks"k FkksM+s jg tkrs gSa vkSj foykse'k%
HkhA ijarq izR;sd Ø; esa nykyh] Mkd&O;; bR;kfn osQ :i esa xSj&C;kt ykxrsa ikbZ tkrh gSa tks [kjhnus okys dks
nsuh iM+rh gSaA blfy, mls cM+h la[;k esa ckaM [kjhnus ij gksus okys O;; osQ eqdkcys de ckaM [kjhnus ls gksus
okyh vk; dh deh dks larqfyr djuk iM+rk gSA ;g fu.kZ; ckaMksa ij feyus okyh C;kt nj ij fuHkZj djrk gSA
C;kt dh nj ftruh gh vfèkd gksxh] iQeZ ckaM [kjhnus esa mruk gh vfèkd [kpZ [kik losQxhA bl fu.kZ; dks
fuèkkZfjr djus okyk ,d vkSj Hkh egÙoiw.kZ dkj.k eqnzk dh og jkf'k gS tks ysu&nsu osQ fy, j[kh tkrh gS D;ksafd
ckaM [kjhnus vkSj cspus dh nykyh vis{kkÑr fLFkj jgrh gS vkSj ysu&nsu dh jkf'k dh vis{kk vfèkd ugha
cnyrhA tc ysu&nsu osQ fy, eqnzk vfèkd gksxh] rks nykyh ykxrsa vis{kkÑr de gksaxhA ¶,d gtkj Mkyj osQ
ckaM [kjhnus ij U;wure nykyh egaxh iM+sxhA nl yk[k Mkyj osQ ckaM [kjhnus ij nykyh ux.; (negligible)
gksxhA blfy, oqQy ysu&nsu dh jkf'k;k¡ ftruh gh vfèkd gksaxh] nykyh dh ykxrsa mruh gh de gksaxh] vkSj mrus
dh ckj&ckj b"Vre fudkl fd, tk,axsA¸ ,slk udnh izcaèk vFkok eqnzk osQ iz;ksx esa iSekus dh cprksa osQ dkj.k
gksrk gSA
bldk eryc gS fd vk; osQ vfèkd Å¡ps Lrjksa ij ysu&nsu dh vkSlr ykxr vFkkZr~ nykyh vis{kkÑr de gksrh
gSA T;ksa&T;ksa vk; c<+rh gS] R;ksa&R;ksa eqnzk dh ysu&nsu ek¡x Hkh c<+rh tkrh gS ij ;g o`f¼ vk; esa o`f¼ dh vis{kk
de ek=kk esa gksrh gSA ;fn vk; pkj xq.kk c<+rh gS] rks b"Vre ysu&nsu 'ks"k osQoy nqxus gksrs gSaA D;ksafd cksey
eqnzk ek¡x dh vk;&yksp 1@2 (vkèkh) ekurk gS] blfy, ftl vuqikr esa vk; c<s+xh] eqnzk dh ek¡x mlh vuqikr
esa ugha c<+sxhA ,slk iSekus dh cPkrksa osQ dkj.k gksrk gSA vk; esa o`f¼ gksus osQ dkj.k tc ysu&nsu esa yxkbZ xbZ
eqnzk dh jkf'k vis{kkÑr vfèkd gksrh gS rc iSekus dh cprsa ckaMksa esa vfèkd fuos'k dks izksRlkgu nsrh gSaA eqnzk
dh ek¡x osQ bl LVkWd fl¼kar esa cksey bl ckr ij Hkh cy nsrk gS fd eqnzk dh ek¡x okLrfod 'ks"kksa osQ fy,
ek¡x gksrh gSA D;ksafd o"kZ&Hkj vkSlr udnh èkkj.kksa dk ewY; K/2 gS] blfy, ysu&nsu osQ fy, okLrfod 'ks"kksa
dh ek¡x ;g gksxh%
M K 2bY
D =
P 2 r
M = 12bY P ---(3)
D
2 r
tgk¡ M eqnzk dh ek¡x gS vkSj dher Lrj gSA lehdj.k (3) ls irk pyrk gS fd ysu&nsu 'ks"kksa dh ek¡x¸
D
ysu&nsuksa dh ek=kk osQ oxZewy osQ lekuqikrh vkSj C;kt dh nj osQ oxZewy osQ izrhikuqikrh (inverse) gksrh gSA¸
bldk eryc gS fd Lrj esa ifjorZuksa vkSj eqnzk dh ysu&nsu ek¡x osQ chp izR;{k ,oa lekuqikfrd lacaèk gksrk
gSA ;fn iQeZ osQ Ø; dk <k¡pk vifjo£rr jgrk gS] rks b"Vre udnh 'ks"k (Y) Bhd mlh vuqikr esa c<sa+xs ftl
vuqikr esa dher Lrj (P) c<+sxkA ;fn dher Lrj nks xq.kk gks tk,xk] rks iQeZ osQ ysu&nsu dk eqnzk ewY; Hkh
nks xq.kk gks tk,xkA tc lc dhersa nks xq.kh gks tk,axh] rks nykyh (b) Hkh nksxquh gks tk,xhA ¶ifj.kker% fuo'kksa
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