NCERT Textbook - मात्रक और मापन Notes | EduRev

NCERT Hindi Textbooks (Class 6 to Class 12)

UPSC : NCERT Textbook - मात्रक और मापन Notes | EduRev

 Page 1


vè;k; 2
ek=kd ,oa ekiu
2.1  Hkwfedk
fdlh HkkSfrd jkf'k dk ekiu] ,d fuf'pr] vk/kjHkwr] ;kn`fPNd :i ls pqus
x, ekU;rkizkIr] lanHkZ&ekud ls bl jkf'k dh rqyuk djuk gSA ;g lanHkZ&ekud
ek=kd dgykrk gSA fdlh Hkh HkkSfrd jkf'k dh eki dks ek=kd osQ vkxs ,d
la[;k (vkafdd la[;k) fy[kdj O;Dr fd;k tkrk gSA ;|fi gekjs }kjk ekih
tkus okyh HkkSfrd jkf'k;ksa dh la[;k cgqr vf/d gS] fiQj Hkh] gesa bu lc
HkkSfrd jkf'k;ksa dks O;Dr djus osQ fy,] ek=kdksa dh lhfer la[;k dh gh
vko';drk gksrh gS] D;ksafd] ;s jkf'k;k¡ ,d nwljs ls ijLij lacaf/r gSaA ewy
jkf'k;ksa dks O;Dr djus osQ fy, iz;qDr ek=kdksa dks ewy ek=kd dgrs gSaA buosQ
vfrfjDr vU; lHkh HkkSfrd jkf'k;kssa osQ ek=kdksa dks ewy ek=kdksa osQ la;kstu
}kjk O;Dr fd;k tk ldrk gSA bl izdkj izkIr fd, x, O;qRiUu jkf'k;ksa osQ
ek=kdksa dks O;qRiUu ek=kd dgrs gSaA ewy&ek=kdksa vkSj O;qRiUu ek=kdksa osQ
lEiw.kZ leqPp; dks ek=kdksa dh iz.kkyh (;k i¼fr) dgrs gSaA
2.2  ek=kdksa dh varjkZ"Vªh; iz.kkyh
cgqr o"kks± rd ekiu osQ fy,] fofHkUu ns'kksa osQ oSKkfud] vyx&vyx ekiu
iz.kkfy;ksa dk mi;ksx djrs FksA vc ls oqQN le;&iwoZ rd ,slh rhu
iz.kkfy;k¡ & CGS iz.kkyh] FPS (;k fczfV'k) iz.kkyh ,oa  MKS  iz.kkyh]
izeq[krk ls iz;ksx esa ykbZ tkrh FkhaA
bu iz.kkfy;ksa esa yEckbZ] nzO;eku ,oa le; osQ ewy ek=kd Øe'k% bl
izdkj gSa %
• CGS iz.kkyh esa] lsUVhehVj] xzke ,oa lsoQUMA
• FPS iz.kkyh esa] iqQV] ikmUM ,oa lsoQUMA
• MKS iz.kkyh esa] ehVj] fdyksxzke ,oa lsoQUMA
vktdy varjkZ"Vªh; Lrj ij ekU; iz.kkyh ¶flLVe bUVjus'kuy fM
;wfuV~l¸ gS (tks izsaQp Hkk"kk esa ¶ek=kdksa dh varjkZ"Vªh; iz.kkyh¸ dguk gS)A
bls laosQrk{kj esa  SI fy[kk tkrk gSA SI  izrhdksa] ek=kdksa vkSj muosQ laosQrk{kjksa
dh ;kstuk 1971 esa] ekirksy osQ egk lEesyu }kjk fodflr dj] oSKkfud]
rduhdh] vkS|ksfxd ,oa O;kikfjd dk;ks± esa varjkZ"Vªh; Lrj ij mi;ksx gsrq
2.1 Hkwfedk
2.2 ek=kdksa dh varjkZ"Vªh; iz.kkyh
2.3 yEckbZ dk ekiu
2.4 nzO;eku dk ekiu
2.5 le; dk ekiu
2.6 ;FkkFkZrk] ;a=kksa dh ifj'kq¼rk ,oa
ekiu esa =kqfV
2.7 lkFkZd vad
2.8 HkkSfrd jkf'k;ksa dh foek,¡
2.9 foeh; lw=k ,oa foeh; lehdj.ksa
2.10 foeh; fo'ys"k.k ,oa blosQ vuqiz;ksx
lkjka'k
vH;kl
vfrfjDr vH;kl
Page 2


vè;k; 2
ek=kd ,oa ekiu
2.1  Hkwfedk
fdlh HkkSfrd jkf'k dk ekiu] ,d fuf'pr] vk/kjHkwr] ;kn`fPNd :i ls pqus
x, ekU;rkizkIr] lanHkZ&ekud ls bl jkf'k dh rqyuk djuk gSA ;g lanHkZ&ekud
ek=kd dgykrk gSA fdlh Hkh HkkSfrd jkf'k dh eki dks ek=kd osQ vkxs ,d
la[;k (vkafdd la[;k) fy[kdj O;Dr fd;k tkrk gSA ;|fi gekjs }kjk ekih
tkus okyh HkkSfrd jkf'k;ksa dh la[;k cgqr vf/d gS] fiQj Hkh] gesa bu lc
HkkSfrd jkf'k;ksa dks O;Dr djus osQ fy,] ek=kdksa dh lhfer la[;k dh gh
vko';drk gksrh gS] D;ksafd] ;s jkf'k;k¡ ,d nwljs ls ijLij lacaf/r gSaA ewy
jkf'k;ksa dks O;Dr djus osQ fy, iz;qDr ek=kdksa dks ewy ek=kd dgrs gSaA buosQ
vfrfjDr vU; lHkh HkkSfrd jkf'k;kssa osQ ek=kdksa dks ewy ek=kdksa osQ la;kstu
}kjk O;Dr fd;k tk ldrk gSA bl izdkj izkIr fd, x, O;qRiUu jkf'k;ksa osQ
ek=kdksa dks O;qRiUu ek=kd dgrs gSaA ewy&ek=kdksa vkSj O;qRiUu ek=kdksa osQ
lEiw.kZ leqPp; dks ek=kdksa dh iz.kkyh (;k i¼fr) dgrs gSaA
2.2  ek=kdksa dh varjkZ"Vªh; iz.kkyh
cgqr o"kks± rd ekiu osQ fy,] fofHkUu ns'kksa osQ oSKkfud] vyx&vyx ekiu
iz.kkfy;ksa dk mi;ksx djrs FksA vc ls oqQN le;&iwoZ rd ,slh rhu
iz.kkfy;k¡ & CGS iz.kkyh] FPS (;k fczfV'k) iz.kkyh ,oa  MKS  iz.kkyh]
izeq[krk ls iz;ksx esa ykbZ tkrh FkhaA
bu iz.kkfy;ksa esa yEckbZ] nzO;eku ,oa le; osQ ewy ek=kd Øe'k% bl
izdkj gSa %
• CGS iz.kkyh esa] lsUVhehVj] xzke ,oa lsoQUMA
• FPS iz.kkyh esa] iqQV] ikmUM ,oa lsoQUMA
• MKS iz.kkyh esa] ehVj] fdyksxzke ,oa lsoQUMA
vktdy varjkZ"Vªh; Lrj ij ekU; iz.kkyh ¶flLVe bUVjus'kuy fM
;wfuV~l¸ gS (tks izsaQp Hkk"kk esa ¶ek=kdksa dh varjkZ"Vªh; iz.kkyh¸ dguk gS)A
bls laosQrk{kj esa  SI fy[kk tkrk gSA SI  izrhdksa] ek=kdksa vkSj muosQ laosQrk{kjksa
dh ;kstuk 1971 esa] ekirksy osQ egk lEesyu }kjk fodflr dj] oSKkfud]
rduhdh] vkS|ksfxd ,oa O;kikfjd dk;ks± esa varjkZ"Vªh; Lrj ij mi;ksx gsrq
2.1 Hkwfedk
2.2 ek=kdksa dh varjkZ"Vªh; iz.kkyh
2.3 yEckbZ dk ekiu
2.4 nzO;eku dk ekiu
2.5 le; dk ekiu
2.6 ;FkkFkZrk] ;a=kksa dh ifj'kq¼rk ,oa
ekiu esa =kqfV
2.7 lkFkZd vad
2.8 HkkSfrd jkf'k;ksa dh foek,¡
2.9 foeh; lw=k ,oa foeh; lehdj.ksa
2.10 foeh; fo'ys"k.k ,oa blosQ vuqiz;ksx
lkjka'k
vH;kl
vfrfjDr vH;kl
vuqeksfnr dh xbZA SI ek=kdksa dh 10 dh ?kkrksa ij vk/kfjr
(nkf'ed) izo`Qfr osQ dkj.k] bl iz.kkyh osQ varxZr :ikarj.k
vR;ar lqxe ,oa lqfo/ktud gSA ge bl iqLrd esa SI  ek=kdksa
dk gh iz;ksx djsaxsA
SI esa lkr ewy ek=kd gSa] tks lkj.kh 2-1 esa fn, x, gSaA
bu lkr ewy ek=kdksa osQ vfrfjDr nks iwjd ek=kd Hkh gSa
ftudks ge bl izdkj ifjHkkf"kr dj ldrs gSa % (i) leryh;
dks.k]  d?  fp=k 2.1(a) esa n'kkZ, vuqlkj o`Ùk osQ pki dh
yEckbZ ds vkSj bldh f=kT;k r dk vuqikr gksrk gSA rFkk
(ii) ?ku&dks.k] 
dO
 fp=k 2.1(b) esa n'kkZ, vuqlkj 'kh"kZ O dks
osQUnz dh Hkkafr iz;qDr djosQ mlosQ ifjr% fu£er xksyh; i`"B
osQ vijks/u {ks=k dA  rFkk f=kT;k r  osQ oxZ dk vuqikr gksrk
gSA leryh; dks.k dk ek=kd jsfM;u gS ftldk izrhd rad
gS ,oa ?ku dks.k dk ek=kd LVsjsfM;u gS ftldk izrhd sr gSA
;s nksuksa gh foekfoghu jkf'k;k¡ gSaA
17
(a)
(b)
fp=k 2.1  (a) leryh; dks.k d? ,oa (b) ?ku dks.k
dO
 dk vkjs[kh; fooj.k
* bu ifjHkk"kkvksa esa iz;qDr la[;kvksa osQ eku] u rks ;kn j[kus dh vko';drk gS] u ijh{kk esa iwNs tkus dhA ;s ;gk¡ ij osQoy buosQ
ekiu dh ;FkkFkZrk dh lhek dk laosQr nsus osQ fy, fn, x, gSaA izkS|ksfxdh osQ fodkl osQ lkFk ekiu dh rduhdksa esa Hkh lq/kj
gksrk gS] ifj.kkeLo:i] ekiu vf/d ifj'kq¼rk ls gksrk gSA bl izxfr osQ lkFk rkyesy cuk, j[kus osQ fy, ewy ek=kdksa dks
la'kksf/r fd;k tkrk gSA
lkj.kh 2.1 SI ewy jkf'k;k¡ ,oa muds ek=kd*
ewy                                       SI ek=kd
jkf'k uke izrhd ifjHkk"kk
yackbZ ehVj m izdk'k }kjk fuokZr esa ,d lsoaQM osQ 299, 792, 458 osa le; varjky
esa r; fd, x, iFk dh yackbZ ,d ehVj gS A (1983 ls ekU;)
nzO;eku fdyksxzke kg izaQkl esa isfjl osQ ikl lsofjl esa fLFkr varjkZ"Vªh; eki&rksy C;wjks esa j[ks
fdyksxzke osQ varjkZ"Vªh; vkfn iz:i (IysfVue&bfjfM;e feJ/krq ls cus
flfyaMj) dk nzO;eku ,d fdyksxzke osQ cjkcj gS A (1889 ls ekU;)
le; lsoaQM s ,d lsoaQM og varjky gS tks lhft+;e 133 ijek.kq osQ fuEure ÅtkZ
Lrj osQ nks vfrlw{e Lrjksa osQ eè; laØe.k osQ rnuq:ih fofdj.k osQ
9]192]631]770 vkorZ dkyksa osQ cjkcj gSA (1967 ls ekU;)
fo|qr /kjk ,sfEIk;j A ,d ,sfEi;j og fu;r fo|qr /kjk gS tks fd fuokZr esa 1 ehVj dh nwjh
ij fLFkr nks lh/s vuar yackbZ okys lekukarj ,oa ux.; o`Ùkh; vuqizLFk
dkV osQ pkydksa esa izokfgr gksus ij] bu pkydksa osQ chp izfr ehVj yackbZ
ij 2 × 10
&7
 U;wVu dk cy mRiUu djrh gS A (1948 ls ekU;)
Å"ekxfrd rki osQfYou K ty osQ f=kd&fcanq osQ mQ"ekxfrd rki osQ 1/273.16 osa Hkkx dks 1 osQfYou
dgrs gSaA (1967 ls ekU;)
inkFkZ dh ek=kk eksy mol 1 eksy fdlh fudk; esa inkFkZ dh og ek=kk gS ftlesa mruh gh ewy  lÙkk,a
gksrh gSa ftruh 0.012 kg dkcZu&12 esa ijek.kqvksa dh la[;k gksrh gSA
(1971 ls ekU;)
T;ksfr&rhozrk oSaQMsyk cd oSaQMsyk] fdlh fn'kk esa 540 × 10
12 
Hz vko`fÙk okys Ïksr dh T;ksfr&rhozrk
gS tks ml fn'kk esa (1@683) okV izfr LVsjsfM;u dh fofdj.k rhozrk
dk ,do.khZ; izdk'k mRlftZr djrk gS (1979 ls ekU;)
ek=kd ,oa ekiu
Page 3


vè;k; 2
ek=kd ,oa ekiu
2.1  Hkwfedk
fdlh HkkSfrd jkf'k dk ekiu] ,d fuf'pr] vk/kjHkwr] ;kn`fPNd :i ls pqus
x, ekU;rkizkIr] lanHkZ&ekud ls bl jkf'k dh rqyuk djuk gSA ;g lanHkZ&ekud
ek=kd dgykrk gSA fdlh Hkh HkkSfrd jkf'k dh eki dks ek=kd osQ vkxs ,d
la[;k (vkafdd la[;k) fy[kdj O;Dr fd;k tkrk gSA ;|fi gekjs }kjk ekih
tkus okyh HkkSfrd jkf'k;ksa dh la[;k cgqr vf/d gS] fiQj Hkh] gesa bu lc
HkkSfrd jkf'k;ksa dks O;Dr djus osQ fy,] ek=kdksa dh lhfer la[;k dh gh
vko';drk gksrh gS] D;ksafd] ;s jkf'k;k¡ ,d nwljs ls ijLij lacaf/r gSaA ewy
jkf'k;ksa dks O;Dr djus osQ fy, iz;qDr ek=kdksa dks ewy ek=kd dgrs gSaA buosQ
vfrfjDr vU; lHkh HkkSfrd jkf'k;kssa osQ ek=kdksa dks ewy ek=kdksa osQ la;kstu
}kjk O;Dr fd;k tk ldrk gSA bl izdkj izkIr fd, x, O;qRiUu jkf'k;ksa osQ
ek=kdksa dks O;qRiUu ek=kd dgrs gSaA ewy&ek=kdksa vkSj O;qRiUu ek=kdksa osQ
lEiw.kZ leqPp; dks ek=kdksa dh iz.kkyh (;k i¼fr) dgrs gSaA
2.2  ek=kdksa dh varjkZ"Vªh; iz.kkyh
cgqr o"kks± rd ekiu osQ fy,] fofHkUu ns'kksa osQ oSKkfud] vyx&vyx ekiu
iz.kkfy;ksa dk mi;ksx djrs FksA vc ls oqQN le;&iwoZ rd ,slh rhu
iz.kkfy;k¡ & CGS iz.kkyh] FPS (;k fczfV'k) iz.kkyh ,oa  MKS  iz.kkyh]
izeq[krk ls iz;ksx esa ykbZ tkrh FkhaA
bu iz.kkfy;ksa esa yEckbZ] nzO;eku ,oa le; osQ ewy ek=kd Øe'k% bl
izdkj gSa %
• CGS iz.kkyh esa] lsUVhehVj] xzke ,oa lsoQUMA
• FPS iz.kkyh esa] iqQV] ikmUM ,oa lsoQUMA
• MKS iz.kkyh esa] ehVj] fdyksxzke ,oa lsoQUMA
vktdy varjkZ"Vªh; Lrj ij ekU; iz.kkyh ¶flLVe bUVjus'kuy fM
;wfuV~l¸ gS (tks izsaQp Hkk"kk esa ¶ek=kdksa dh varjkZ"Vªh; iz.kkyh¸ dguk gS)A
bls laosQrk{kj esa  SI fy[kk tkrk gSA SI  izrhdksa] ek=kdksa vkSj muosQ laosQrk{kjksa
dh ;kstuk 1971 esa] ekirksy osQ egk lEesyu }kjk fodflr dj] oSKkfud]
rduhdh] vkS|ksfxd ,oa O;kikfjd dk;ks± esa varjkZ"Vªh; Lrj ij mi;ksx gsrq
2.1 Hkwfedk
2.2 ek=kdksa dh varjkZ"Vªh; iz.kkyh
2.3 yEckbZ dk ekiu
2.4 nzO;eku dk ekiu
2.5 le; dk ekiu
2.6 ;FkkFkZrk] ;a=kksa dh ifj'kq¼rk ,oa
ekiu esa =kqfV
2.7 lkFkZd vad
2.8 HkkSfrd jkf'k;ksa dh foek,¡
2.9 foeh; lw=k ,oa foeh; lehdj.ksa
2.10 foeh; fo'ys"k.k ,oa blosQ vuqiz;ksx
lkjka'k
vH;kl
vfrfjDr vH;kl
vuqeksfnr dh xbZA SI ek=kdksa dh 10 dh ?kkrksa ij vk/kfjr
(nkf'ed) izo`Qfr osQ dkj.k] bl iz.kkyh osQ varxZr :ikarj.k
vR;ar lqxe ,oa lqfo/ktud gSA ge bl iqLrd esa SI  ek=kdksa
dk gh iz;ksx djsaxsA
SI esa lkr ewy ek=kd gSa] tks lkj.kh 2-1 esa fn, x, gSaA
bu lkr ewy ek=kdksa osQ vfrfjDr nks iwjd ek=kd Hkh gSa
ftudks ge bl izdkj ifjHkkf"kr dj ldrs gSa % (i) leryh;
dks.k]  d?  fp=k 2.1(a) esa n'kkZ, vuqlkj o`Ùk osQ pki dh
yEckbZ ds vkSj bldh f=kT;k r dk vuqikr gksrk gSA rFkk
(ii) ?ku&dks.k] 
dO
 fp=k 2.1(b) esa n'kkZ, vuqlkj 'kh"kZ O dks
osQUnz dh Hkkafr iz;qDr djosQ mlosQ ifjr% fu£er xksyh; i`"B
osQ vijks/u {ks=k dA  rFkk f=kT;k r  osQ oxZ dk vuqikr gksrk
gSA leryh; dks.k dk ek=kd jsfM;u gS ftldk izrhd rad
gS ,oa ?ku dks.k dk ek=kd LVsjsfM;u gS ftldk izrhd sr gSA
;s nksuksa gh foekfoghu jkf'k;k¡ gSaA
17
(a)
(b)
fp=k 2.1  (a) leryh; dks.k d? ,oa (b) ?ku dks.k
dO
 dk vkjs[kh; fooj.k
* bu ifjHkk"kkvksa esa iz;qDr la[;kvksa osQ eku] u rks ;kn j[kus dh vko';drk gS] u ijh{kk esa iwNs tkus dhA ;s ;gk¡ ij osQoy buosQ
ekiu dh ;FkkFkZrk dh lhek dk laosQr nsus osQ fy, fn, x, gSaA izkS|ksfxdh osQ fodkl osQ lkFk ekiu dh rduhdksa esa Hkh lq/kj
gksrk gS] ifj.kkeLo:i] ekiu vf/d ifj'kq¼rk ls gksrk gSA bl izxfr osQ lkFk rkyesy cuk, j[kus osQ fy, ewy ek=kdksa dks
la'kksf/r fd;k tkrk gSA
lkj.kh 2.1 SI ewy jkf'k;k¡ ,oa muds ek=kd*
ewy                                       SI ek=kd
jkf'k uke izrhd ifjHkk"kk
yackbZ ehVj m izdk'k }kjk fuokZr esa ,d lsoaQM osQ 299, 792, 458 osa le; varjky
esa r; fd, x, iFk dh yackbZ ,d ehVj gS A (1983 ls ekU;)
nzO;eku fdyksxzke kg izaQkl esa isfjl osQ ikl lsofjl esa fLFkr varjkZ"Vªh; eki&rksy C;wjks esa j[ks
fdyksxzke osQ varjkZ"Vªh; vkfn iz:i (IysfVue&bfjfM;e feJ/krq ls cus
flfyaMj) dk nzO;eku ,d fdyksxzke osQ cjkcj gS A (1889 ls ekU;)
le; lsoaQM s ,d lsoaQM og varjky gS tks lhft+;e 133 ijek.kq osQ fuEure ÅtkZ
Lrj osQ nks vfrlw{e Lrjksa osQ eè; laØe.k osQ rnuq:ih fofdj.k osQ
9]192]631]770 vkorZ dkyksa osQ cjkcj gSA (1967 ls ekU;)
fo|qr /kjk ,sfEIk;j A ,d ,sfEi;j og fu;r fo|qr /kjk gS tks fd fuokZr esa 1 ehVj dh nwjh
ij fLFkr nks lh/s vuar yackbZ okys lekukarj ,oa ux.; o`Ùkh; vuqizLFk
dkV osQ pkydksa esa izokfgr gksus ij] bu pkydksa osQ chp izfr ehVj yackbZ
ij 2 × 10
&7
 U;wVu dk cy mRiUu djrh gS A (1948 ls ekU;)
Å"ekxfrd rki osQfYou K ty osQ f=kd&fcanq osQ mQ"ekxfrd rki osQ 1/273.16 osa Hkkx dks 1 osQfYou
dgrs gSaA (1967 ls ekU;)
inkFkZ dh ek=kk eksy mol 1 eksy fdlh fudk; esa inkFkZ dh og ek=kk gS ftlesa mruh gh ewy  lÙkk,a
gksrh gSa ftruh 0.012 kg dkcZu&12 esa ijek.kqvksa dh la[;k gksrh gSA
(1971 ls ekU;)
T;ksfr&rhozrk oSaQMsyk cd oSaQMsyk] fdlh fn'kk esa 540 × 10
12 
Hz vko`fÙk okys Ïksr dh T;ksfr&rhozrk
gS tks ml fn'kk esa (1@683) okV izfr LVsjsfM;u dh fofdj.k rhozrk
dk ,do.khZ; izdk'k mRlftZr djrk gS (1979 ls ekU;)
ek=kd ,oa ekiu
HkkSfrdh
18
è;ku nhft,] eksy dk mi;ksx djrs le; ewy lÙkkvksa dk
fo'ks"k :i ls mYys[k fd;k tkuk pkfg,A ;s ewy lÙkk,¡
ijek.kq] v.kq] vk;u] bysDVªkWu] vU; dksbZ d.k vFkok blh
izdkj osQ d.kksa dk fof'k"V lewg gks ldrk gSA
ge ,slh HkkSfrd jkf'k;ksa osQ ek=kdksa dk Hkh mi;ksx djrs
gSa ftUgsa lkr ewy jkf'k;ksa ls O;qRiUu fd;k tk ldrk gS
(ifjf'k"V A 6)A SI ewy ek=kdksa osQ inksa esa O;Dr oqQN
O;qRiUu ek=kd (ifjf'k"V A 6.1) esa fn, x, gSaA oqQN O;qRiUu
SI  ek=kdksa  dks fof'k"V uke fn, x, gSa (ifjf'k"V A  6.2)
vkSj oqQN O;qRiUu SI ek=kd bu fof'k"V ukeksa okys O;qRiUu
ek=kdksa vkSj lkr ewy&ek=kdksa osQ la;kstu ls curs gSa (ifjf'k"V
A 6.3)A vkidks rkRdkfyd lanHkZ rFkk ekxZn'kZu iznku djus
osQ fy, bu ek=kdksa dks ifjf'k"V  (A 6.2)  ,oa  (A 6.3)  esa
fn;k x;k gSA lkekU; O;ogkj esa vkus okys vU; ek=kd lkj.kh
2-2 esa fn, x, gSaA
SI ek=kdksa osQ lkekU; xq.kt vkSj viorZdksa dks O;Dr djus
okys milxZ vkSj muosQ izrhd ifjf'k"V (A2) esa fn, x, gSaA
HkkSfrd jkf'k;ksa] jklk;fud rRoksa vkSj ukfHkdksa osQ laosQrksa osQ
mi;ksx laca/h lkekU; funsZ'k ifjf'k"V (A7) eas fn, x, gSa vkSj
vkiosQ ekxZn'kZu rFkk rkRdkfyd lanHkZ osQ fy, SI ek=kdksa ,oa
vU; ek=kdksa laca/h funsZ'k ifjf'k"V (A8) esa fn, x, gSaA
2.3  yEckbZ dk ekiu
yEckbZ ekiu dh oqQN izR;{k fof/;ksa ls vki igys gh ls
ifjfpr gSaA mnkgj.k osQ fy,] vki tkurs gSa fd  10
–3 
m  ls
10
2 
m rd dh yEckb;k¡ ehVj iSekus dk mi;ksx djosQ Kkr
dh tkrh gSaA 10
–4 
m dh yEckbZ dks ;FkkFkZrk ls ekius osQ fy,
ge ofuZ;j oSQfyilZ dk mi;ksx djrs gSaA LowzQ&xst (isapekih)
vkSj xksykbZekih (LisQjksehVj) dk mi;ksx  10
–5 
m rd dh
yEckb;ksa dks ekius esa fd;k tkrk gSA bu ifjljksa ls ckgj dh
yEckb;ksa dks ekius osQ fy, gesa oqQN ijks{k fof/;ksa dk lgkjk
ysuk gksrk gSA
2.3.1  cM+h nwfj;ksa dk ekiu
cgqr cM+h nwfj;k¡] tSls fdlh xzg vFkok rkjs dh i`Foh ls nwjh]
izR;{k&:i ls fdlh ehVj iSekus dh lgk;rk ls
Kkr ugha dh tk ldrh gSA ,slh n'kkvksa esa egRoiw.kZ fof/
ftls yEcu&fof/ dgrs gSa] dk mi;ksx fd;k tkrk gSA
tc vki fdlh isafly dks vius lkeus idM+rs gSa vkSj
i`"BHkwfe (ekuk nhokj) osQ fdlh fof'k"V fcUnq osQ lkis{k
isafly dks igys viuh ck;ha vk¡[k  A  ls (nk;ha vk¡[k can
j[krs gq,) ns[krs gSa] vkSj fiQj nk;ha vk¡[k  B  ls (ck;ha vk¡[k
can j[krs gq,)] rks vki ikrs gSa] fd nhokj osQ ml fcUnq osQ
lkis{k isafly dh fLFkfr ifjo£rr gksrh izrhr gksrh gSA bls
yEcu dgk tkrk gSA nks izs{k.k fcUnqvksa (A ,oa B) osQ chp
dh nwjh dks vk/kjd dgk tkrk gSA bl mnkgj.k esa nksuksa
vk¡[kksa osQ chp dh nwjh vk/kjd gSA
yEcu fof/ }kjk fdlh nwjLFk xzg S dh nwjh D  Kkr djus
osQ fy,] ge bldks] i`Foh ij nks fofHkUu fLFkfr;ksa (os/
'kkykvksa) A ,oa B ls] ,d gh le; ij ns[krs gSaA A ,oa B
lkj.kh 2.2 lkekU; iz;ksx osQ fy, SI ek=kdksa osQ vfrfjDr oqQN vU; ek=kd
uke izrhd SI ek=kd osQ inksa esa eku
feuV min 60 s
?kaVk h 60 min = 3600 s
fnu d 24 h = 86400 s
o"kZ y 365.25 d = 3.156 × 10
7 
s
fMxzh
o
1
o
 = (p/180) rad
fyVj L1 dm
3
 = 10
–3 
m
3
Vu t10
3
 kg
oSQjV c 200 mg
ckj bar 0.1 MPa = 10
5
 Pa
D;wjh Ci 3.7 × 10
10
 s
–1
jksatu R 2.58 × 10
–4
 C kg
–1
fDoaVy q 100 kg
ckuZ b 100 fm
2
 = 10
–28
 m
2
vkj a 1 dam
2
 = 10
2 
m
2
gsDVkj ha 1 hm
2
 = 10
4 
m
2
ekud ok;qeaMyh; nkc atm 101 325 Pa = 1.013 × 10
5
 Pa
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