NCERT पाठ्यपुस्तक पाठ 10 - गुरुत्वाकर्षण, कक्षा 9, विज्ञान | विज्ञान (कक्षा 9) - नोट्स, वीडियोस तथा सैंपल पेपर्स - Class 9 PDF Download

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vè;k; 8 rFkk 9 esa geus oLrqvksa dh xfr osQ ckjs
esa rFkk cy dks xfr osQ dkjd osQ :i esa vè;;u
fd;k gSA geus lh[kk gS fd fdlh oLrq dh pky ;k
xfr dh fn'kk cnyus osQ fy, cy dh vko';drk
gksrh gSA ge lnSo ns[krs gSa fd tc fdlh oLrq dks
Å¡pkbZ ls fxjk;k tkrk gS rks og i`Foh dh vksj  gh
fxjrh gSA ge tkurs gSa fd lHkh xzg lw;Z osQ pkjksa
vksj pDdj yxkrs gSaA panzek i`Foh dh ifjØek
djrk gSA bu lHkh voLFkkvksa esa] oLrqvksa ij] xzgksa
ij rFkk panzek ij yxus okyk dksbZ cy vo'; gksuk
pkfg,A vkbtd U;wVu bl rF; dks le> x, Fks
fd bu lHkh osQ fy, ,d gh cy mÙkjnk;h gSA bl
cy dks xq#Rokd"kZ.k cy dgrss gSaA
bl vè;k; esa ge xq#Rokd"kZ.k rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e osQ ckjs esa vè;;u djsaxsA ge
i`Foh ij xq#Rokd"kZ.k cy osQ izHkko osQ varxZr
oLrqvksa dh xfr ij fopkj djsaxsA ge vè;;u djsaxs
fd fdlh oLrq dk Hkkj ,d LFkku ls nwljs LFkku ij
fdl izdkj ifjo£rr gksrk gSA nzoksa esa oLrqvksa osQ
Iyou dh 'krks± osQ ckjs esa Hkh ge fopkj&foe'kZ
djsaxsA
10.1 xq#Rokd"kZ.k
ge tkurs gSa fd panzek i`Foh dk pDdj yxkrk gSA
fdlh oLrq dks tc Åij dh vksj isaQdrs gSa] rks og
oqQN Å¡pkbZ rd Åij igq¡prh gS vkSj fiQj uhps dh
vksj fxjus yxrh gSA dgrs gSa fd tc U;wVu ,d
isM+ osQ uhps cSBs Fks rks ,d lsc mu ij fxjkA lsc
osQ fxjus dh fØ;k us U;wVu dks lkspus osQ fy, izsfjr
fd;kA mUgksaus lkspk fd ;fn i`Foh lsc dks viuh
vksj vkd£"kr dj ldrh gS rks D;k ;g panzek dks
vkd£"kr ugha dj ldrh\ D;k nksuksa fLFkfr;ksa esa
ogh cy yx jgk gS\ mUgksaus vuqeku yxk;k fd
nksuksa voLFkkvksa esa ,d gh izdkj dk cy mÙkjnk;h
gSA mUgksaus roZQ fn;k fd viuh d{kk osQ izR;sd ¯cnq
ij panzek fdlh ljy js[kh; iFk ij xfr ugha djrk
oju~ i`Foh dh vksj fxjrk jgrk gSA vr% og vo';
gh i`Foh }kjk vkd£"kr gksrk gSA ysfdu ge okLro
esa panzek dks i`Foh dh vksj fxjrs gq, ugha ns[krsA
vkb, panzek dh xfr dks le>us osQ fy,
fØ;kdyki 8.11 ij iqu% fopkj djsaA
fØ;kdyki _ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ _1 1 10 0 0. . .1 1 1
• /kxs dk ,d VqdM+k yhft,A blosQ ,d fljs
ij ,d NksVk iRFkj ck¡f/,A
• /kxs osQ nwljs fljs dks idfM+, vkSj iRFkj dks
o`Ùkkdkj iFk esa ?kqekb, tSlk fd fp=k 10-1 esa
fn[kk;k x;k gSA
10
xq#Rokd"kZ.k
(Gravitation)
vè;k;
fp=k 10.1: iRFkj }kjk fu;r ifjek.k osQ osx ls o`Ùkkdkj
iFk esa xfr
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vè;k; 8 rFkk 9 esa geus oLrqvksa dh xfr osQ ckjs
esa rFkk cy dks xfr osQ dkjd osQ :i esa vè;;u
fd;k gSA geus lh[kk gS fd fdlh oLrq dh pky ;k
xfr dh fn'kk cnyus osQ fy, cy dh vko';drk
gksrh gSA ge lnSo ns[krs gSa fd tc fdlh oLrq dks
Å¡pkbZ ls fxjk;k tkrk gS rks og i`Foh dh vksj  gh
fxjrh gSA ge tkurs gSa fd lHkh xzg lw;Z osQ pkjksa
vksj pDdj yxkrs gSaA panzek i`Foh dh ifjØek
djrk gSA bu lHkh voLFkkvksa esa] oLrqvksa ij] xzgksa
ij rFkk panzek ij yxus okyk dksbZ cy vo'; gksuk
pkfg,A vkbtd U;wVu bl rF; dks le> x, Fks
fd bu lHkh osQ fy, ,d gh cy mÙkjnk;h gSA bl
cy dks xq#Rokd"kZ.k cy dgrss gSaA
bl vè;k; esa ge xq#Rokd"kZ.k rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e osQ ckjs esa vè;;u djsaxsA ge
i`Foh ij xq#Rokd"kZ.k cy osQ izHkko osQ varxZr
oLrqvksa dh xfr ij fopkj djsaxsA ge vè;;u djsaxs
fd fdlh oLrq dk Hkkj ,d LFkku ls nwljs LFkku ij
fdl izdkj ifjo£rr gksrk gSA nzoksa esa oLrqvksa osQ
Iyou dh 'krks± osQ ckjs esa Hkh ge fopkj&foe'kZ
djsaxsA
10.1 xq#Rokd"kZ.k
ge tkurs gSa fd panzek i`Foh dk pDdj yxkrk gSA
fdlh oLrq dks tc Åij dh vksj isaQdrs gSa] rks og
oqQN Å¡pkbZ rd Åij igq¡prh gS vkSj fiQj uhps dh
vksj fxjus yxrh gSA dgrs gSa fd tc U;wVu ,d
isM+ osQ uhps cSBs Fks rks ,d lsc mu ij fxjkA lsc
osQ fxjus dh fØ;k us U;wVu dks lkspus osQ fy, izsfjr
fd;kA mUgksaus lkspk fd ;fn i`Foh lsc dks viuh
vksj vkd£"kr dj ldrh gS rks D;k ;g panzek dks
vkd£"kr ugha dj ldrh\ D;k nksuksa fLFkfr;ksa esa
ogh cy yx jgk gS\ mUgksaus vuqeku yxk;k fd
nksuksa voLFkkvksa esa ,d gh izdkj dk cy mÙkjnk;h
gSA mUgksaus roZQ fn;k fd viuh d{kk osQ izR;sd ¯cnq
ij panzek fdlh ljy js[kh; iFk ij xfr ugha djrk
oju~ i`Foh dh vksj fxjrk jgrk gSA vr% og vo';
gh i`Foh }kjk vkd£"kr gksrk gSA ysfdu ge okLro
esa panzek dks i`Foh dh vksj fxjrs gq, ugha ns[krsA
vkb, panzek dh xfr dks le>us osQ fy,
fØ;kdyki 8.11 ij iqu% fopkj djsaA
fØ;kdyki _ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ _1 1 10 0 0. . .1 1 1
• /kxs dk ,d VqdM+k yhft,A blosQ ,d fljs
ij ,d NksVk iRFkj ck¡f/,A
• /kxs osQ nwljs fljs dks idfM+, vkSj iRFkj dks
o`Ùkkdkj iFk esa ?kqekb, tSlk fd fp=k 10-1 esa
fn[kk;k x;k gSA
10
xq#Rokd"kZ.k
(Gravitation)
vè;k;
fp=k 10.1: iRFkj }kjk fu;r ifjek.k osQ osx ls o`Ùkkdkj
iFk esa xfr
foKku
146
xfr osQ rhljs fu;e osQ vuqlkj lsc Hkh i`Foh
dks vkd£"kr djrk gSA ysfdu xfr osQ nwljs fu;e
osQ vuqlkj] fdlh fn, gq, cy osQ fy, Roj.k oLrq
osQ nzO;eku osQ O;qRØekuqikrh gksrk gS [lehdj.k
(9-4)]A i`Foh dh vis{kk lsc dk nzO;eku ux.;
gSA blhfy, ge i`Foh dks lsc dh vksj xfr djrs
ugha ns[krsA blh roZQ dk foLrkj ;g tkuus osQ fy,
dhft, fd i`Foh panzek dh vksj xfr D;ksa ugha
djrhA
gekjs lkSj ifjokj esa] lHkh xzg lw;Z dh ifjØek
djrs gSaA igys dh Hkk¡fr roZQ djosQ ge dg ldrs
gSa fd lw;Z rFkk xzgksa osQ chp ,d cy fo|eku gSA
mijksDr rF;ksa osQ vk/kj ij U;wVu us fu"d"kZ fudkyk
fd osQoy i`Foh gh lsc vkSj panzek dks vkd£"kr
ugha djrh] cfYd fo'o osQ lHkh fiaM ,d&nwljs
dks vkd£"kr djrs gSaaaA oLrqvksa osQ chp ;g vkd"kZ.k
cy xq#Rokd"kZ.k cy dgykrk gSA
10.1.1 xq#Rokd"kZ.k dk lkoZf=kd fu;e
fo'o dk izR;sd fiaM izR;sd vU; fiaM dks ,d
cy ls vkd£"kr djrk gS] tks nksuksa fiaMksa osQ nzO;ekuksa
osQ xq.kuiQy osQ lekuqikrh rFkk muosQ chp dh nwjh
osQ oxZ osQ O;qRØekuqikrh gksrk gSA ;g cy nksuksa
fiaMksa dks feykus okyh js[kk dh fn'kk esa yxrk gSA
• iRFkj dh xfr dh fn'kk dks nsf[k,A
• vc /kxs dks NksfM+,A
• fiQj ls iRFkj dh xfr dh fn'kk dks nsf[k,A
/kxs dks NksM+us ls igys iRFkj ,d fuf'pr
pky ls o`Ùkkdkj iFk esa xfr djrk gS rFkk izR;sd
¯cnq ij mldh xfr dh fn'kk cnyrh gSA fn'kk osQ
ifjorZu esa osx&ifjorZu ;k Roj.k lfEefyr gSA
ftl cy osQ dkj.k ;g Roj.k gksrk gS rFkk tks oLrq
dks o`Ùkkdkj iFk esa xfr'khy j[krk gS] og cy osaQnzz
dh vksj yxrk gSA bl cy dks vfHkosaQnz cy dgrs
gSaA bl cy dh vuqifLFkfr esa iRFkj ,d ljy js[kk
esa eqDr :i ls xfr'khy gks tkrk gSA ;g ljy js[kk
o`Ùkh; iFk ij Li'kZ js[kk gksxhA
bls Hkh tkusa
i`Foh osQ pkjksa vksj panzek dh xfr vfHkosaQnz cy
osQ dkj.k gSA vfHkosaQnz cy i`Foh osQ vkd"kZ.k cy
osQ dkj.k fey ikrk gSA ;fn ,slk dksbZ cy u gks rks
panzek ,dleku xfr ls ljy js[kh; iFk ij pyrk
jgsxkA
;g ns[kk x;k gS fd fxjrk gqvk lsc i`Foh dh
vksj vkd£"kr gksrk gSA D;k lsc Hkh i`Foh dks
vkd£"kr djrk gS\ ;fn ,slk gS] rks ge i`Foh dks
lsc dh vksj xfr djrs D;ksa ugha ns[k ikrs\
o`Ùk ij Li'kZ js[kk
dksbZ ljy js[kk tks o`Ùk ls osQoy ,d gh
¯cnq ij feyrh gS] o`Ùk ij Li'kZ js[kk
dgykrh gSA bl fp=k esa ljy js[kk ABC
o`Ùk osQ ¯cnq  B ij Li'kZ js[kk gSA
G
2
Mm
F=
d
fp=k 10.2: fdUgha nks ,dleku fiaMksa osQ chp xq#Rokd"kZ.k
cy muosQ osaQnzzksa dks feykus okyh js[kk dh
fn'kk esa funsf'kr gksrk gS
Page 3


vè;k; 8 rFkk 9 esa geus oLrqvksa dh xfr osQ ckjs
esa rFkk cy dks xfr osQ dkjd osQ :i esa vè;;u
fd;k gSA geus lh[kk gS fd fdlh oLrq dh pky ;k
xfr dh fn'kk cnyus osQ fy, cy dh vko';drk
gksrh gSA ge lnSo ns[krs gSa fd tc fdlh oLrq dks
Å¡pkbZ ls fxjk;k tkrk gS rks og i`Foh dh vksj  gh
fxjrh gSA ge tkurs gSa fd lHkh xzg lw;Z osQ pkjksa
vksj pDdj yxkrs gSaA panzek i`Foh dh ifjØek
djrk gSA bu lHkh voLFkkvksa esa] oLrqvksa ij] xzgksa
ij rFkk panzek ij yxus okyk dksbZ cy vo'; gksuk
pkfg,A vkbtd U;wVu bl rF; dks le> x, Fks
fd bu lHkh osQ fy, ,d gh cy mÙkjnk;h gSA bl
cy dks xq#Rokd"kZ.k cy dgrss gSaA
bl vè;k; esa ge xq#Rokd"kZ.k rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e osQ ckjs esa vè;;u djsaxsA ge
i`Foh ij xq#Rokd"kZ.k cy osQ izHkko osQ varxZr
oLrqvksa dh xfr ij fopkj djsaxsA ge vè;;u djsaxs
fd fdlh oLrq dk Hkkj ,d LFkku ls nwljs LFkku ij
fdl izdkj ifjo£rr gksrk gSA nzoksa esa oLrqvksa osQ
Iyou dh 'krks± osQ ckjs esa Hkh ge fopkj&foe'kZ
djsaxsA
10.1 xq#Rokd"kZ.k
ge tkurs gSa fd panzek i`Foh dk pDdj yxkrk gSA
fdlh oLrq dks tc Åij dh vksj isaQdrs gSa] rks og
oqQN Å¡pkbZ rd Åij igq¡prh gS vkSj fiQj uhps dh
vksj fxjus yxrh gSA dgrs gSa fd tc U;wVu ,d
isM+ osQ uhps cSBs Fks rks ,d lsc mu ij fxjkA lsc
osQ fxjus dh fØ;k us U;wVu dks lkspus osQ fy, izsfjr
fd;kA mUgksaus lkspk fd ;fn i`Foh lsc dks viuh
vksj vkd£"kr dj ldrh gS rks D;k ;g panzek dks
vkd£"kr ugha dj ldrh\ D;k nksuksa fLFkfr;ksa esa
ogh cy yx jgk gS\ mUgksaus vuqeku yxk;k fd
nksuksa voLFkkvksa esa ,d gh izdkj dk cy mÙkjnk;h
gSA mUgksaus roZQ fn;k fd viuh d{kk osQ izR;sd ¯cnq
ij panzek fdlh ljy js[kh; iFk ij xfr ugha djrk
oju~ i`Foh dh vksj fxjrk jgrk gSA vr% og vo';
gh i`Foh }kjk vkd£"kr gksrk gSA ysfdu ge okLro
esa panzek dks i`Foh dh vksj fxjrs gq, ugha ns[krsA
vkb, panzek dh xfr dks le>us osQ fy,
fØ;kdyki 8.11 ij iqu% fopkj djsaA
fØ;kdyki _ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ _1 1 10 0 0. . .1 1 1
• /kxs dk ,d VqdM+k yhft,A blosQ ,d fljs
ij ,d NksVk iRFkj ck¡f/,A
• /kxs osQ nwljs fljs dks idfM+, vkSj iRFkj dks
o`Ùkkdkj iFk esa ?kqekb, tSlk fd fp=k 10-1 esa
fn[kk;k x;k gSA
10
xq#Rokd"kZ.k
(Gravitation)
vè;k;
fp=k 10.1: iRFkj }kjk fu;r ifjek.k osQ osx ls o`Ùkkdkj
iFk esa xfr
foKku
146
xfr osQ rhljs fu;e osQ vuqlkj lsc Hkh i`Foh
dks vkd£"kr djrk gSA ysfdu xfr osQ nwljs fu;e
osQ vuqlkj] fdlh fn, gq, cy osQ fy, Roj.k oLrq
osQ nzO;eku osQ O;qRØekuqikrh gksrk gS [lehdj.k
(9-4)]A i`Foh dh vis{kk lsc dk nzO;eku ux.;
gSA blhfy, ge i`Foh dks lsc dh vksj xfr djrs
ugha ns[krsA blh roZQ dk foLrkj ;g tkuus osQ fy,
dhft, fd i`Foh panzek dh vksj xfr D;ksa ugha
djrhA
gekjs lkSj ifjokj esa] lHkh xzg lw;Z dh ifjØek
djrs gSaA igys dh Hkk¡fr roZQ djosQ ge dg ldrs
gSa fd lw;Z rFkk xzgksa osQ chp ,d cy fo|eku gSA
mijksDr rF;ksa osQ vk/kj ij U;wVu us fu"d"kZ fudkyk
fd osQoy i`Foh gh lsc vkSj panzek dks vkd£"kr
ugha djrh] cfYd fo'o osQ lHkh fiaM ,d&nwljs
dks vkd£"kr djrs gSaaaA oLrqvksa osQ chp ;g vkd"kZ.k
cy xq#Rokd"kZ.k cy dgykrk gSA
10.1.1 xq#Rokd"kZ.k dk lkoZf=kd fu;e
fo'o dk izR;sd fiaM izR;sd vU; fiaM dks ,d
cy ls vkd£"kr djrk gS] tks nksuksa fiaMksa osQ nzO;ekuksa
osQ xq.kuiQy osQ lekuqikrh rFkk muosQ chp dh nwjh
osQ oxZ osQ O;qRØekuqikrh gksrk gSA ;g cy nksuksa
fiaMksa dks feykus okyh js[kk dh fn'kk esa yxrk gSA
• iRFkj dh xfr dh fn'kk dks nsf[k,A
• vc /kxs dks NksfM+,A
• fiQj ls iRFkj dh xfr dh fn'kk dks nsf[k,A
/kxs dks NksM+us ls igys iRFkj ,d fuf'pr
pky ls o`Ùkkdkj iFk esa xfr djrk gS rFkk izR;sd
¯cnq ij mldh xfr dh fn'kk cnyrh gSA fn'kk osQ
ifjorZu esa osx&ifjorZu ;k Roj.k lfEefyr gSA
ftl cy osQ dkj.k ;g Roj.k gksrk gS rFkk tks oLrq
dks o`Ùkkdkj iFk esa xfr'khy j[krk gS] og cy osaQnzz
dh vksj yxrk gSA bl cy dks vfHkosaQnz cy dgrs
gSaA bl cy dh vuqifLFkfr esa iRFkj ,d ljy js[kk
esa eqDr :i ls xfr'khy gks tkrk gSA ;g ljy js[kk
o`Ùkh; iFk ij Li'kZ js[kk gksxhA
bls Hkh tkusa
i`Foh osQ pkjksa vksj panzek dh xfr vfHkosaQnz cy
osQ dkj.k gSA vfHkosaQnz cy i`Foh osQ vkd"kZ.k cy
osQ dkj.k fey ikrk gSA ;fn ,slk dksbZ cy u gks rks
panzek ,dleku xfr ls ljy js[kh; iFk ij pyrk
jgsxkA
;g ns[kk x;k gS fd fxjrk gqvk lsc i`Foh dh
vksj vkd£"kr gksrk gSA D;k lsc Hkh i`Foh dks
vkd£"kr djrk gS\ ;fn ,slk gS] rks ge i`Foh dks
lsc dh vksj xfr djrs D;ksa ugha ns[k ikrs\
o`Ùk ij Li'kZ js[kk
dksbZ ljy js[kk tks o`Ùk ls osQoy ,d gh
¯cnq ij feyrh gS] o`Ùk ij Li'kZ js[kk
dgykrh gSA bl fp=k esa ljy js[kk ABC
o`Ùk osQ ¯cnq  B ij Li'kZ js[kk gSA
G
2
Mm
F=
d
fp=k 10.2: fdUgha nks ,dleku fiaMksa osQ chp xq#Rokd"kZ.k
cy muosQ osaQnzzksa dks feykus okyh js[kk dh
fn'kk esa funsf'kr gksrk gS
xq#Rokd"kZ.k
147
vkbtd U;wVu dk tUe
baXySaM esa xzSaFke osQ fudV
owYlFkksisZ esa gqvk FkkA foKku
osQ bfrgkl esa og izk;%
lcls vfèkd ekSfyd rFkk
izHkko'kkyh fl¼karoknh osQ
:i esa tkus tkrs gSaA os ,d
fu/Zu o`Q"kd ifjokj eas tUes
FksA ysfdu os [ksrh osQ dke
esa oqQ'ky ugha FksA 1661 esa
f'k{kk xzg.k djus osQ fy, mUgas dSafczt fo'ofo|ky;
Hkst fn;k x;kA lu~ 1665 esa oSaQfczt esa Iysx iSQy
x;k vkSj U;wVu dks ,d o"kZ dh Nqêðh fey xbZA ,slk
dgk tkrk gS fd blh o"kZ muosQ Åij lsc fxjus dh
?kVuk ?kfVr gqbZA bl ?kVuk us U;wVu dks] panzek dks
mldh d{kk eas cuk, j[kus okys cy rFkk xq#Ro cy
osQ chp laca/ dh laHkkouk dh [kkst djus dks izsfjr
fd;kA blls mUgksaus xq#Rokd"kZ.k dk lkoZf=kd fu;e
[kkst fudkykA fof'k"V ckr ;g gS fd muls igys
Hkh cgqr ls egku oSKkfud xq#Ro osQ ckjs esa tkurs
Fks] fdarq os mlosQ egRo dks le>us esa vliQy jgsA
U;wVu us xfr osQ lqizfl¼ fu;eksa dk izfriknu
fd;kA mUgksaus izdk'k rFkk jaxksa osQ fl¼karksa ij dk;Z
fd;kA mUgksaus [kxksyh; izs{k.kksa osQ fy, [kxksyh;
nwjn'khZ dh jpuk dhA U;wVu ,d egku xf.krK Hkh
FksA mUgksaus xf.kr dh ,d ubZ 'kk[kk dh [kkst dh
ftls dyu (Calculus) dgrs gSaA bldk mi;ksx
mUgksaus ;g fl¼ djus osQ fy, fd;k fd fdlh
,dleku ?kuRo okys xksys osQ ckgj fLFkr oLrqvksa
osQ fy, xksys dk O;ogkj bl izdkj dk gksrk gS tSls
fd mldk laiw.kZ nzO;eku mlosQ osaQnzz ij fLFkr gksA
U;wVu us vius xfr osQ rhu fu;eksa rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e ls HkkSfrdh; foKku osQ <k¡ps dks
cny fn;kA l=kgoha 'krkCnh dh izeq[k oSKkfud Økafr
vkbtd U;wVu
(1642 – 1727)
U;wVu us O;qRØe oxZ fu;e dk
vuqeku oSQls yxk;k\
xzgksa dh xfr osQ vè;;u esa lnSo ls gh gekjh
xgjh #fp jgh gSA lksygoha 'krkCnh rd vusd
[kxksy'kkfL=k;ksa us xzgksa dh xfr ls lacaf/r
cgqr ls vk¡dM+s ,df=kr dj fy, FksA tksgkal
oSQIyj us bu vk¡dM+ksa osQ vk/kj ij rhu fu;e
O;qRiUu fd,A bUgsa oSQIyj osQ fu;e dgk tkrk
gSA ;s fu;e bl izdkj gSa%
1. izR;sd xzg dh d{kk ,d nh?kZo`Ùk gksrh gS
vkSj lw;Z bl nh?kZo`Ùk osQ ,d iQksdl ij
gksrk gS tSlk fd fuEu fp=k esa fn[kk;k x;k
gSA bl fp=k esa lw;Z dh fLFkfr dks O ls
n'kkZ;k x;k gSA
2. lw;Z rFkk xzg dks feykus okyh js[kk leku
le; esa leku {ks=kiQy r; djrh gSA bl
izdkj ;fn A ls B rd xfr djus esa yxk le; C
ls D rd xfr djus esa yxs le; osQ cjkcj gks rks
{ks=kiQy OAB rFkk {ks=kiQy OCD cjkcj gkssaxsA
3. lw;Z ls fdlh xzg dh vkSlr nwjh (r ) dk ?ku
ml xzg osQ lw;Z osQ ifjr% ifjØe.k dky T
osQ oxZ osQ lekuqikrh gksrk gSA
vFkok  r
3
/T
2
 = fLFkjkadA
osQ :i esa U;wVu us dkWijfudl] oSQIyj] xSyhfy;ks
rFkk vU; osQ ;ksxnku dks vius dk;ks± osQ lkFk ,d
u, 'kfDr'kkyh la'ys"k.k osQ :i esa lfEefJr fd;kA
;g ,d fof'k"V ckr gS fd ml le; rd xq#Roh;
fl¼kar dk lR;kiu ugha gks ldk Fkk ;|fi mldh
lR;rk osQ ckjs esa dksbZ lansg ugha FkkA bldk dkj.k
Fkk fd U;wVu dk fl¼kar Bksl oSKkfud rdks± ij
vk/kfjr Fkk vkSj xf.kr ls mldh iqf"V Hkh dh xbZ
FkhA blls ;g fl¼kar ljy o ifj"o`Qr gks x;kA ;s
fo'ks"krk,¡ vkt Hkh fdlh vPNs oSKkfud fl¼kar
osQ fy, visf{kr gSaA
Page 4


vè;k; 8 rFkk 9 esa geus oLrqvksa dh xfr osQ ckjs
esa rFkk cy dks xfr osQ dkjd osQ :i esa vè;;u
fd;k gSA geus lh[kk gS fd fdlh oLrq dh pky ;k
xfr dh fn'kk cnyus osQ fy, cy dh vko';drk
gksrh gSA ge lnSo ns[krs gSa fd tc fdlh oLrq dks
Å¡pkbZ ls fxjk;k tkrk gS rks og i`Foh dh vksj  gh
fxjrh gSA ge tkurs gSa fd lHkh xzg lw;Z osQ pkjksa
vksj pDdj yxkrs gSaA panzek i`Foh dh ifjØek
djrk gSA bu lHkh voLFkkvksa esa] oLrqvksa ij] xzgksa
ij rFkk panzek ij yxus okyk dksbZ cy vo'; gksuk
pkfg,A vkbtd U;wVu bl rF; dks le> x, Fks
fd bu lHkh osQ fy, ,d gh cy mÙkjnk;h gSA bl
cy dks xq#Rokd"kZ.k cy dgrss gSaA
bl vè;k; esa ge xq#Rokd"kZ.k rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e osQ ckjs esa vè;;u djsaxsA ge
i`Foh ij xq#Rokd"kZ.k cy osQ izHkko osQ varxZr
oLrqvksa dh xfr ij fopkj djsaxsA ge vè;;u djsaxs
fd fdlh oLrq dk Hkkj ,d LFkku ls nwljs LFkku ij
fdl izdkj ifjo£rr gksrk gSA nzoksa esa oLrqvksa osQ
Iyou dh 'krks± osQ ckjs esa Hkh ge fopkj&foe'kZ
djsaxsA
10.1 xq#Rokd"kZ.k
ge tkurs gSa fd panzek i`Foh dk pDdj yxkrk gSA
fdlh oLrq dks tc Åij dh vksj isaQdrs gSa] rks og
oqQN Å¡pkbZ rd Åij igq¡prh gS vkSj fiQj uhps dh
vksj fxjus yxrh gSA dgrs gSa fd tc U;wVu ,d
isM+ osQ uhps cSBs Fks rks ,d lsc mu ij fxjkA lsc
osQ fxjus dh fØ;k us U;wVu dks lkspus osQ fy, izsfjr
fd;kA mUgksaus lkspk fd ;fn i`Foh lsc dks viuh
vksj vkd£"kr dj ldrh gS rks D;k ;g panzek dks
vkd£"kr ugha dj ldrh\ D;k nksuksa fLFkfr;ksa esa
ogh cy yx jgk gS\ mUgksaus vuqeku yxk;k fd
nksuksa voLFkkvksa esa ,d gh izdkj dk cy mÙkjnk;h
gSA mUgksaus roZQ fn;k fd viuh d{kk osQ izR;sd ¯cnq
ij panzek fdlh ljy js[kh; iFk ij xfr ugha djrk
oju~ i`Foh dh vksj fxjrk jgrk gSA vr% og vo';
gh i`Foh }kjk vkd£"kr gksrk gSA ysfdu ge okLro
esa panzek dks i`Foh dh vksj fxjrs gq, ugha ns[krsA
vkb, panzek dh xfr dks le>us osQ fy,
fØ;kdyki 8.11 ij iqu% fopkj djsaA
fØ;kdyki _ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ _1 1 10 0 0. . .1 1 1
• /kxs dk ,d VqdM+k yhft,A blosQ ,d fljs
ij ,d NksVk iRFkj ck¡f/,A
• /kxs osQ nwljs fljs dks idfM+, vkSj iRFkj dks
o`Ùkkdkj iFk esa ?kqekb, tSlk fd fp=k 10-1 esa
fn[kk;k x;k gSA
10
xq#Rokd"kZ.k
(Gravitation)
vè;k;
fp=k 10.1: iRFkj }kjk fu;r ifjek.k osQ osx ls o`Ùkkdkj
iFk esa xfr
foKku
146
xfr osQ rhljs fu;e osQ vuqlkj lsc Hkh i`Foh
dks vkd£"kr djrk gSA ysfdu xfr osQ nwljs fu;e
osQ vuqlkj] fdlh fn, gq, cy osQ fy, Roj.k oLrq
osQ nzO;eku osQ O;qRØekuqikrh gksrk gS [lehdj.k
(9-4)]A i`Foh dh vis{kk lsc dk nzO;eku ux.;
gSA blhfy, ge i`Foh dks lsc dh vksj xfr djrs
ugha ns[krsA blh roZQ dk foLrkj ;g tkuus osQ fy,
dhft, fd i`Foh panzek dh vksj xfr D;ksa ugha
djrhA
gekjs lkSj ifjokj esa] lHkh xzg lw;Z dh ifjØek
djrs gSaA igys dh Hkk¡fr roZQ djosQ ge dg ldrs
gSa fd lw;Z rFkk xzgksa osQ chp ,d cy fo|eku gSA
mijksDr rF;ksa osQ vk/kj ij U;wVu us fu"d"kZ fudkyk
fd osQoy i`Foh gh lsc vkSj panzek dks vkd£"kr
ugha djrh] cfYd fo'o osQ lHkh fiaM ,d&nwljs
dks vkd£"kr djrs gSaaaA oLrqvksa osQ chp ;g vkd"kZ.k
cy xq#Rokd"kZ.k cy dgykrk gSA
10.1.1 xq#Rokd"kZ.k dk lkoZf=kd fu;e
fo'o dk izR;sd fiaM izR;sd vU; fiaM dks ,d
cy ls vkd£"kr djrk gS] tks nksuksa fiaMksa osQ nzO;ekuksa
osQ xq.kuiQy osQ lekuqikrh rFkk muosQ chp dh nwjh
osQ oxZ osQ O;qRØekuqikrh gksrk gSA ;g cy nksuksa
fiaMksa dks feykus okyh js[kk dh fn'kk esa yxrk gSA
• iRFkj dh xfr dh fn'kk dks nsf[k,A
• vc /kxs dks NksfM+,A
• fiQj ls iRFkj dh xfr dh fn'kk dks nsf[k,A
/kxs dks NksM+us ls igys iRFkj ,d fuf'pr
pky ls o`Ùkkdkj iFk esa xfr djrk gS rFkk izR;sd
¯cnq ij mldh xfr dh fn'kk cnyrh gSA fn'kk osQ
ifjorZu esa osx&ifjorZu ;k Roj.k lfEefyr gSA
ftl cy osQ dkj.k ;g Roj.k gksrk gS rFkk tks oLrq
dks o`Ùkkdkj iFk esa xfr'khy j[krk gS] og cy osaQnzz
dh vksj yxrk gSA bl cy dks vfHkosaQnz cy dgrs
gSaA bl cy dh vuqifLFkfr esa iRFkj ,d ljy js[kk
esa eqDr :i ls xfr'khy gks tkrk gSA ;g ljy js[kk
o`Ùkh; iFk ij Li'kZ js[kk gksxhA
bls Hkh tkusa
i`Foh osQ pkjksa vksj panzek dh xfr vfHkosaQnz cy
osQ dkj.k gSA vfHkosaQnz cy i`Foh osQ vkd"kZ.k cy
osQ dkj.k fey ikrk gSA ;fn ,slk dksbZ cy u gks rks
panzek ,dleku xfr ls ljy js[kh; iFk ij pyrk
jgsxkA
;g ns[kk x;k gS fd fxjrk gqvk lsc i`Foh dh
vksj vkd£"kr gksrk gSA D;k lsc Hkh i`Foh dks
vkd£"kr djrk gS\ ;fn ,slk gS] rks ge i`Foh dks
lsc dh vksj xfr djrs D;ksa ugha ns[k ikrs\
o`Ùk ij Li'kZ js[kk
dksbZ ljy js[kk tks o`Ùk ls osQoy ,d gh
¯cnq ij feyrh gS] o`Ùk ij Li'kZ js[kk
dgykrh gSA bl fp=k esa ljy js[kk ABC
o`Ùk osQ ¯cnq  B ij Li'kZ js[kk gSA
G
2
Mm
F=
d
fp=k 10.2: fdUgha nks ,dleku fiaMksa osQ chp xq#Rokd"kZ.k
cy muosQ osaQnzzksa dks feykus okyh js[kk dh
fn'kk esa funsf'kr gksrk gS
xq#Rokd"kZ.k
147
vkbtd U;wVu dk tUe
baXySaM esa xzSaFke osQ fudV
owYlFkksisZ esa gqvk FkkA foKku
osQ bfrgkl esa og izk;%
lcls vfèkd ekSfyd rFkk
izHkko'kkyh fl¼karoknh osQ
:i esa tkus tkrs gSaA os ,d
fu/Zu o`Q"kd ifjokj eas tUes
FksA ysfdu os [ksrh osQ dke
esa oqQ'ky ugha FksA 1661 esa
f'k{kk xzg.k djus osQ fy, mUgas dSafczt fo'ofo|ky;
Hkst fn;k x;kA lu~ 1665 esa oSaQfczt esa Iysx iSQy
x;k vkSj U;wVu dks ,d o"kZ dh Nqêðh fey xbZA ,slk
dgk tkrk gS fd blh o"kZ muosQ Åij lsc fxjus dh
?kVuk ?kfVr gqbZA bl ?kVuk us U;wVu dks] panzek dks
mldh d{kk eas cuk, j[kus okys cy rFkk xq#Ro cy
osQ chp laca/ dh laHkkouk dh [kkst djus dks izsfjr
fd;kA blls mUgksaus xq#Rokd"kZ.k dk lkoZf=kd fu;e
[kkst fudkykA fof'k"V ckr ;g gS fd muls igys
Hkh cgqr ls egku oSKkfud xq#Ro osQ ckjs esa tkurs
Fks] fdarq os mlosQ egRo dks le>us esa vliQy jgsA
U;wVu us xfr osQ lqizfl¼ fu;eksa dk izfriknu
fd;kA mUgksaus izdk'k rFkk jaxksa osQ fl¼karksa ij dk;Z
fd;kA mUgksaus [kxksyh; izs{k.kksa osQ fy, [kxksyh;
nwjn'khZ dh jpuk dhA U;wVu ,d egku xf.krK Hkh
FksA mUgksaus xf.kr dh ,d ubZ 'kk[kk dh [kkst dh
ftls dyu (Calculus) dgrs gSaA bldk mi;ksx
mUgksaus ;g fl¼ djus osQ fy, fd;k fd fdlh
,dleku ?kuRo okys xksys osQ ckgj fLFkr oLrqvksa
osQ fy, xksys dk O;ogkj bl izdkj dk gksrk gS tSls
fd mldk laiw.kZ nzO;eku mlosQ osaQnzz ij fLFkr gksA
U;wVu us vius xfr osQ rhu fu;eksa rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e ls HkkSfrdh; foKku osQ <k¡ps dks
cny fn;kA l=kgoha 'krkCnh dh izeq[k oSKkfud Økafr
vkbtd U;wVu
(1642 – 1727)
U;wVu us O;qRØe oxZ fu;e dk
vuqeku oSQls yxk;k\
xzgksa dh xfr osQ vè;;u esa lnSo ls gh gekjh
xgjh #fp jgh gSA lksygoha 'krkCnh rd vusd
[kxksy'kkfL=k;ksa us xzgksa dh xfr ls lacaf/r
cgqr ls vk¡dM+s ,df=kr dj fy, FksA tksgkal
oSQIyj us bu vk¡dM+ksa osQ vk/kj ij rhu fu;e
O;qRiUu fd,A bUgsa oSQIyj osQ fu;e dgk tkrk
gSA ;s fu;e bl izdkj gSa%
1. izR;sd xzg dh d{kk ,d nh?kZo`Ùk gksrh gS
vkSj lw;Z bl nh?kZo`Ùk osQ ,d iQksdl ij
gksrk gS tSlk fd fuEu fp=k esa fn[kk;k x;k
gSA bl fp=k esa lw;Z dh fLFkfr dks O ls
n'kkZ;k x;k gSA
2. lw;Z rFkk xzg dks feykus okyh js[kk leku
le; esa leku {ks=kiQy r; djrh gSA bl
izdkj ;fn A ls B rd xfr djus esa yxk le; C
ls D rd xfr djus esa yxs le; osQ cjkcj gks rks
{ks=kiQy OAB rFkk {ks=kiQy OCD cjkcj gkssaxsA
3. lw;Z ls fdlh xzg dh vkSlr nwjh (r ) dk ?ku
ml xzg osQ lw;Z osQ ifjr% ifjØe.k dky T
osQ oxZ osQ lekuqikrh gksrk gSA
vFkok  r
3
/T
2
 = fLFkjkadA
osQ :i esa U;wVu us dkWijfudl] oSQIyj] xSyhfy;ks
rFkk vU; osQ ;ksxnku dks vius dk;ks± osQ lkFk ,d
u, 'kfDr'kkyh la'ys"k.k osQ :i esa lfEefJr fd;kA
;g ,d fof'k"V ckr gS fd ml le; rd xq#Roh;
fl¼kar dk lR;kiu ugha gks ldk Fkk ;|fi mldh
lR;rk osQ ckjs esa dksbZ lansg ugha FkkA bldk dkj.k
Fkk fd U;wVu dk fl¼kar Bksl oSKkfud rdks± ij
vk/kfjr Fkk vkSj xf.kr ls mldh iqf"V Hkh dh xbZ
FkhA blls ;g fl¼kar ljy o ifj"o`Qr gks x;kA ;s
fo'ks"krk,¡ vkt Hkh fdlh vPNs oSKkfud fl¼kar
osQ fy, visf{kr gSaA
foKku
148
2
1
F
d
(10.2)
lehdj.kksa (10.1) rFkk (10.2) ls gesa izkIr gksxk
F  
2
M m
d
(10.3)
;k]  
G
2
M × m
F=
d
(10.4)
tgk¡  G ,d vkuqikfrdrk fLFkjkad gS vkSj bls lkoZf=kd
xq#Roh; fLFkjkad dgrs gSaA
otz&xq.ku djus ij] lehdj.k (10-4) ls izkIr
gksxk
 F × d 
2
 = G M × m
;k  
2
G 
F d
Mm
(10.5)
lehdj.k (10-5) esa cy] nwjh rFkk nzO;eku osQ
ek=kd izfrLFkkfir djus ij gesa  G osQ SI ek=kd
izkIr gksaxs tks N m
2
 kg
–2  
gSA
gSujh oSQosafMl (1731&1810) us ,d lqxzkgh
rqyk dk mi;ksx djosQ G dk eku Kkr fd;kA  G dk
orZeku ekU; eku 6.673 × 10
–11
 N m
2
 kg
–2  
gSA
ge tkurs gSa fd fdUgha Hkh nks oLrqvksa osQ chp
vkd"kZ.k cy fo|eku gksrk gSA vki vius rFkk
lehi cSBs vius fe=k osQ chp yxus okys bl cy
osQ eku dk vfHkdyu dhft,A fu"d"kZ fudkfy,
fd vki bl cy dk vuqHko D;ksa ugha djrsA
;g fu;e lkoZf=kd bl vfHkizk; ls gS fd
;g lHkh oLrqvksa ij ykxw gksrk gS] pkgs ;s
oLrq,¡ cM+h gksa ;k NksVh] pkgs ;s [kxksyh; gksa
;k ik£FkoA
O;qRØe&oxZ
F, d  osQ oxZ osQ O;qRØekuqikrh gS bl dFku
dk vFkZ gS fd ;fn d  dks 6 xq.kk dj fn;k
tk,] rks  F  dk eku 36 ok¡ Hkkx jg tk,xkA
eku yhft,  M  rFkk  m  nzO;eku osQ nks fiaM  A
rFkk B ,d&nwljs ls d nwjh ij fLFkr gSa (fp=k 10-
2)A eku yhft, nksuksa fiaMksa osQ chp vkd"kZ.k cy
F  gSA xq#Rokd"kZ.k osQ lkoZf=kd fu;e osQ vuqlkj]
nksuksa fiaMksa osQ chp yxus okyk cy muosQ nzO;ekuksa
osQ xq.kuiQy osQ lekuqikrh gSA vFkkZr~]
F M × m (10.1)
rFkk nksuksa ¯iMksa osQ chp yxus okyk cy muosQ chp
dh nwjh osQ oxZ osQ O;qRØekuqikrh gS] vFkkZr~]
;g tkuuk egRoiw.kZ
gS fd xzgksa dh xfr
dh O;k[;k djus osQ
fy, oSQIyj dksbZ
fl¼kar izLrqr ugha
dj losQA U;wVu us gh ;g fn[kk;k fd xzgksa dh
xfr dk dkj.k xq#Rokd"kZ.k dk og cy gS tks
lw;Z mu ij yxkrk gSA U;wVu us oSQIyj osQ
rhljs fu;e dk mi;ksx xq#Rokd"kZ.k cy dk
ifjdyu djus esa fd;kA i`Foh dk xq#Rokd"kZ.k
cy nwjh osQ lkFk ?kVrk tkrk gSA ,d ljy roZQ
bl izdkj gSA ge dYiuk dj ldrs gSa fd xzgksa
dh d{kk,¡ o`Ùkkdkj gSaA eku yhft, fd d{kh;
osx v rFkk xzg dh d{kk dh f=kT;k r gSA rc
ifjØek djrs gq, xzg ij yxus okyk cy]
F v
2
/r
;fn ifjØe.k dky T gS] rc v = 2pr/T,
vFkkZr~ v
2 
 r
2
/T
2
bl laca/ dks bl izdkj Hkh fy[kk tk ldrk gS
v
2 
 (1/r) × ( r
3
/T
2
) D;ksafd r
3
/T
2
 oSQIyj ds
rhljs fu;e osQ vuqlkj ,d fLFkjkad gSA
vr%
v
2 
 (1/r)
bls F  v
2
/r osQ lkFk la;ksftr djus ij gesa
izkIr gksrk gS]  F
 
 1/ r
2
.
A
B
C
D
O
bls Hkh tkuas
Page 5


vè;k; 8 rFkk 9 esa geus oLrqvksa dh xfr osQ ckjs
esa rFkk cy dks xfr osQ dkjd osQ :i esa vè;;u
fd;k gSA geus lh[kk gS fd fdlh oLrq dh pky ;k
xfr dh fn'kk cnyus osQ fy, cy dh vko';drk
gksrh gSA ge lnSo ns[krs gSa fd tc fdlh oLrq dks
Å¡pkbZ ls fxjk;k tkrk gS rks og i`Foh dh vksj  gh
fxjrh gSA ge tkurs gSa fd lHkh xzg lw;Z osQ pkjksa
vksj pDdj yxkrs gSaA panzek i`Foh dh ifjØek
djrk gSA bu lHkh voLFkkvksa esa] oLrqvksa ij] xzgksa
ij rFkk panzek ij yxus okyk dksbZ cy vo'; gksuk
pkfg,A vkbtd U;wVu bl rF; dks le> x, Fks
fd bu lHkh osQ fy, ,d gh cy mÙkjnk;h gSA bl
cy dks xq#Rokd"kZ.k cy dgrss gSaA
bl vè;k; esa ge xq#Rokd"kZ.k rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e osQ ckjs esa vè;;u djsaxsA ge
i`Foh ij xq#Rokd"kZ.k cy osQ izHkko osQ varxZr
oLrqvksa dh xfr ij fopkj djsaxsA ge vè;;u djsaxs
fd fdlh oLrq dk Hkkj ,d LFkku ls nwljs LFkku ij
fdl izdkj ifjo£rr gksrk gSA nzoksa esa oLrqvksa osQ
Iyou dh 'krks± osQ ckjs esa Hkh ge fopkj&foe'kZ
djsaxsA
10.1 xq#Rokd"kZ.k
ge tkurs gSa fd panzek i`Foh dk pDdj yxkrk gSA
fdlh oLrq dks tc Åij dh vksj isaQdrs gSa] rks og
oqQN Å¡pkbZ rd Åij igq¡prh gS vkSj fiQj uhps dh
vksj fxjus yxrh gSA dgrs gSa fd tc U;wVu ,d
isM+ osQ uhps cSBs Fks rks ,d lsc mu ij fxjkA lsc
osQ fxjus dh fØ;k us U;wVu dks lkspus osQ fy, izsfjr
fd;kA mUgksaus lkspk fd ;fn i`Foh lsc dks viuh
vksj vkd£"kr dj ldrh gS rks D;k ;g panzek dks
vkd£"kr ugha dj ldrh\ D;k nksuksa fLFkfr;ksa esa
ogh cy yx jgk gS\ mUgksaus vuqeku yxk;k fd
nksuksa voLFkkvksa esa ,d gh izdkj dk cy mÙkjnk;h
gSA mUgksaus roZQ fn;k fd viuh d{kk osQ izR;sd ¯cnq
ij panzek fdlh ljy js[kh; iFk ij xfr ugha djrk
oju~ i`Foh dh vksj fxjrk jgrk gSA vr% og vo';
gh i`Foh }kjk vkd£"kr gksrk gSA ysfdu ge okLro
esa panzek dks i`Foh dh vksj fxjrs gq, ugha ns[krsA
vkb, panzek dh xfr dks le>us osQ fy,
fØ;kdyki 8.11 ij iqu% fopkj djsaA
fØ;kdyki _ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ _1 1 10 0 0. . .1 1 1
• /kxs dk ,d VqdM+k yhft,A blosQ ,d fljs
ij ,d NksVk iRFkj ck¡f/,A
• /kxs osQ nwljs fljs dks idfM+, vkSj iRFkj dks
o`Ùkkdkj iFk esa ?kqekb, tSlk fd fp=k 10-1 esa
fn[kk;k x;k gSA
10
xq#Rokd"kZ.k
(Gravitation)
vè;k;
fp=k 10.1: iRFkj }kjk fu;r ifjek.k osQ osx ls o`Ùkkdkj
iFk esa xfr
foKku
146
xfr osQ rhljs fu;e osQ vuqlkj lsc Hkh i`Foh
dks vkd£"kr djrk gSA ysfdu xfr osQ nwljs fu;e
osQ vuqlkj] fdlh fn, gq, cy osQ fy, Roj.k oLrq
osQ nzO;eku osQ O;qRØekuqikrh gksrk gS [lehdj.k
(9-4)]A i`Foh dh vis{kk lsc dk nzO;eku ux.;
gSA blhfy, ge i`Foh dks lsc dh vksj xfr djrs
ugha ns[krsA blh roZQ dk foLrkj ;g tkuus osQ fy,
dhft, fd i`Foh panzek dh vksj xfr D;ksa ugha
djrhA
gekjs lkSj ifjokj esa] lHkh xzg lw;Z dh ifjØek
djrs gSaA igys dh Hkk¡fr roZQ djosQ ge dg ldrs
gSa fd lw;Z rFkk xzgksa osQ chp ,d cy fo|eku gSA
mijksDr rF;ksa osQ vk/kj ij U;wVu us fu"d"kZ fudkyk
fd osQoy i`Foh gh lsc vkSj panzek dks vkd£"kr
ugha djrh] cfYd fo'o osQ lHkh fiaM ,d&nwljs
dks vkd£"kr djrs gSaaaA oLrqvksa osQ chp ;g vkd"kZ.k
cy xq#Rokd"kZ.k cy dgykrk gSA
10.1.1 xq#Rokd"kZ.k dk lkoZf=kd fu;e
fo'o dk izR;sd fiaM izR;sd vU; fiaM dks ,d
cy ls vkd£"kr djrk gS] tks nksuksa fiaMksa osQ nzO;ekuksa
osQ xq.kuiQy osQ lekuqikrh rFkk muosQ chp dh nwjh
osQ oxZ osQ O;qRØekuqikrh gksrk gSA ;g cy nksuksa
fiaMksa dks feykus okyh js[kk dh fn'kk esa yxrk gSA
• iRFkj dh xfr dh fn'kk dks nsf[k,A
• vc /kxs dks NksfM+,A
• fiQj ls iRFkj dh xfr dh fn'kk dks nsf[k,A
/kxs dks NksM+us ls igys iRFkj ,d fuf'pr
pky ls o`Ùkkdkj iFk esa xfr djrk gS rFkk izR;sd
¯cnq ij mldh xfr dh fn'kk cnyrh gSA fn'kk osQ
ifjorZu esa osx&ifjorZu ;k Roj.k lfEefyr gSA
ftl cy osQ dkj.k ;g Roj.k gksrk gS rFkk tks oLrq
dks o`Ùkkdkj iFk esa xfr'khy j[krk gS] og cy osaQnzz
dh vksj yxrk gSA bl cy dks vfHkosaQnz cy dgrs
gSaA bl cy dh vuqifLFkfr esa iRFkj ,d ljy js[kk
esa eqDr :i ls xfr'khy gks tkrk gSA ;g ljy js[kk
o`Ùkh; iFk ij Li'kZ js[kk gksxhA
bls Hkh tkusa
i`Foh osQ pkjksa vksj panzek dh xfr vfHkosaQnz cy
osQ dkj.k gSA vfHkosaQnz cy i`Foh osQ vkd"kZ.k cy
osQ dkj.k fey ikrk gSA ;fn ,slk dksbZ cy u gks rks
panzek ,dleku xfr ls ljy js[kh; iFk ij pyrk
jgsxkA
;g ns[kk x;k gS fd fxjrk gqvk lsc i`Foh dh
vksj vkd£"kr gksrk gSA D;k lsc Hkh i`Foh dks
vkd£"kr djrk gS\ ;fn ,slk gS] rks ge i`Foh dks
lsc dh vksj xfr djrs D;ksa ugha ns[k ikrs\
o`Ùk ij Li'kZ js[kk
dksbZ ljy js[kk tks o`Ùk ls osQoy ,d gh
¯cnq ij feyrh gS] o`Ùk ij Li'kZ js[kk
dgykrh gSA bl fp=k esa ljy js[kk ABC
o`Ùk osQ ¯cnq  B ij Li'kZ js[kk gSA
G
2
Mm
F=
d
fp=k 10.2: fdUgha nks ,dleku fiaMksa osQ chp xq#Rokd"kZ.k
cy muosQ osaQnzzksa dks feykus okyh js[kk dh
fn'kk esa funsf'kr gksrk gS
xq#Rokd"kZ.k
147
vkbtd U;wVu dk tUe
baXySaM esa xzSaFke osQ fudV
owYlFkksisZ esa gqvk FkkA foKku
osQ bfrgkl esa og izk;%
lcls vfèkd ekSfyd rFkk
izHkko'kkyh fl¼karoknh osQ
:i esa tkus tkrs gSaA os ,d
fu/Zu o`Q"kd ifjokj eas tUes
FksA ysfdu os [ksrh osQ dke
esa oqQ'ky ugha FksA 1661 esa
f'k{kk xzg.k djus osQ fy, mUgas dSafczt fo'ofo|ky;
Hkst fn;k x;kA lu~ 1665 esa oSaQfczt esa Iysx iSQy
x;k vkSj U;wVu dks ,d o"kZ dh Nqêðh fey xbZA ,slk
dgk tkrk gS fd blh o"kZ muosQ Åij lsc fxjus dh
?kVuk ?kfVr gqbZA bl ?kVuk us U;wVu dks] panzek dks
mldh d{kk eas cuk, j[kus okys cy rFkk xq#Ro cy
osQ chp laca/ dh laHkkouk dh [kkst djus dks izsfjr
fd;kA blls mUgksaus xq#Rokd"kZ.k dk lkoZf=kd fu;e
[kkst fudkykA fof'k"V ckr ;g gS fd muls igys
Hkh cgqr ls egku oSKkfud xq#Ro osQ ckjs esa tkurs
Fks] fdarq os mlosQ egRo dks le>us esa vliQy jgsA
U;wVu us xfr osQ lqizfl¼ fu;eksa dk izfriknu
fd;kA mUgksaus izdk'k rFkk jaxksa osQ fl¼karksa ij dk;Z
fd;kA mUgksaus [kxksyh; izs{k.kksa osQ fy, [kxksyh;
nwjn'khZ dh jpuk dhA U;wVu ,d egku xf.krK Hkh
FksA mUgksaus xf.kr dh ,d ubZ 'kk[kk dh [kkst dh
ftls dyu (Calculus) dgrs gSaA bldk mi;ksx
mUgksaus ;g fl¼ djus osQ fy, fd;k fd fdlh
,dleku ?kuRo okys xksys osQ ckgj fLFkr oLrqvksa
osQ fy, xksys dk O;ogkj bl izdkj dk gksrk gS tSls
fd mldk laiw.kZ nzO;eku mlosQ osaQnzz ij fLFkr gksA
U;wVu us vius xfr osQ rhu fu;eksa rFkk xq#Rokd"kZ.k
osQ lkoZf=kd fu;e ls HkkSfrdh; foKku osQ <k¡ps dks
cny fn;kA l=kgoha 'krkCnh dh izeq[k oSKkfud Økafr
vkbtd U;wVu
(1642 – 1727)
U;wVu us O;qRØe oxZ fu;e dk
vuqeku oSQls yxk;k\
xzgksa dh xfr osQ vè;;u esa lnSo ls gh gekjh
xgjh #fp jgh gSA lksygoha 'krkCnh rd vusd
[kxksy'kkfL=k;ksa us xzgksa dh xfr ls lacaf/r
cgqr ls vk¡dM+s ,df=kr dj fy, FksA tksgkal
oSQIyj us bu vk¡dM+ksa osQ vk/kj ij rhu fu;e
O;qRiUu fd,A bUgsa oSQIyj osQ fu;e dgk tkrk
gSA ;s fu;e bl izdkj gSa%
1. izR;sd xzg dh d{kk ,d nh?kZo`Ùk gksrh gS
vkSj lw;Z bl nh?kZo`Ùk osQ ,d iQksdl ij
gksrk gS tSlk fd fuEu fp=k esa fn[kk;k x;k
gSA bl fp=k esa lw;Z dh fLFkfr dks O ls
n'kkZ;k x;k gSA
2. lw;Z rFkk xzg dks feykus okyh js[kk leku
le; esa leku {ks=kiQy r; djrh gSA bl
izdkj ;fn A ls B rd xfr djus esa yxk le; C
ls D rd xfr djus esa yxs le; osQ cjkcj gks rks
{ks=kiQy OAB rFkk {ks=kiQy OCD cjkcj gkssaxsA
3. lw;Z ls fdlh xzg dh vkSlr nwjh (r ) dk ?ku
ml xzg osQ lw;Z osQ ifjr% ifjØe.k dky T
osQ oxZ osQ lekuqikrh gksrk gSA
vFkok  r
3
/T
2
 = fLFkjkadA
osQ :i esa U;wVu us dkWijfudl] oSQIyj] xSyhfy;ks
rFkk vU; osQ ;ksxnku dks vius dk;ks± osQ lkFk ,d
u, 'kfDr'kkyh la'ys"k.k osQ :i esa lfEefJr fd;kA
;g ,d fof'k"V ckr gS fd ml le; rd xq#Roh;
fl¼kar dk lR;kiu ugha gks ldk Fkk ;|fi mldh
lR;rk osQ ckjs esa dksbZ lansg ugha FkkA bldk dkj.k
Fkk fd U;wVu dk fl¼kar Bksl oSKkfud rdks± ij
vk/kfjr Fkk vkSj xf.kr ls mldh iqf"V Hkh dh xbZ
FkhA blls ;g fl¼kar ljy o ifj"o`Qr gks x;kA ;s
fo'ks"krk,¡ vkt Hkh fdlh vPNs oSKkfud fl¼kar
osQ fy, visf{kr gSaA
foKku
148
2
1
F
d
(10.2)
lehdj.kksa (10.1) rFkk (10.2) ls gesa izkIr gksxk
F  
2
M m
d
(10.3)
;k]  
G
2
M × m
F=
d
(10.4)
tgk¡  G ,d vkuqikfrdrk fLFkjkad gS vkSj bls lkoZf=kd
xq#Roh; fLFkjkad dgrs gSaA
otz&xq.ku djus ij] lehdj.k (10-4) ls izkIr
gksxk
 F × d 
2
 = G M × m
;k  
2
G 
F d
Mm
(10.5)
lehdj.k (10-5) esa cy] nwjh rFkk nzO;eku osQ
ek=kd izfrLFkkfir djus ij gesa  G osQ SI ek=kd
izkIr gksaxs tks N m
2
 kg
–2  
gSA
gSujh oSQosafMl (1731&1810) us ,d lqxzkgh
rqyk dk mi;ksx djosQ G dk eku Kkr fd;kA  G dk
orZeku ekU; eku 6.673 × 10
–11
 N m
2
 kg
–2  
gSA
ge tkurs gSa fd fdUgha Hkh nks oLrqvksa osQ chp
vkd"kZ.k cy fo|eku gksrk gSA vki vius rFkk
lehi cSBs vius fe=k osQ chp yxus okys bl cy
osQ eku dk vfHkdyu dhft,A fu"d"kZ fudkfy,
fd vki bl cy dk vuqHko D;ksa ugha djrsA
;g fu;e lkoZf=kd bl vfHkizk; ls gS fd
;g lHkh oLrqvksa ij ykxw gksrk gS] pkgs ;s
oLrq,¡ cM+h gksa ;k NksVh] pkgs ;s [kxksyh; gksa
;k ik£FkoA
O;qRØe&oxZ
F, d  osQ oxZ osQ O;qRØekuqikrh gS bl dFku
dk vFkZ gS fd ;fn d  dks 6 xq.kk dj fn;k
tk,] rks  F  dk eku 36 ok¡ Hkkx jg tk,xkA
eku yhft,  M  rFkk  m  nzO;eku osQ nks fiaM  A
rFkk B ,d&nwljs ls d nwjh ij fLFkr gSa (fp=k 10-
2)A eku yhft, nksuksa fiaMksa osQ chp vkd"kZ.k cy
F  gSA xq#Rokd"kZ.k osQ lkoZf=kd fu;e osQ vuqlkj]
nksuksa fiaMksa osQ chp yxus okyk cy muosQ nzO;ekuksa
osQ xq.kuiQy osQ lekuqikrh gSA vFkkZr~]
F M × m (10.1)
rFkk nksuksa ¯iMksa osQ chp yxus okyk cy muosQ chp
dh nwjh osQ oxZ osQ O;qRØekuqikrh gS] vFkkZr~]
;g tkuuk egRoiw.kZ
gS fd xzgksa dh xfr
dh O;k[;k djus osQ
fy, oSQIyj dksbZ
fl¼kar izLrqr ugha
dj losQA U;wVu us gh ;g fn[kk;k fd xzgksa dh
xfr dk dkj.k xq#Rokd"kZ.k dk og cy gS tks
lw;Z mu ij yxkrk gSA U;wVu us oSQIyj osQ
rhljs fu;e dk mi;ksx xq#Rokd"kZ.k cy dk
ifjdyu djus esa fd;kA i`Foh dk xq#Rokd"kZ.k
cy nwjh osQ lkFk ?kVrk tkrk gSA ,d ljy roZQ
bl izdkj gSA ge dYiuk dj ldrs gSa fd xzgksa
dh d{kk,¡ o`Ùkkdkj gSaA eku yhft, fd d{kh;
osx v rFkk xzg dh d{kk dh f=kT;k r gSA rc
ifjØek djrs gq, xzg ij yxus okyk cy]
F v
2
/r
;fn ifjØe.k dky T gS] rc v = 2pr/T,
vFkkZr~ v
2 
 r
2
/T
2
bl laca/ dks bl izdkj Hkh fy[kk tk ldrk gS
v
2 
 (1/r) × ( r
3
/T
2
) D;ksafd r
3
/T
2
 oSQIyj ds
rhljs fu;e osQ vuqlkj ,d fLFkjkad gSA
vr%
v
2 
 (1/r)
bls F  v
2
/r osQ lkFk la;ksftr djus ij gesa
izkIr gksrk gS]  F
 
 1/ r
2
.
A
B
C
D
O
bls Hkh tkuas
xq#Rokd"kZ.k
149
(ii) i`Foh osQ pkjksa vksj panzek dh xfr_
(iii) lw;Z osQ pkjksa vksj xzgksa dh xfr_ rFkk
(iv) panzek rFkk lw;Z osQ dkj.k Tokj&HkkVkA
10.2 eqDr iru
eqDr iru dk vFkZ tkuus osQ fy, vkb, ,d
fØ;kdyki djsaA
fØ;kdyki _ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ __ _ _1 1 10 0 0. . .2 2 2
• ,d iRFkj yhft,A
• bls Åij dh vksj isaQfd,A
• ;g ,d fuf'pr Å¡pkbZ rd igq¡prk gS vkSj
rc  uhps fxjus yxrk gSA
ge tkurs gSa fd i`Foh oLrqvksa dks viuh vksj
vkd£"kr djrh gSA i`Foh osQ bl vkd"kZ.k cy dks
xq#Roh; cy dgrs gSaA vr% tc oLrq,¡ i`Foh dh
vksj osQoy blh cy osQ dkj.k fxjrh gSa] ge dgrs
gSa fd oLrq,¡ eqDr iru esa gSaA D;k fxjrh gqbZ
oLrqvksa osQ osx esa dksbZ ifjorZu gksrk gS\ fxjrs
le; oLrqvksa oQh xfr dh fn'kk esa dskbZ ifjorZu
ugha gksrkA ysfdu i`Foh osQ vkd"kZ.k osQ dkj.k osx
osQ ifjek.k esa ifjorZu gksrk gSA osx esa dksbZ Hkh
ifjorZu Roj.k dks mRiUu djrk gSA tc Hkh dksbZ
oLrq i`Foh dh vksj fxjrh gS] Roj.k dk;Z djrk gSA
;g Roj.k i`Foh osQ xq#Roh; cy osQ dkj.k gSA
blfy, bl Roj.k dks i`Foh osQ xq#Roh; cy osQ
dkj.k Roj.k ;k xq#Roh; Roj.k dgrs gSaA bls 'g' ls
fu£n"V djrs gSaA g osQ ek=kd ogh gSa tks Roj.k osQ gSa]
vFkkZr~  m s
–2
A
xfr osQ nwljs fu;e ls gesa Kkr gS fd cy
nzO;eku rFkk Roj.k dk xq.kuiQy gSA eku yhft,
fØ;kdyki 10-2 esa iRFkj dk nzO;eku m gSA ge
igys ls gh tkurs gSa fd eqDr :i ls fxjrh oLrqvksa
esa xq#Roh; cy osQ dkj.k Roj.k yxrk gS vkSj bls
mnkgj.k 10.1 i`Foh dk nzO;eku 6 × 10
24
 kg gS
rFkk panzek dk nzO;eku 7.4 × 10
22
 kg gSA
;fn i`Foh rFkk panzek osQ chp dh nwjh
3.84 × 10
5 
km gS rks i`Foh }kjk panzek ij
yxk, x, cy dk ifjdyu dhft,A
G = 6.7 × 10
–11
 N m
2
 kg
-2
gy%
i`Foh dk nzO;eku] M = 6 × 10
24
 kg
panzek dk nzO;eku] m = 7.4 × 10
22
 kg
i`Foh rFkk panzek osQ chp dh nwjh]
d = 3.84 × 10
5 
km
= 3.84 × 10
5 
× 1000 m
= 3.84 × 10
8
 m
G = 6.7 × 10
–11
 N m
2
 kg
–2
lehdj.k (10-4) ls] i`Foh }kjk panzek ij
yxk;k x;k cy]
G
2
M × m
F =
d
11 2 –2 24 22
8 2
6.7 10N m kg 6 10 kg 7.4 10 kg
(3.84 10 m)
= 2.01 × 10
20
 N.
vr% i`Foh }kjk panzek ij yxk;k x;k cy
2.01 × 10
20
 N gSA
'u
1 . xq#Rokd"kZ.k dk lkoZf=kd fu;e crkb,A
2 . i`Foh rFkk mldh lrg ij j[kh fdlh
oLrq osQ chp yxus okys xq#Rokd"kZ.k cy
dk ifjek.k Kkr djus dk lw=k fyf[k,A
10.1.2 xq#Rokd"kZ.k osQ lkoZf=kd fu;e dk
egRo
xq#Rokd"kZ.k dk lkoZf=kd fu;e vusd ,slh ifj?kVukvksa
dh liQyrkiwoZd O;k[;k djrk gS tks vlac¼ ekuh
tkrh Fkha%
(i) gesa i`Foh ls ck¡/s j[kus okyk cy_
iz