www.sura
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s.comáfu« bjhLnth«
ïa‰ãaš
òâa
11-M« tF¥ò
Ruh g¥Ënfõ‹°
br‹id.
2018-M« M©L¡fhd òâa nj®î¤â£l¤â‹go jahÇ¡f¥g£LŸsJ.
2017-18 M©L¡fhd (bjhFâ I k‰W« II) ghlüšfË‹ 2 & 3
kâ¥bg© Édh-ÉilfŸ, ghlthÇahf¤ ju¥g£LŸsd.
x›bthU ghl¤â‰F« K¡»a Édh ÉilfŸ.
2018 bghJ¤nj®î¡F ga‹jU« tifÆš jahÇ¡f¥g£LŸsJ.
áw¥g«r§fŸ
lh®bf£
kâ¥bg©
Édh-Éil2 & 3
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(ii)
2017-18 gâ¥ò
© btËp£lhs®fŸ
ISBN : 978-93-81650-78-3 F¿p£L v© : SG190
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1620, `n#’ ãsh¡,
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(iii)
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(iv)
bghUsl¡f«
bjhFâ I
1. ïašcyf¤â‹j‹ikí«mså£oaY« ......1 - 10
2. ïa¡fÉaš ................................................................. 11 - 18
3. RHš ïa¡f ÉirÆaš ..........................................19 - 24
4. <®¥ãaY«É©btËm¿ÉaY«.......................25 - 36
5. âl,ghŒk¥bghUŸfË‹ïaªâuÉaš .......... 37 - 44
bjhFâ II
6. miyîfŸ .................................................................. 45 - 63
7. miyïa¡f« .......................................................... 64 - 79
8. bt¥gK«bt¥gïa¡fÉaY« ............................80 - 95
9. fâ®xËÆaš ...........................................................96 - 109
10. fhªjÉaš ...............................................................110 - 124
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ïa‰ãaš
11M« tF¥ò
1. ïaš cyf¤â‹ j‹ikí« mså£oaY«
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. bjhÊšE£g¤âšïa‰ãaÈ‹g§FahJ?
� ï a ‰ ã a š n f h £ g h L f i s , e i l K i w Æ š
ga‹gL¤JtJ bjhÊš E£g« vd¥gL«.
� ÚuhÉ vªâu¤â‹ f©Lão¥ò mQ¡fËš ïUªJ
M‰wiy bgw Koí«.
� ínuÅa¤ij Ãô£uhid¡ bfh©L ãs¡f Koí«.
� M‰wÈ‹ kh‰W _y§fis¡ f©l¿jš
� ïa‰ãaÈ‹ k‰bwhU ga‹ghL bjhF¥ò¢R‰W. ïªj
IC-¡fË‹ ts®¢á f bjhÊiy ts®¢áaila¢
brŒJŸsJ.
2. mo¥gilmyFfisí«tÊmyFfisí«ntWgL¤Jf.
mo¥gil myFfŸ tÊ myFfŸ
m o ¥ g i l m s î f i s
m s ª j ¿ í « m y F f Ÿ
m o ¥ g i l m y F f Ÿ
vd¥gL«.k‰w vªj ïa‰ãaš
myFfshY« F¿¥ãl¥gl
Koahj myFfŸ mo¥gil
myFfŸ vd¥gL«.
vfh:- Ús«, Ãiw, fhy«,
bt¥gÃiy.
tÊ msîfis msªj¿í«
m y F f Ÿ t Ê m y F f Ÿ
vd¥gL«.
m o ¥ g i l m y F f s h š
F¿¥ãl¡ Toa myFfis
tÊ myFfŸ vdyh«.
vfh : - gu¥ò , fd msî,
ml®¤â.
[1]
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 3
j‹ kâ¥ÕL-fz¡FfŸ
1. 1Û£lÇšv¤jidthÅašmyFfŸcŸsd?
1.496 × 1011 Û£l® = 1 thÅaš myF
1 Û£l® = 1
1.496 × 1011 = 10-11
1.496
= 6.683 × 10-12 thÅaš myF
∴1 Û£lÇš 6.683 × 10-12 thÅaš myFfŸ cŸsd.
2. vy¡£uh‹x‹¿‹Ãiw9.11 × 10–31 kgvÅšv¤jid
vy¡£uh‹fË‹bkh¤jÃiw1 kgMfïU¡F«?
9.11 × 10-31 kg = 1 vy¡£uh‹ Ãiw
1 kg = 1
9.11 × 10-31 = 1031
9.11 = 1.097 × 1030
∴1.097 × 1030 vy¡£uh‹fË‹ bkh¤j Ãiw 1 kg Mf
ïU¡F«.
3. Ñœ¡fh©gdt‰¿‹K¡»av©QU¡fŸahit?
(i) 600900 - 4
(ii) 5212.0 - 5
(iii) 6.320 - 4
(iv) 0.0631 - 3
(v) 2.64 × 1024 - 3
4. π = 3.14vÅšπ2 kâ¥igK¡»av©QUɉFrkkhf¡
fz¡»Lf.
π = 3.14 ; = π2 = 3.14 × 3.14 = 9.858
π -‹ K¡»a v©QU = 3
π2 -‹ kâ¥ò = 9.86
vdnt π2 -‹ kâ¥ò K¡»a v©QUɉF¢ 9.86 rk«.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 5
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ :
1. Éirv‹whšv‹d?
b g h U Ë ‹ X Œ î à i y i a n a h m š y J ï a ¡ f Ãiyianah kh‰w mj‹ ÛJ brašgL¤j¥gL« òw¡fhu ÉirahF«.
2. Ús«v‹whšv‹d?
ïU òŸËfS¡F ïil¥g£l bjhiyî Ús« vd
tiuaW¡f¥gL»wJ. Ús¤â‹ SI myF Û£l® MF«.
3. Ãiwv‹whšv‹d?
bghUŸ x‹W bg‰WŸs gU¥bghUË‹ msî Ãiw
MF«. ÃiwÆ‹ SI myF »nyh»uh«.
4. M«ãa®-tiuaW.
bt‰¿l¤âš, xU Û£l® ïilbtËÆš it¡f¥g£l òw¡f¡f¤j¡f FW¡F¥ gu¥ò cila, ïU KoÉšyh Ús§fŸ cila ïiz¡ fl¤âfŸ tÊna xU Û£l® Ús¤âš ghí« Óuhd Ä‹ndh£l«, m›ÉU
fl¤âfS¡»ilna 2×10–7 N Éiria V‰gL¤âdhš, m«Ä‹ndh£l« xU M«ãa® MF«.
5. bfšÉ‹-tiuaW
bfšÉ‹ v‹gJ ÚÇ‹ K¥òŸËÆš bt¥g ïa¡fÉaÈ‹
bt¥gÃiyÆš 1
273.16 ã‹d¥gFâ MF«.
6. SI myFKiwv‹whšv‹d?
� xU Óuhd xG§FKiwia ã‹g‰Wtj‰fhf 1960«
M©oš eilbg‰w vilfŸ k‰W« msåLfŸ
kheh£oš , SI myF Kiw cUth¡f¥g£L
midtuhY« V‰W¡ bfhŸs¥g£lJ.
� ï«KiwahdJ áy kh‰w§fSl‹ Toa mks KiwahF«.
� mjhtJ Ãahakhd mksA v‹gJ SI KiwahF«.
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6 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
7. m¿ÉašKiwfŸv‹whšv‹d?
Kiwahd c‰W neh¡f§fŸ, fhuz« m¿jš, khâÇfŸ
k‰W«, fU¤âaš És¡f« jUɤjš ngh‹wt‰iw
cŸsl¡»anj m¿Éaš KiwfŸ vd¥gL«.
8. ïa‰ãašv‹whšv‹d?
ïa‰ãaÈ‹ bghUŸ ïa‰if v‹gjhF«.
Äfî« mo¥gil m¿Éayhd ïa‰ãaš, ïa‰if k‰W«
ïa‰if Ãfœîfis És¡F»wJ. ms¤j¿a¥gL«
mo¥gil m¿Éaš ïa‰ãaš vd¥gL»wJ.
9. ïaªâuÉašv‹whšv‹d?
JfŸfŸ mšyJ bghUŸfË‹ XŒî Ãiy mšyJ
ïa¡f Ãiy g‰¿ TWtJ ïaªâuÉaš MF«.
10. mQk‰W«mQ¡fUïa‰ãašv‹whšv‹d?
gU¥bghUË‹ f£lik¥ãidí« cŸËU¥gd t‰iwí«,
mQ¡fS«, mQ¡fU¡fS« v›thW vy¡£uh‹,
ngh£lh‹ ngh‹w mo¥gil¤ JfŸfSl‹ ïilÉil
òÇ»‹wd v‹gijí« mQ k‰W« mQ¡fU ïa‰ãaš
vd¥gL«.
11. nf©oyh-tiuaW.
xË _y« x‹W cÄG« 540×1012Hz mâ®bt© cila
x‰iw Ãw¡ fâ®å¢á‹ br¿î, xU F¿¥ã£l âirÆš
xU °onuoaD¡F 1
683th£ vÅš m¤âirÆš
xË¢br¿î xU nf©oyh MF«.
12. nkhš-tiuaW.
0.012 »nyh »uhÄš cŸs fh®g‹-12 mQ¡fŸ ngh‹w
gy mo¥gil¤ JfŸfis cŸsl¡»a bghUË‹ msî
nkhš MF«.
13. ÚÇ‹K¥òŸËv‹whšv‹d?
bjÉ£L ÚuhÉ, Jha Ú® k‰W« cUF« gÅ¡f£o M»a
_‹W« rkÃiyÆš cŸs nghJ ïU¡F« bt¥gÃiy
ÚÇ‹ K¥òŸË vd¥gL«. ÚÇ‹ K¥òŸË bt¥gÃiy
273.16 K.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 11
2. ïa¡fÉaš
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. »H¡Fneh¡»4 km elªJãwFtl¡Fneh¡»elªJ
3 km elªJbršY«khzt®xUt®(i)fl¡F«bjhiyî
k‰W«(ii) V‰gL¤J«ïl¥bga®¢áia¡fz¡»Lf.
(i) fl¡F« bjhiyî = AB+BC = 4+3 = 7 km(ii) ïl¥bga®¢á = AC = AB BC2 2+
42 32 16 9 25+ += = = 5 km.
2. Äât©o X£Lgt® xUKG¢R‰W R‰¿ tU«nghJ
(i) flªj bjhiyîk‰W« (ii) V‰g£lïl¥bga®¢á
v‹d?
(i) flªj bjhiyî = 2πr(ii) V‰g£l ïl¥bga®¢á = 0.
3. bghUË‹ntf«k‰W«âirntf¤ijntWgL¤Jf.
ntf« âirntf«
1. XuyF fhy¤âš
flªj bjhiyî
ntf« vd¥gL«.
ï l ¥ b g a ® ¢ á k h W « å j «
âirntf« vd¥gL«. F¿¥ã£l
âirÆš JfË‹ ntf« vdî«
ïij tiuaW¡fyh«.
2. ïJ xU °nfyh®
msî MF«.
ïJ xU bt¡l® msî. ïj‰F
v© kâ¥ò« âirí« c©L.
3. ïj‹ myF ms-1 ïj‹ myF ms-1. ïj‹ gÇkhz
thδghL LT-1
4. vâ®KL¡f«v‹gJv‹d?
� fhy¤ij rh®ªJ âirntf« Fiwªjhš KL¡f«
v⮡F¿ bgW«.
� v⮡F¿ cila KL¡f« vâ® KL¡f« vd¥gL«.
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12 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
5. âirntf«-fhy«tiugl¤â‹K¡»a¤Jt«ahJ?
� fhy¤â‹ rh®ghf JfË‹ âirntf¤ij¡ fh£LtJ âirntf« - fhy« tiuglkhF«.
� v–t tiugl¤â‹ Ñœ cŸs gu¥ò F¿¥ã£l fhy ïilbtËÆš V‰gL« JfË‹ ïl¥bga®¢á kh‰w¤ij¡ fh£L»wJ mšyJ JfŸ ef®ªj bjhiyit¡ fh£L»wJ.
6. ÉirÆ‹jh¡f¤ij-tiuaW.
� t fhy¤âš brašgL« F v‹w khwhj ÉirÆ‹
jh¡f« J v‹gJ Éir k‰W« fhy¤â‹ bgU¡f‰gy‹
v‹W tiuaW¡f¥gL»wJ.
� mjhtJ, ÉirÆ‹ jh¡f« = Éir × fhy«.
∴J = F × t. � ÉirÆ‹ jh¡f« xU bt¡l® msî mj‹ myF Ns.
7. ikaÉy¡Fv⮢brašv‹whšv‹d?
� Ãô£lÅ‹ _‹wh« ïa¡f Éâ¥go, x›bthU braY¡F« rkkhd k‰W« vâuhd v⮢braš x‹W c©L.
� ikaneh¡F Éir¡F¢ rkkhd k‰W« vâuhd, v⮢ braš ikaÉy¡F v⮢braš vd¥gL«.
� R‰¿ tU« bghUË‹ KL¡f¤â‹ fhuzkhf¢ brašgL« mšyJ brašgLtjhf Ãid¡f¡Toa xU kha« mšyJ njh‰w Éirna ika Éy¡F v⮢ brayhF«.
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. ÃiyÆašv‹whšv‹d?
bghUŸfË‹ XŒîÃiyia¥ g‰¿aJ ÃiyÆaš MF«.
ï¥ãÇÉš ÉirfŸ rkÃiyÆš brašgl nt©oŸsJ.
2. ïa¡fÉirÆašv‹whšv‹d?
É i r f Ë š j h ¡ f ¤ â ‹ f h u z k h f b g h U Ÿ f Ÿ
ïa§Ftij¥ g‰¿ TWtJ ïa¡f ÉirÆaš MF«.
ïa¡fÉirÆaÈš ïa¡fÉaš k‰W« ÉirÆaš v‹w
ïU c£ãÇîfŸ cŸsd.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 13
3. ïa¡fÉašv‹whšv‹d?
ïa¡f¤ij V‰gL¤J« Éirfis¡ fUjhkš,
ïa¡f¤â‹ ïl¥bga®¢á, âirntf«, KL¡f« k‰W«
fhy« ngh‹wt‰¿‰»ilnaahd¤ bjhl®ig¥ g‰¿¡
TWtJ ïa¡fÉaš MF«.
4. ÉirÆašv‹whšv‹d?
bghUŸfË‹ ïa¡f¤â‰F« brašgL« ÉirfS¡F«
ïilÆyhd bjhl®ig¥ g‰¿ TWtJ ÉirÆaš MF«.
5. JfŸv‹whšv‹d?
gÇkhz§fŸ m‰w, Ãiy¥òŸË cila áWgFâ mšyJ
gU¥bghUË‹ msî JfŸ vd¥gL«.
6. XŒîÃiy,ïa¡fÃiyv‹whšv‹d?
bghUbsh‹W fhy¤ij¢ rh®ªJ jdJ Ãiyia kh‰¿¡
bfhŸshkš ïUªjhš mJ XŒî ÃiyÆš cŸsJ
vd¥gL«.
ïa¡f Ãiy : fhy¤ij¢ rh®ªJ, bghUË‹ Ãiy
kh¿dhš, mJ ïa¡f¤âš cŸsJ vd¥gL«.
7. xUgÇkhzïa¡f«v‹whšv‹d?
fhy¤ij¢ rh®ªJ bghUË‹ Ãiy khWtij xU
T¿id¡ bfh©L F¿¥ã£lhš mjid xU gÇkhz
ïa¡f« vdyh«.
v.fh. ne®nfh£oš vW«ò x‹W efUtJ, Xo¡
bfh©oU¡F« jlfs åu®.
8. xUgÇkhzïa¡f«(ne®¡nfh£oa¡f«)v‹whšv‹d?
ne®¡nfhL x‹¿š V‰gL« ïa¡f« ne®¡nfh£oa¡f«
MF«. ï›Éa¡f¤ij¥ g‰¿ m¿a Ãiy, ïl¥bga®¢á,
âirntf« KL¡f« ngh‹w K¡»akhd¥ g©gsîfŸ
njit¥gL»‹wd.
9. ïl¥bga®¢áv‹whšv‹d?
JfË‹ bjhl¡f Ãiy¡F« ïWâ Ãiy¡F« ïil¥g£l
FW»a bjhiyî ïl¥bga®¢á vd¥gL«.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 19
3. RHš ïa¡f ÉirÆaš
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. rkÃiyÆ‹tiffŸahit?
(i) cW⢠rkÃiy
(ii) cWâa‰w rkÃiy
(iii) eLÃiy rkÃiy.
2. nfhzcªjmÊÉ‹ikÉâia¡TWf.
bghUË‹ ÛJ òw¤âU¥ò Éir brašglhjnghJ, RHY«
â©k¥ bghUË‹ bkh¤j nfhz cªj« khwhkÈU¡F«.
ïJ, nfhz cªj mÊÉ‹ik Éâ vd¥gL«.
bghUË‹ bkh¤j nfhz cªj« = kh¿È.
3. óidÑnHÉG«nghJ,mj‹fhšfŸjiuÆšg⻋wd.
ïa‰ãaÈ‹vªjj¤Jt«ga‹gL»wJ?És¡Ff.
nfhz cªj mÊÉ‹ik Éâ :
óid ÑnH ÉG«nghJ jdJ cliy FW¡Ftj‹
Ãiyk¤ âU¥òâw‹ FiwªJ nfhz âirntf«
mâfÇ¡»wJ. óid jiuia bjhL»‹w nghJ, jdJ
fhšfis Ú£Ltjhš, Ãiyk¤ âU¥òâw‹ mâfǤJ
nfhz¤ âirntf« Fiw»wJ. óid jdJ rhjhuz¤
âirntf¤Jl‹ fhšfis jiuÆš gâ¡»‹wd.
j‹ kâ¥ÕL-fz¡FfŸ
1. 10kg k‰W« 20kg ÃiwfSilaïU nfhs§fŸ 5m ïilbtËÆšcŸsd.ÃiwfS¡»ilnaahd<®¥ãaš
ft®¢áÉiria¡fz¡»Lf?
Kjš nfhs¤â‹ Ãiw m1 = 15kgïu©lh« nfhs¤â‹ Ãiw m2 = 45kgïU nfhs§fS¡F ïilna cŸs Jhu« r =5mbghJ <®¥ò kh¿È G = 66.7 × 1011Nm2kg–2
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20 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
<®¥ãaš ft®¢á Éir F = Gm m
r1 2
2
= 6.67×10 ×10× 20
5= 6.67× 200×10
2511
2
11
= 53.36 ×1011N~ <®¥ãaš ft®¢á Éir = 53.36 × 1011N
2. òÉÆ‹Mu«6400Km vÅš500Km F¤Jau¤âš<®¥ã‹
KL¡f«v‹d?
òÉÆ‹ Mu« R = 6400KmF¤Jau« n = 500KmòÉ <®¥ò KL¡f« g = 9.8ms–2
F¤Jau¤ij¢ rh®ªjJ
òÉ<®¥ò KL¡f« gn = g 1 2hR
-
= 9.8× 1 2×5006400
-
= 9.8× 1 532
-
= 9.8× 27
32
= 8.269ms–2
~500Km F¤Jau¤âš òÉ<®¥ò KL¡f« =8.269ms–2
3. òÉ¥gu¥ã‰FmU»šÉ©btË¡f¥gšx‹WòÉia
t£l¥ghijÆšR‰¿tUkhWbrY¤j¥gL»wJ.<®¥ãaš
ÉirÆÅ‹W ÉLgl mªj É©btË¡ f¥gY¡F
m¢R‰W¥ ghijÆš bfhL¡f¥gl nt©oa TLjš
âirntf«v‹d?(R=6400Km, g=9.8mls2)É © b t Ë ¡ f ¥ g š R ‰ ¿ t U « g h i j Æ š M u «
R = 6400Km = 64 × 105m
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 21
∴ 6400 Km Þ 6400000m Þ 64 × 105mòÉ<®¥ò KL¡f« g = 9.8ms–2
É©btË¡f¥gÈ‹ ÉLgL ntf«, V = gRe
= 9.8× 64×10 = 98× 64×105 4
= 49× 2× 64×104
= 7×8×1.414×10= 5600×10414= 7918m / s= 7.918Km / s
2
òÉÆ‹ ÉLgL âirntf« = 11.2km/s bfhL¡f nt©oa TLjš âirntf« = 11.2–7.918 = 3.282km/s~bfhL¡f¥gl nt©oa TLjš âirntf« = 3.282km/s
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. ÃiwÆ‹ika«v‹whšv‹d?
mik¥ãš, bghUbsh‹¿‹ x£L bkh¤j Ãiwí«
br¿ªâU¡F« òŸË bghUË‹ ÃiwÆ‹ ika«
vd¥gL«.
2. cWârkÃiyv‹whšv‹d?
mik¥ã‹ ÛJ brašgL« ÉirfŸ, Ãiyah‰wš
áWkkhf ïU¡F« bjhl¡f Ãiy¡F tUkhW brŒjhš,
mJ cW⢠rkÃiy vd¥gL«.
3. cWâa‰wrkÃiyv‹whšv‹d?
mik¥ã‹ ÛJ brašgL« ÉirfŸ, Ãiyah‰wš
bgUkkhf ïU¡F« ÃiyÆÈUªJ efu¢ brŒjhš, mJ
cWâa‰w rkÃiy vd¥gL«.
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22 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
4. eLÃiyrkÃiyv‹whšv‹d?
mik¥ã‹ ÛJ brašgL« ÉirfŸ Ãiyah‰wš
khwhâU¡FkhW, v¥go nt©LkhdhY« efu¢ brŒjhš,
mJ eLÃiy rkÃiyahF«.
5. rkÃiyiavt‰iwbfh©Ltif¥gL¤jyh«?
áWk«, bgUk« mšyJ khwhj Ãiyah‰wš bfh©L,
cWâ, cWâa‰w mšyJ eLÃiy vd rkÃiyia¡
F¿¥ãlyh«.
6. RH‰áÆ‹Mu«vj‰FrkkhF«?
bghUË‹ RH‰áÆ‹ m¢áÈUªJ JfŸfË‹ ïUko
_y¢ ruhrÇ ïUko¤ bjhiyɉF (rms) RH‰áÆ‹
Mu« rkkhF«.
K = r r r rn
n12
22 2
32+ + +.....
7. RH‰á-Mu«tiuaW.
bghUË‹ x£Lbkh¤j vilí« br¿ªJŸs òŸË¡F«
RH‰á m¢R¡F« ïil¥g£l br§F¤J¤ bjhiyî vdî«
RH‰á Mu« tiuaW¡f¥gL»wJ.
K = I
M8. ïu£ilv‹whšv‹d?
brašgh£o‹ nfhLfŸ x‹Wl‹ x‹W bghUªjhkš,
brašgl¡Toa ïU rkkhd vâbuâ® ÉirfŸ ïu£il
vd¥gL«.
9. nfhzcªj«-tiuaW.
JfË‹ ne®¡nfh£L cªj¤â‹ âU¥ò âw‹, mj‹
nfhz cªj« vd¥gL«.
→L =
→r ×
→p .
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 25
4. <®¥ãaY« É©btË m¿ÉaY«
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. rhjhuzkhf,eh«ga‹gL¤J«ïUbghUŸfS¡»ilna
<®¥ãašft®¢áÉiriaczuKotâšiy.V‹?
� òÉÆ‹ nk‰gu¥ãYŸs ïU bghUŸfS«, òÉÆ‹
ika¤âÈUªJ rkbjhiyÉš ïU¥gjhš, rk
<®¥ãaš Éir brašgL»wJ.
(mšyJ)
� òÉÆ‹ ika¤âÈUªJ, ïUbghU£fŸ bt›ntW
bjhiyÉš ïU¥gjhš, bghU£fS¡F«, òÉ¡F«
ïilnaahd <®¥ãaš Éir khW»wJ.
(mšyJ)
� ïU rhjhuz bghU£fS¡»ilnaíŸs <®¥ò Éir,
mâf Ãiwbfh©l bghU£fS¡»ilnaŸs <®¥ò
Éiria Él Fiwthf ïU¥gâdhY« <®¥ãaš
Éiria czuKotâšiy.
2. bghJ<®¥ãašÉâiaTWf.
m©l¤âš cŸs gU¥bghUË‹ x›bthU JfS«
k‰bwhU Jfis, mt‰¿‹ ÃiwfË‹ bgU¡f‰gyD¡F
ne®¤jfÉY« mt‰¿‰»ilnaahd bjhiyÉ‹
ïUko¡F vâ®jfÉY« ïU¡F« Éiríl‹ ftU»‹wd.
ï¡T‰W bghJ <®¥ãaš Éâ vd¥gL«.
3. <®¥ãaš kh¿ÈiatiuaW¤J. mj‹my»idí«
gÇkhzthŒ¥gh£ilí«TWf.
x›bthU 1 kg Ãiwíila ïU bghUŸfS¡»ilna
1m bjhiyî ïU¡F«nghJ, mt‰¿‰»ilnaahd,
<®¥ãaš ft®¢á Éir <®¥ãaš kh¿È ‘G’ vd
tiuaW¡f¥gL»wJ. G-‹ kâ¥ò 6.67 ×10-11 N m2 kg-2. mj‹ gÇkhz thŒ¥ghL [M–1 L3 T-2].
4. g-kâ¥ãid¥ghâ¡F«fhuÂfŸahit?
(i) F¤Jau«
(ii) MH«
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26 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
(iii) FW¡F¡nfhL
(iv) òÉ¥gu¥ã‰F nkš, cau« mâfÇ¡F«nghJ <®¥ã‹
KL¡f« Fiw»wJ.
(v) ÃyeL¡nfh£L¥ gFâÆš g-‹ kâ¥ò áWk«.
(vi) ÃyeL¡nfh£L¥ gFâÆÈUªJ JUt§fS¡F
bršY«nghJ g-‹ kâ¥ò mâfÇ¡F«.
5. <®¥ò¥òy¢br¿ÉidtiuaW.
xU òŸËÆš it¡f¥g£l xuyF ÃiwÆ‹ ÛJ
brašgL« Éir, m¥òŸËÆš <®¥ò¥ òy¢ br¿î mšyJ
tÈik vd tiuaW¡f¥gL»wJ. ïj‹ myF Nkg–1.6. <®¥òmG¤j¤ijtiuaW.
<®¥ò¥ òy¤â‰F vâuhf, xU òŸËÆÈUªJ <¿šyh¤
bjhiyɉF, XuyF Ãiwia ef®¤J«nghJ
brŒa¥gL« ntiyÆ‹ msî, m¥òŸËÆš <®¥ò
mG¤j« vd tiuaW¡f¥gL»wJ. ïj‹ myF Nmkg–1.7. ÃyÉštËk©ly«ïšiy,V‹?
ÃyÉš cŸs nyrhd thí¡fË‹ âirntf§fŸ,
ÃyÉ‹ ÉLgL ntf¤â‰F Vw¤jhH rkkhf ïU¥gjhš,
ÃyÉš ïUªJ mit ÉLg£L¢ br‹WÉL«, ÃyÉš
<®¥ò¥ òy« tÈik F‹¿ajhf cŸsjhš, ÃyÉš
ï›thí¡fŸ bjhl®ªJ ïU¡f KoahJ. mjdhš ÃyÉš
tËk©ly« ïšiy.
8. òÉ-Ãiy¤Jiz¡nfhŸfŸv‹gitahit?
� ÃyeL¡nfh£L¥ gFâ¡F nkš, xU F¿¥ã£l
cau¤âš Ãiyahd ïl§fËš ïU¥gJ ngh‹W
njh‹W« bjhiy¤bjhl®ò¤ Jiz¡nfhŸfŸ,
x ¤ â U ¡ F « J i z ¡ n f h Ÿ f Ÿ m š y J ò É -
Ãiy¤Jiz¡ nfhŸfŸ vd¥gL»‹wd.
� Jiz¡nfhshdJ, òÉ¡F nkny xU F¿¥ã£l
ïl¤âš Ãiyahf ïU¥gJ nghš njh‹w
nt©LbkÅš, mjDila R‰W¡fhyK«, òÉÆ‹
j‹Å¢ir¥ g‰¿a RH‰á¡ fhyK« rkkhf ïU¡f
nt©L«.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 27
9. fâut-ika¡bfhŸifia¡TWf.
fâut ika¡ bfhŸifgo mid¤J¡nfhŸfS«
XŒî ÃiyÆš ïU¡F« NÇaid t£l¥ghijfËš
R‰¿tU»‹wd.
10. òÉika¡bfhŸifiaTWf.
òÉ-ika¡ bfhŸifgo m©l¤â‹ ika¤âš òÉí«,
òÉia ikakhf¡ bfh©L mid¤J nfhŸfS«,
ÃyîfS« É©Û‹fS«, bt›ntW R‰W¥ ghijfËš
R‰¿ tU»‹wd.
11. NÇa¡FL«g«v‹gJahJ?
mik¥ã‹ ika¤âš NÇa‹ ïU¡f, mik¥ãš cŸs
nfhŸfŸ, ÃyîfŸ, áWnfhŸfŸ, thšÛ‹fŸ ngh‹w
mid¤J th‹ bghUŸfisí« NÇa‹ j‹Dl‹
ãiz¤J it¤âU¡F«, m©l¤â‹ xU gFâia
NÇa¡FL«g« v‹»nwh«.
12. áWnfhŸfŸv‹gitahit?
b r › t h Œ k ‰ W « É a h H ‹ n f h Ÿ f Ë ‹ R ‰ W ¥
ghijfS¡»ilna NÇaid¢ R‰¿ tU« á¿a th‹
bghUŸfŸ áW nfhŸfŸ vd¥gL«. ÉahH‹ nfhË‹
<®¥ò fhuzkhf, cilªJ nghd Äf¥bgÇa nfhË‹
cilªJ nghd áW J©LfŸ áWnfhŸfshF«.
13. totÉ©Û‹FG¡fŸv‹gitahit?
bgU«ghyhd É©Û‹fŸ, thd¤âš FG¡fshf
x‹W nr®ªJ Éy§FfŸ mšyJ kÅj®fŸ tot¤âš
mikªJŸsd. ïªj FG¡fis tot É©Û‹ FG¡fŸ
vdyh«.
j‹ kâ¥ÕL-fz¡FfŸ
1. cUisahdFHhŒfË‹budhšL v© Vw¤jho 200 MF«. FHhÆ‹ É£l« 2br.Û v‹whš, mâš ghí«
ÚÇ‹âirntf¤ij¡fz¡»Lf.ÚÇ‹gh»ašv©n = 10–3Nsm–2
budhšL v© NR = 2000FHhÆ‹ É£l« D = 2cm = 2 × 10–2
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28 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
ÚÇ‹ gh»aš v© N = 10–3Nsm–2
ÚÇ‹ ml®¤â P = 10–3kg/m3
ghí« ÚÇ‹ âirntf« Vc = nNP
RD = ×
× ×
-
-10 2000
10 2 10
3
3 2
= 10–1
= 0.1m/s~ghí« ÚÇ‹ âirntf« = 0.1m/s
2. 0.02m Mu« bfh©l t£lkhd j£blh‹w ÚÇ‹
nk‰gu¥ãÈUªJmf‰Wt¤wF¤njit¥gL«Éiria¡
fz¡»Lf.ÚÇ‹gu¥òïGÉir0.07mNm–1vd¡bfhŸf.
t£l¤j£o‹ Mu« r = 0.02mÚÇ‹ gu¥ò ïGÉir T = 0.07Nm–1
njitahd Éir F = T × 2pr = 0.07 × 2 × 3.14×0.02 = 12.56 × 7 × 10–4
= 8.792 × 10–3N~ njit¥gL« Éir = 8.8 × 10–3N
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. <u¥ãašÉâÆ‹áw¥ò¤j‹ikfŸahit?
� ïU bghUŸfS¡»ilnaahd <®¥ãaš ÉirahdJ,
xU braš - v⮢braš nrhoahF«.
� nyrhd bghUŸfS¡»ilna, <®¥ãaš Éir Äf¡
Fiwthf ïU¡F«. fdkhd bghUŸfS¡F Éir
mâfkhf ïU¡F«. NÇaD¡F« òÉ¡F« ïilna
cŸs <®¥ãaš Éir Äf mâf«.
2. <®¥ãašKL¡f«v‹whšv‹d?
<®¥ã‹ ÉirÆdhš bghUËš V‰gL« KL¡f« <®¥ã‹
KL¡f« vd¥gL«.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 37
5. âl, ghŒk¥ bghUŸfË‹ ïaªâuÉaš
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. tiuaW.
(i) ۣᤠj‹ikíŸs bghUŸ :
j‹ÛJ brašgL¤j¥g£l cU¡FiyÉ¡F« ÉirfŸ Ú¡f¥g£lîl‹ jdJ bjhl¡f Ãiyia Û©L« bgW« bghUË‹ j‹ik bghUË‹ ۣᥠg©ò vd¥gL»wJ. ï¥g©gig bg‰¿U¡F« bghUŸfŸ ۣᤠj‹ikíŸs bghUŸfŸ vd¥gL»‹wd.
(ii) ۣᤠj‹ika‰w bghUŸ :
ۣᥠg©ò ïšyhj bghUŸfŸ ۣᡠj‹ika‰w
bghUŸ vd¥gL«. v.fh: ãsh°o¡.
(iii) jifî :
cU¡Fiyªj bghUË‹ XuyF gu¥ãš bra‰gL«
ÛŸÉir, jifî vd¥gL«.
jifî = ÛŸÉir
gu¥ò
ïj‹ myF N m-2 ïj‹ gÇkhz thŒ¥ghL
ML-1T-2 MF«.
(iv) âÇò :
xU bghUËš V‰g£l gÇkhz kh‰w¤â‰F« mj‹ bjhl¡f Ãiy¥ gÇkhz¤â‰F« ïilnaahd jfî
âÇò vd¥gL»wJ.
âÇò = gÇkhz¤âš kh‰w«
bjhl¡f Ãiy¥ gÇkhz«
(v) Û£á všiy :
Ãuªju cU¡Fiyî V‰gL« všiy, Û£á všiy vd miH¡f¥gL»wJ.
(vi) ÛŸ Éir :
cU¡Fiy É¡F« ÉirfŸ Ú¡f¥g£lhš,
bghUshdJ jdJ bjhl¡f Ãiyia miltj‰F
m¥bghUËš njh‹W« Éir fhuzkh»wJ. ïªj
Éir ÛŸÉir v‹W miH¡f¥gL»wJ.
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40 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. gU¥bghUË‹x›bthUÃiy¡F«áyâd¥g©òfŸc©L,khWg£lg©òfS¡fhdfhuÂfŸahit?
(i) mQÉil mšyJ _y¡TW Éir k‰W«
(ii) bt¥g¤âdhš ÃfG« _y¡TWfË‹ Óu‰w ïa¡f« mšyJ »s®ªbjGjš ngh‹witahF«.
2. mQÉilÉirv‹whšv‹d?
Ãiy Ä‹}£lÉaš ïilÉidfË‹ fhuzkhf
mQ¡fË‹ Ä‹}£l‡fË¡»ilna bra‰gL« Éir
mQÉil Éir vd¥gL«.
3. ghŒk§fŸv‹whšv‹d?
òwÉir x‹¿‹ bra‰gh£odhš, gha¡Toa bghUŸfŸ
ghŒk§fshF«.
(v.fh) Ú®k«, tËk«.
4. ghFÃiyv‹whšv‹d?
� mL¤jL¤JŸs Ú®k VLfshš V‰gL« cuhŒî
Éiria ghFÃiy Éir v‹W« ï¤j‹ikÆid
ghFÃiy v‹W« miH¡f¥gL»wJ.
� j‹ bt›ntW VLfË‹ rh®ò ïa¡f¤ij v⮡F«
Ú®k¤â‹ j‹ikna ghFÃiy MF«.
5. gh»ašv©v‹whšv‹d?
XuyF¥ gu¥òŸs, br§F¤jhf XuyF¤ âirntf¢
rÇit¡ bfh©l ïu©L Ú®k VLfS¡»ilna
bjhLnfh£o‹ âirÆš bra‰gL« ghFÃiy ÉirÆ‹
v© kâ¥ng gh»aš v© MF«.
6. tÇ¢Ó®X£l«v‹whšv‹d?
Ú®k¤â‹ x›bthU JfS« mj‰F K‹ bršY«
JfË‹ ghijÆnyí«, x›bthU òŸËÆY« fl¡F«
JfË‹ âirntf« mj‰F K‹ bršY« JfË‹
âirntf¤ânyí« bršY« Óuhd X£l« tÇ¢Ó® X£l«
vd¥gL«.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 45
6. miyîfŸ
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. jÅ¢ÓÇir ïa¡f¤ij tiuaW¤J, ïa¡f¤â‰fhd
Ãgªjidfis¡TWf.(VnjD«_‹W)
JfË‹ KL¡fkhdJ, Ãiyahd òŸËÆÈUªJ mJ
milªj ïl¥bga®¢á¡F ne®¤jfÉY«, m¥òŸËia
neh¡»na ïa¡f« ïU¥ãD«, m¤JfŸ jÅ¢ ÓÇir
ïa¡f¤â‰F c£gL»wJ vdyh«.
mik¥bgh‹¿š miyîfŸ V‰gl, Û£á¥g©ò k‰W«
Ãiyk« M»a ïU mo¥gil¥ g©òfŸ fhuzkhf
cŸsd. bghUbsh‹W ika¥òŸËÆÈUªJ ïl«
bgau¢ brŒa¥g£LŸsjhf¡ fUjî«. ÛŸ ÉirahdJ
m¥bghUis Û©L« ika¥òŸË¡F¡ bfh©LtU«.
(i) mâ®É‹ bgUk¥òŸËÆš ïl¥bga®¢á bgUk«;
âirntf« RÊ; KL¡f« bgUk«; bghUshdJ
ika¥òŸËia neh¡» tU«.
(ii) Û Ÿ É i r Æ ‹ f h u z k h f , b g h U Ÿ Û © L «
ika¥òŸËia tªjilí«. m§F irntfkhdJ
v⮥bgUkkhf ïU¥gjhš, bghUŸ ika¥òŸËia¡
flªJbršY«.
(iii) mâ®É‹ v⮥ bgUk¥òŸËÆš ïl¥ga®¢á
v⮥ bgUk«; âirntf« RÊ; KL¡f« ne®¥
bgUk«. vdnt, bghUshJ ika¥òŸËia neh¡»
efU»wJ. Û©L« ika¥òŸËÆš ïl¥bga®¢á
RÊahF« nghJ âirntf« ne®¥bgUkkh»wJ.
(iv) bghUË‹ Ãiyk« fhuzkhf ika¥òŸËia¡
flªJ brš»wJ. ïJngh‹w Ãfœî Û©L«
V‰gLtjhš mik¥ò miyîW»wJ.
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46 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
2. ÓÇirïa¡f§fŸmid¤J«miyîWïa¡f§fshF«.
miyîWïa¡f§fŸmid¤J«ÓÇirïa¡f§fŸMfhJ
V‹?vL¤J¡fh£Ll‹És¡F.
Óuhd ïa¡f§fŸ, Óuiyî ïa¡fK« mšyJ miyîW
ïa¡f§fshF«. VbdÅš ÓÇir ïa¡f¤â‰F
c£g£l xU JfË‹ KL¡fkhdJ ÛŸ ÉirÆ‹
ïl¥bga®¢á¡F ne®¤jfÉY«, m¥òŸËia neh¡»na
ïU¡F«. vL¤J¡fh£lhf xÈ miyfŸ v‹gJ
mG¤j khWgh£lhš V‰gL« ÛŸ Éirahš Clf¤âš
mâ®îW»wJ. Mdhš óÄ, NÇaid¢ R‰WtJ Óuhd
fhy ïilbtËÆš Û©L« Û©L« R‰¿ tU»wJ.
Mdš ÛŸÉir brašgLtâšiy. khwhf òÉ <®¥g:
ÉirahdJ t£l ïa¡f¤â‰fhd ika neh¡F Éiria
mË¡»wJ. ïâš ÛŸÉir ïšyhjjhš (Restore force)
jÅ¢ ÓÇir ïa¡f« MfhJ.
3. Óuhd t£l ïa¡f¤â‹ É£l¤â‹ Ûjhd 圢á
jÅ¢ÓÇir ïa¡f¤â‰F c£gLtij bkŒ¥ã¡fî«.
Óuhd t£l ïa¡f¤â‹ É£l¤â‹ Ûjhd 圢á
jÅ¢ÓÇir ïa¡f« :
Óuhd t£l ïa¡f¤â‹ 圢á
O v ‹ w i k a K « a v ‹ w M u K « c i l a
t £ l ¤ â ‹ g Ç â t Ê n a J f b s h ‹ W v v‹w Óuhd ntf¤Jl‹ ïlŠRʤ âirÆš
ïa§Ftjhf¡ fUjî«. XX' k‰W« YY' v‹gd ïU
br§F¤J É£l§fshF«.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 47
t fhy¤â‰F¥ ãwF JfŸ P-Æš ïU¥gjhf¡ fUjî«.
wv‹gJ nfhz¤âirntf« vÅš, t fhy¤âš V‰g£l
nfhz ïl¥bga®¢á q =wt MF«. P-ÆÈUªJ YY’-¡F PN v‹w br§F¤J¡nfhL tiuaî«. JfshdJ X-ÈUªJ
Y-¡F efU« nghJ, br§F¤J¡nfh£o‹ mo¥òŸË
N-MdJ. O-ÉÈUªJ Y-¡F efU»wJ. nkY«, JfshdJ
Y-ÆÈUªJ X'-¡F« ãwFY'-¡F« Û©L« X-¡F«
ef®ªjhš, 圢á N-MdJ Y-ÆÈUªJ O-ɉF« ãwF
Y'-¡F« Û©L« O-ɉF« efU«. JfshdJ gÇâÆ‹
tÊna xU KG¢ R‰¿a¡f¤ij nk‰bfh©lhš, N v‹w
òŸË O v‹w eLÃiyia¥ bghU¤J xU miyɉF
c£gL»wJ.YY' É£l¤â‹ Ûjhd òŸË N-‹ ïa¡f«
jÅ¢ ÓÇir ïa¡fkhF«.
vdnt, Óuhd t£l ïa¡f¤â‹ É£l¤â‹ Ûjhd 圢á
xU jÅ¢ÓÇir ïa¡fkhF«.
4. jÅ¢ÓÇirïa¡f¤â‰Fc£gL«JfË‹,ïl¥bga®¢á,
âirntf«, KL¡f« M»ait fhy¤ij¢ rh®ªJ
khWgLtijtiugl¤âšfh£Lf.
fhy¤ij¢ rh®ªJ khWgL« ïl¥ bga®¢á, âirntf«
k‰W« KL¡f« M»ait gl¤âš cŸs tiugl§fËš
F¿¥ãl¥g£LŸsd.
(i) ïl¥bga®¢á tiugl« xU ir‹ (sine) tisnfhlhF«.
JfË‹ bgUk ïl¥bga®¢á y = ±a.(ii) mâ®tilí« JfË‹ âirntf« eLÃiy¥ òŸËÆš
bgUkkhF«. mjhtJ, v = ±aw mâ®É‹ bgUk¥
òŸËÆš mj‹ kâ¥ò RÊ MF«.
T4
3T4
T2
aO
–a
T
ïl
¥b
ga
®¢á
(iii) m â ® t i l í « J f Ë ‹ K L ¡ f «
eLeLÃiy¥ òŸËÆš RÊahfî« mâ®É‹
bgUk¥òŸËÆš bgUkkhfî«mjhtJ, aw2 Mf
ïU¡F«.
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48 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
T4
3T4
T2O
âi
rnt
f«
(iv) ï l ¥ b g a ® ¢ á i a É l â i r n t f « p2
f £ l K «
âirntf¤ij Él KL¡f« p2
f£lK« ïl¥bga®¢áia
Él KL¡f« pf£lK« K‹ndh¡» cŸsd. mjhtJ,
ïl¥bga®¢áÆ‹ ne®¡F¿ bgUkkhf ïU¥ã‹,
KL¡f¤â‹ v⮡F¿ bgUkkhf ïU¡F«.
T4
3T4
T2
O
KL
¡f
«
5. mâ®tilí« JfË‹ ( i ) âirntf¤â‰F«
K L ¡ f ¤ â ‰ F « ( i i ) K L ¡ f ¤ â ‰ F « , ï l ¥
bga®¢á¡F« ïilÆyhd f£l ntWghL v‹d?
(i) âirntf¤ij Él KL¡f« p2
f£l« K‹ndh¡»
cŸsJ.
(ii) KL¡f« ïl¥bga®¢áiaÉl p f£l« K‹ndh¡»
cŸsJ. mjhtJ, ïl¥bga®¢á ne®¡F¿ bgUkkhf
ïU¥ã‹, KL¡f« v⮡F¿ bgUkkhf ïU¡F«.
6. tiuaW ( i ) miyî¡f hy« ( i i ) mâ ®bt©
(iii)nfhzmâ®bt©.
(i) miyî¡fhy« : Jfbsh‹W xU KG miyɉF
vL¤J¡bfhŸS« fhy«, miyî¡ fhy« (T)MF«.
wp
=2T
mšyJ T =2pw
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 57
3. 250Nm–1 RUŸkh¿Èíilax¤jRUŸÉšfŸïu©L
ikamik¥ãš gl¤âš fh£oaJ ngh‹W 5kg Ãiw
bjh§fÉl¥g£LŸsJ.mik¥ã‹miyî¡fhy«v‹d?
Ãiw m=5kgmiyî¡ fhy« T= 2 m
2kp
= 2×3.14 5
2× 250
= 6.28 5500
= 6.28
1100
= 6.2810
T = 0.628s
4. ÓuhdFW¡f¥gu¥òila,br§F¤jhfU tot¡FHhÆš
0.3m cau¤â‰FÚ®cŸsJ.Ú®k£l«ÓÇirïa¡f¤â‰F
c£gL«nghJmiyî¡fhy¤ij¡fz¡»Lf?
U tot¡ FHhÆš Ú®¤j«g cau« (l) =0.3mU’ tot¡ FHhÆš Ú®milªj miyî¡ fhy«
(T) = 2wp
= 2 12g
p l : Ús«
= 2×3.14 0.32×9.8
g : òÉ<®¥ò KL¡f« = 9.8ms–2
= 6.28 0.319.6
.
= 6.28 3
196 = 0.7769 = 0.78smiyî fhy« = 0.78s
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58 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. Óuiyîïa¡f«v‹whšv‹d?vL¤J¡fh£LjUf.
Óuhd fhy ïilbtËfËš Û©L« Û©L« ÃfG« vªjbthU
ïa¡fK« Óuiyî ïa¡f« (Periodic motion) v‹gL«.
(v.fh) NÇaid¢ R‰¿ tU« nfhŸfË‹ ïa¡f«,
fofhu« x‹¿‹ KšÈ‹ ïa¡f«, if¡fofhu¤âš
rk‹ brŒa¥g£l r¡fu¤â‹ ïa¡f«, òÉÆ‹ ÛâUªJ
fhz¡Toa 76 M©LfS¡F xU Kiw NÇaid¢
R‰¿tU« nAÈÆ‹ th‹Û‹.
2. miyîWïa¡f« v‹whš v‹d?ïU vL¤J¡fh£L
jUf.
bghUbsh‹W ika¥ òŸËia¥ bghU¤J Û©L« Û©L«
K‹D« ã‹Dldhd ïa¡f¤ij nk‰bfhŸSkhdhš
mJ miyîW ïa¡f« vd¥gL«.
(v.fh) »£lh® f«ãfË‹ mâ®îfŸ, bjhiyngá
k‰W« xÈbgU¡»Æš cŸs bkšny£o‹ mâ®îfŸ.
3. ïa¡f¤â‰fhd fhuz«ahJ? jÅ¢ÓÇirïa¡¤â‰F
vL¤J¡fh£LfŸjUf.
ïa¡f¤â‰fhd fhuz« Éir (ne®¡nfh£L ÓÇir ïa¡f«) mšyJ âU¥òÉirahf (nfhz¢ÓÇir ïa¡f«) ïU¡fyh«.
jÅ¢ÓÇir ïa¡f¤â‹ vL¤J¡fh£LfŸ:(i) gS V‰w¥g£l RUŸÉšÈ‹ »il¤js k‰W«
br§F¤J miyîfŸ
(ii) U-tot¡ FHhÆš ÚÇ‹ br§F¤J miyîfŸ
(iii) Äj¡F« cUisÆ‹ miyîfŸ
(iv) jÅ CrÈ‹ miyîfŸ
(v) ïir¡ fitbah‹¿‹ mâ®îfŸ.
4. âU¥òÉirkh¿Èv‹whšv‹d?ïj‹myFahJ?
XuyF nfhz ïl¥bga®¢áÆid V‰gL¤â¤ njitahd ïu£ilÆ‹ âU¥ò¤ âwid âU¥òÉir kh¿È vdyh«.
τ = –Cqïâš ‘C’ v‹gJ âU¥òÉir kh¿ÈahF«. myF Nm rad–1.
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64 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
7. miy ïa¡f«
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. miyÆa¡f«tiuaW.miyguî«Clf¤â‹g©òfŸ
ahit?
� Clf¤â‹ JfŸfŸ, mt‰¿‹ ika¥ òŸËfis¥
bghU¤J Óuiyî ïa¡f¤â‰F c£gLtjhš,
Clf¤âš V‰gL« xU tif khWghL miyÆa¡f«
vd¥gL«.
� Clf« Û£á¥g©igí«, Ãiyk g©igí«
bg‰¿U¡f nt©L«.
2. miyÆa¡f¤â‹K¡»a¥g©òfŸahit?
(i) Clf¤âš, Clf¤JfŸfË‹ Óuiyî ïa¡f«
fhuzkhf V‰g£L bršy¡Toa xU tif khWghL
miy ïa¡f« MF«.
(ii) Clf«, ۣᥠg©igí« Ãiyk¥ g©igí«
bg‰¿U¡f nt©L«.
(iii) Clf¤ JfŸfŸ mid¤J« xnu neu¤âš
khWgh£il (disturbance) V‰gâšiy. x›bthU
JfS« mj‰F K‹ cŸs JfisÉl á¿J neu«
fʤJ mâ®tila¤ bjhl§F«.
(iv) miyÆ‹ âirntf« JfË‹ âirntf¤âÈUªJ
khWg£ljhF«. Clf« x‹¿š miyÆ‹ âirntf«
k h ¿ È a h F « . M d h š , J f Ë ‹ â i r n t f «
ika¥òŸËÆš bgUkkhfî« mâ®É‹ bgUk¥
òŸËÆš RÊahfî« kh¿¡ bfh©nl ïU¡F«.
(v) miy ïa¡f« guî« nghJ, Clf¤âš JfŸfŸ
kh‰w¥glhkš, xU JfËÈUªJ k‰bwhU JfS¡F
M‰wš k£Lnk kh‰w¥gL«.
(vi) vâbuhȤjš, Éyfš, ÉË«ò Éisî k‰W«
FW¡Ñ£L Éisî ngh‹w g©òfS¡F miyfŸ
c£gL»‹wd.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 65
3. FWfiyfisí«,be£liyfisí«ntWgL¤Jf.
FW¡fiyfŸ be£liyfŸ
1. C l f ¤ â š c Ÿ s JfŸfŸ miy guî« âir¡F¢ br§F¤jhf mâU»‹wd.
Clf¤âYŸs JfŸfŸ miy guî«âir¡F ïizahf mâU»‹wd.
2. KfLfS« mfLfS« c©lh»‹wd.
ïW¡fK« js®¢áí« c©lh»‹wd.
3. â l ¥ b g h U Ë Y « , â u t ¤ â ‹ nk‰gu¥òfËY« guî«.
â l , â u t , t h í ¥ C l f § f Ÿ t Ê a h f ¥ guî«.
4. v â b u h Ë ¥ ò , É Ë « ò Éisî, js Éisit milí«.
js Éisit milahJ.
4. âl¥bghUŸfËšFW¡fiyí« be£liyí« guî«
Mdhšthí¡fËšFW¡fiyfŸgutKoahJ.V‹?
thí¡fËš x£Ljš g©ò ïšiy. Mifahš thí¡fË‹
tÊahf FWfiyfŸ guîtâšiy. FW¡fiyfŸ
gUîtj‰F ClfkhdJ x£Ljš g©ò k‰W« gUk
ۣᥠg©ãid¥ bg‰¿U¤jš nt©L«.
5. kiHbgŒí«ehËšxÈntfkhfbrš»wJ.V‹?
fh‰¿‹ <u¥gj« mâfǤjhš, ÚuhÉÆ‹ msî«
mâfÇ¡»wJ. vdnt, ml®¤â Fiw»wJ. VbdÅš,
ÚuhÉÆ‹ ml®¤â cy®ªj fh‰¿‹ ml®¤âiaÉl¡
Fiwî. xÈÆ‹ âirntf«, ml®¤âÆ‹ ïUko
_y¤â‰F v⮤jfÉš ïU¥gjhš, xÈahdJ cy®ªj
fh‰¿š brštijÉl <u¥gj« Ä¡f fh‰¿š ntfkhf¢
bršY«. ïj‹ fhuzkhfnt, kiH bgŒí« ehËš xÈ
ntfkhf¢ brš»wJ.
6. xÈÆ‹br¿ití«cu¥igí«ntWgL¤Jf.
(i) miy guî« âir¡F¢ br§F¤jhf, XuyF fhy¤âš
XuyF¥ gu¥ãš fl¡F« M‰wÈ‹ msÉid¢ br¿î
vd tiuaW¡fyh«. br¿É‹ myF Wm–2.
(ii) xÈÆ‹ cu¥ò (loudness), xÈÆ‹ br¿î k‰W«
brÉÆ‹ cz®âwidiaí« rh®ªjJ.
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66 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
7. blágšv‹gJg‰¿ÚÉ®m¿ªjJV‹?
xÈ¢ br¿É‹ msî blábgš (decibel) v‹wmyfhš
msÉl¥gL»wJ. btg® ~bg¡d® ÉâÆ‹go,
blágš msî (b) = 10 log10 II0
ïâš I0 v‹gJ nf£lÈ‹ ga‹ bjhl¡f« MF«.
(10-12 Wm-2) ïj‹ msî 0 dB MF«. I v‹gJ brÉ
jh§»¡ bfhŸs¡Toa bgUk¢ br¿thF«. 1Wm-2-¡F¢
rkkhd 120 dB MF«.
8. xÈÆ‹br¿îv¡fhuÂfis¢rh®ªjJ?
xÈÆ‹ br¿î :
(i) xÈ _y¤â‹ å¢R (I α a2)(ii) xÈ _y¤â‹ nk‰gu¥ò (I α A)(iii) Clf¤â‹ ml®¤â (I α r)(iv) mâ®bt© (I α n2) k‰W«
(v) xÈ _y¤âÈUªJ nf£Fe® ïU¡F« bjhiyî
I a 12r
ngh‹wt‰iw¢ rh®ªâU¡F«.
9. vâbuhÈv‹whšv‹d?á¿amiwx‹¿švâbuhÈ
V‰glhJV‹?
� nf£FeÇlÄUªJ, bjhiyÉš cŸs bghUË‹
gu¥ãš vâbuhȤJ tU« xÈ miyfŸ vâbuhÈ
vd¥gL«.
� xË _y¤âš ïUªJ 17m bjhiyɉF« Fiwthf
vâbuhÈ¥ò bghUŸ ïU¥ã‹ vâbuhÈ V‰glhJ.
vdnt á¿a miw x‹¿š vâbuhÈ V‰glhJ.
10. bkJthf¥ngR«Tl«g‰¿¡F¿¥bgGJf.
� bgUik thŒªj bkJthf¥ ngR« Tl« òÅj ghš
fÔ£uÈš mikªJŸsJ. t£l toÉš cŸs
ïjDŸ, XÇl¤âš xUt® mk®ªJ bkšÈa FuÈš
ngádhY«, Û©L« Û©L« vâbuhȤJ tU« xÈ,
Tl¤âDŸ mk®ªâU¡F« midtÇ‹ brÉiaí«
milí«.
� Rt®fŸ tisî¥ gu¥ghf ïU¥gjhš, g‹Kf
vâbuhÈ¥ò V‰gL»wJ.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 67
11. nk‰bghUªJjšj¤Jt¤ij¡TWf.
x›bth‹W« jŤjÅahd ïa¡fkhf¡ fUj¡Toa,
ïu©L mšyJ mj‰F« nk‰g£l miyfŸ xnu
neu¤âš XU Clf¤â‹ tÊna bršY«nghJ,
vªjbthU òŸËÆY« bjhFga‹ ïl¥bga®¢áahdJ.
m›tiyfË‹ jŤjÅahd ïl¥bga®¢áfË‹ bt¡l®
TLjY¡F¢ rkkhF«.
12. É«kšfŸcUthf¤njitahdÃgªidfŸahit?
(i) rk mâ®bt©fŸ cila ïU miyfŸ ïU¡f
nt©L«.
(ii) ïU miyfS« xnu âirÆš bršY«nghJ x‹Wl‹
k‰bwh‹W nk‰bghUªj nt©L«.
13. É«kšfŸ v‹whš v‹d? xU behoÆš cUthF«
É«kšfË‹v©Â¡if,mâ®bt©fË‹ntWgh£L¡F¢
rk«vd¡fh£Lf.
r‰nww¡Fiwa rk mâ®bt©fŸ cila ïU xÈ
miyfŸ Clfbkh‹¿š xnu âirÆš bršY«nghJ
x‹Wl‹ k‰bwh‹W nk‰bghUªâdhš É«kšfŸ
cUth»‹wd. r‰nww¡Fiwa rk mâ®bt©fŸ cila
ïU xÈ miyfŸ FW¡»Ltjhš V‰gL« xÈ ts®¢á
k‰W« xȤ njŒî Ãfœî É«kšfŸ vd¥gL«.
(v.fh) 252 Hz k‰W« 256 Hz mâ®bt© cila ïU
ïir¡fitfŸ nr®ªJ mâU«nghJ xU behoÆš njh‹W«
É«kšfË‹ v©Â¡if =256 – 252 = 4 É«kš/beho.
xU behoÆš njh‹W« É«kšfË‹ v©Â¡if =
mâ®î v©fË‹ ntWghL.
4 É«kšfŸ = (256 – 252) = 4 Hz.
14. nk‰Ru§fŸk‰W«ÓÇirfŸv‹gitahit?
� ïG¤J¡ f£l¥g£l f«ãÆš V‰gL« Äf¡Fiwªj
mâ®bt© mo¥gil mâ®bt© vd¥gL«. k‰w
mâ®bt©fŸ nk‰Ru§fŸ vd¥gL«.
� n k ‰ R u § f Ë ‹ m â ® b t © f Ÿ m o ¥ g i l
mâ®bt©Â‹ KG kl§FfshF«. ïitna ÓÇir
bjhl® vd¥gL»‹wd. mo¥gil mâ®bt©Q¡F
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68 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
m â f k h d m â ® b t © c Ÿ s i t Ó Ç i r f Ÿ
vd¥gL»‹wd.
� x›bthU ÓÇirí« nk‰RukhF«. Mdhš x›bthU
nk‰RuK« ÓÇirahfhJ.
15. òšyh§FHšbrŒtj‰FâwªjM®f‹FHhŒáwªjJV‹?
� òšyh§FHš brŒtj‰F âwªj M®f‹ FHhŒ
áwªjJ. VbdÅš _oa M®f‹ FHhia Él âwªj
M®f‹ FHhÆš ÓÇirfŸ mâf«. _oa M®f‹
FHhÆš ïu£il¥gil ÓÇirfŸ V‰gLtâšiy.
Mdhš âwªj M®f‹ FHhÆš x‰iw¥gil k‰W«
ïu£il¥gilíl‹ Toa všyh ïaš ÓÇirfS«
V‰gL»‹wd.
� âwªj M®f‹ FHhÆš mâfkhd ÓÇirfŸ
V‰gL»‹wd. ïjdhš xÈÆ‹ g©ò áwªJ
fhz¥gL«
16. Kid¤âU¤j«v‹whšv‹d?
v⮡fQthdJ JšÈakhf¡, FHhÆ‹ âwªj KidÆš
cUthfhkš, âwªj Kid¡F¢ r‰W bjhiyÉš
cUthF«. ï¤bjhiyî Kid¤âU¤j« vd¥gL«.
l1 + e = l4 k‰W« l2 + e =
34l
v‹gdt‰¿ÈUªJ
e = l l2 132-
r v‹gJ FHhÆ‹ Mu« vÅš e = 0 .61r , v‹W
Kid¤âU¤j¤â‹ kâ¥ò f©l¿a¥gL»wJ.
j‹ kâ¥ÕL-fz¡FfŸ
1. 0.6cm ÚsKŸsmiy,fh‰¿‹ 340ms–1 âirntf¤âš
guî»wJ.kÅj¢brÉmjidczUkh?
xÈÆ‹ âirntf«V = 340ms–1
miy Ús« l = 0.6cm = 6 × 10–3mmâ®bt© == n
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 69
v = n : n = v
= 3406×10
= 56.666×10= 56.667Hz
-3
3
ll
= 56.666 × 106
= 56.667Hzk Å j ¢ b r É c z u ¡ T o a x È Æ ‹ m s î
(20Hz – 2000Hz)vdnt, kÅj¢ brÉ czu Koí«.
2. mâf¥gL¤j¥g£lbr¿É‹fhuÂ60 vÅšxÈÆ‹
msîv¤jidblágšmâfkhF«?
br¿É‹ fhu = II0
= 60xÈÆ‹ msî = 10log I
I= 10log 60= 10×1.7782
100
10
= 17.782 blágš
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. miyïa¡f«v‹whšv‹d?
(i) miy ïa¡f« v‹gJ Clf¤â‹ tÊna M‰wš
guîjÈ‹ xU KiwahF«.
(ii) Clf¤â‹ JfŸfŸ, mt‰¿‹ ika¥ òŸËfis¥
bghU¤J Óuiyî ïa¡f¤â‰F c£gLtjhš,
Clf¤âš V‰gL« xU tif khWghL miyÆa¡f«
vd¥gL«.
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80 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
8. bt¥gK« bt¥g ïa¡fÉaY«
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. ïUbt›ntwhdthí¡fŸxnubt¥gÃiyÆšïU¥ã‹
mt‰¿‹_y¡TWfŸxnuRMS ntf§fis¥bg‰¿U¡Fkh?
thí x‹¿‹ ïUko _y¢ ruhrÇ ïUko¤ âirntf«
mj‹ bt¥gÃiyÆš ïUko_y¤â‰F ne®É»j¥
bghU¤jKilaJ. vdnt xnu bt¥gÃiyÆš cŸs
thí¡fË‹ _y¡TWfŸ rkkhd âirntf§fis
bg‰WŸsd.
2. cÇik¥gofŸv‹gitahit?
ïa§F« bjhFâ x‹¿‹ cÇik¥gofŸ v‹gJ
KGikahf m¤bjhFâÆ‹ ïa¡f¤ij És¡f¥
ga‹gL« jÅ¥g£l msitfË‹ bkh¤j v©Â¡if
MF«.
3. khwhmG¤j¤âšnkhyh®j‹bt¥gV‰ò¤âw‹v‹gij
tiuaW.
mG¤j« khwhJ ïU¡F«nghJ xU nkhš msîŸs
thíÉ‹ bt¥gÃiyia 1 bfšÉ‹ bt¥gÃiy¡F
ca®¤Jtj‰F¤ njitahd M‰wÈ‹ msî thíÉ‹
mG¤j«, khwh mG¤j¤âš nkhyh® j‹ bt¥g
V‰ò¤âw‹ vd tiuaW¡f¥gL»wJ.
4. xUthíïUj‹bt¥gV‰ò¤âw‹fisí«,âut«k‰W«
â©k¥bghUŸxnubahU j‹bt¥g V‰ò¤âwidí«
bfh©LŸsd.V‹?
btË¥òw Ãiyfis¡ f£L¥gL¤jhkš ïU¡F«nghJ
xU thíÉ‹ j‹ bt¥g V‰ò¤âwÅ‹ kâ¥ò + ∞ +Kjš
- ∞ tiu khWgL»wJ.+vdnt xU thíÉ‹ j‹bt¥g
V‰ò¤âwid¡ fh©gj‰F mjDila mG¤j« mšyJ
gUk‹ kh¿Èahf it¡f¥gl nt©oíŸsJ. Mfnt
thíɉF ïU bt¥g V‰ò¤âw‹fŸ cŸsd. Mdhš
â©k, âut¥ bghUŸfS¡F ïªj khWghL V‰glhjjhš
mit xnubahU j‹bt¥g V‰ò¤ âwid¡ bfh©LŸsd.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 81
5. R£L¥gl¤â‹tiuaiwjUf.
xU bghUË‹ gUk‹ khWgh£il x m¢áY«, mG¤j
khWgh£il y m¢áY« fh£L« tiugl« R£L¥ gl«
mšyJ P - V tiugl« vd¥gL«.
6. bt¥g¤ijmË¡fhknyna thíÉ‹ bt¥gÃiyia
mâfÇ¡fïaYkh?És¡Ff.
bt¥g¤ij mË¡fhknyna thíÉ‹ bt¥gÃiyia
mâfÇ¡f ïaY«. VbdÅš thíÉ‹ mK¡f« k‰W«
ÉÇÉ‹nghJ bt¥g gÇkh‰w¤â‰F neu« ïšyhj
tifÆš âO® Ãfœîfshf ïU¡F«nghJ bt¥gÃiy
khWghL v¥nghJ« V‰gL»wJ.
7. °T£l® x‹¿id btFneu« X£oaã‹ mj‹
r¡fu¤âYŸsfh‰wG¤j«á¿JmâfÇ¥gj‰F¡fhuz«
v‹d?
°T£l® x‹¿id btFneu« X£oaã‹ mj‹ r¡fu¤âš
bt¥gÃiy mâfÇ¡»wJ. mjdhš r¡fu¤âYŸs
fh‰wG¤j« á¿J mâfÇ¡»wJ. ïnj Ãiy Úo¤jhš
r¡fu¤âYŸs u¥g® FHhŒ bto¤JÉl thŒ¥òfŸ
mâf«.
8. »sháa°T‰iw¡TWf.
òw cjÉÆ‹¿ jhnd ïa§F« ïaªâu¤â‹ _y«
Fiwªj bt¥gÃiyÆYŸs xU bghUËÈUªJ mâf
bt¥gÃiyÆYŸs k‰bwhU bghUS¡F bt¥g¤ij
kh‰w ïayhJ.
9. bt¥g ïa¡fÉaÈš ïu©lhtJ Éâ, bt¥g
ïa¡fÉaÈ‹KjšÉâÆÈUªJv›Éj«khWgL»‹wJ?
bt¥g ïa¡fÉaÈ‹ Kjš ÉâahdJ ntiy k‰W«
bt¥g« ït‰¿‰»ilna cŸs rkkhd Ãiyia
v L ¤ J i u ¡ » w J . b t ¥ g ï a ¡ f É a È ‹ K j š
ÉâÆ‹go V‰gL¤j¡Toa ÃfœîfŸ c©ikÆš
eilbgw ïaYkh mšyJ ïšiyah vd m¿a
bt¥gÉa¡fÉaÈ‹ ïu©lh« Éâ M‰wš khW¥gh£o‹
msî k‰W« âiria¥ g‰¿¡ TW»wJ.
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84 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
18. tiuaW-NÇakh¿È
NÇakh¿È v‹gJ tËk©ly« ïšyhjnghJ
òÉ¥gu¥ã‹ ÛJ NÇa¡ fâ®å¢á‹ âir¡F ne®¡F¤jhf
it¡f¥gLŸs KG¡fU«bghUŸ x‹W xU behoÆš
XuyF¥ gu¥ãdhš bgw¥gL« fâ®å¢R M‰wÈ‹
msthF«.
NÇakhwÈ, S = 1.388 × 103 Wm-2 .
19. M‰wšg§Ñ£LÉâia¡TWf.miwbt¥gÃiyÆš
<uQ thí x‹¿‰F, mj‹ ïU j‹ bg¥g V‰ò¤
âw‹fË‹jfî7/5vdÃWîf.
� bt¥g¢ rkÃyÆš, ïa§F« bjhFâbah‹¿‹
bkh¤j M‰wš bjhFâÆ‹ cÇik¥ gofS¡F«
rkkhf¥ g§»l¥gL»wJ. ïJ M‰wš rkg§Ñ£L
ÉâahF«.
� xU <uQ thí x‹W 5 cUik¥ gofis¥ bg‰WŸsd.
<uQ thíÉ‹ n nkhšfË‹ bkh¤j M‰wš
U =52
kT
N =
52
RT
vdnt C UT
R TT
RV = ∆∆
= ∆∆
=5 2 52
/
nka® Éâ¥go CP+ CV + R v‹gjhš = 52
72
R R R+ =
<uQ thíÉ‹ j‹bt¥g V‰ò¤âw‹fË‹ jfî
v CC
RR
P
V
= =( )( ) =7 25 2
72
//
MF«.
20. tiuaW:bt¥gÃiyth£l«.
ïU rk bt¥gÃiy Ãfœî gu¥òfËilna öu¤Jl‹
bt¥gÃy khW« åj« bt¥gÃiy th£l« mšyJ
b t ¥ g à i y ¢ r Ç î v d ¥ g L « . ï J ∆∆
Tx
v d ¡
F¿¥ãlgL»wJ.
21. bt¥g§fl¤J«ÃiyahdÃiyv‹gijtiuaW.
bt¥g¡ fl¤J v© (Coefficient of thermal conductivity) :
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 85
Óuhd FW¡F¥ gu¥ò A bfh©l cnyhf¤ j©o‹
xU Kid bt¥g¥gL¤j¥gLtjhf¡ fUjî«. á¿J
neu« fʤJ¤ j©o‹ x›bthU gFâí« khwhj
bt¥gÃiyia¥ bgW«. Mdhš j©o‹ bt›ntW
gFâfŸ bt›ntwhd bt¥gÃiyia¥ bgW«. ïJnt
Ãiyahd Ãiy MF«. ïªÃiyÆš bt¥g« c£ft®jš
nkY« eilbgWtâšiy.
22. »®¢rh~¥ÉâÆ‹ga‹ghLfŸahit?
(i) bj®kh° FLitÆš gsgs¥ghd btŸË¥ó¢R
brŒa¥g£l Rt®fŸ ïU¥gjhš mJ bt¥g«
c£ft®jš k‰W« cÄœtâš Äf¡ Fiwªj
âwid¥ bg‰WŸsd. vdnt m¡FLitÆYŸs
gÅ¡f£o cldoahf cUFtâšiy. mâYŸs
Nlhd âut§fŸ ÉiuÉš FË®tâšiy.
(ii) nrhoa« MÉahdJ bt¥g¥gL¤j¥g£lhš ïU
bghÈthd kŠrŸ Ãw tÇfis btËÆL»‹wd.
mit nrhoa¤â‹ D1 k‰W« D
2 tÇfŸ vd¥gL«.
bjhl®Ãwkhiyia¤ jU« fh®g‹ Éš És¡»ÈUªJ
tU« btŸbshË Fiwªj bt¥gÃiyÆYŸs nrhoa
MÉÆ‹ tÊ brY¤j¥g£lhš bjhl®ÃwkhiyÆš
ïU miyÚs§fŸ D1 k‰W« D
2 c£ftu¥g£L fUik
tÇfshf¤ njh‹W«. ïªÃfœî »®¢rh~¥ ÉâÆ‹go
eilbgW»wJ.
j‹ kâ¥ÕL-fz¡FfŸ
1. 320N bt¥gÃiyÆYŸs <uQ thíÉ‹ _y¡TW
x‹¿‹ne®¡nfh£Lïa¡f¤â‰fhdïa¡fM‰wiy¡
fz¡»Lf?
_y¡T¿‹ j‹ik : <uQ thí _y¡TW
thí _y¡T¿‹ bt¥gÃiy (T) = 320K K = 1.38x10–23Jk–1
<uQ thí _y¡T¿‹ ne®¡nfh£L ïa¡f¤â‰fhd
ïa¡f M‰wš K.E = 32
KT
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86 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
( )
23
23
23
23
21
3 1.38 10 3202
3 1.38 10 160
4.14 160 10
662.4 10
6.624 10 J
−
−
−
−
−
= × × ×
= × × ×
= × ×
= ×
= ×
KT
2. NÇaÅ‹nk‰gu¥òbt¥gÃiyia¡fz¡»L.
l = 4753A°
bgUk M‰wY¡FÇa miyÚs« l = 4753A°
= 4753 × 10–10mÉa‹ ïl¥bga®¢á Éâ¥go
3 mT mT = 2.898×10−λ = λkh¿È
T = 2.898×10 3m
2.898×104753×10
= 2898×104753
6
10
4
- =-
-l
== 6096K
~NÇaÅ‹ nk‰gu¥ò bt¥gÃiy =6096K.
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. mtf£nuhv©-tiuaW.
mtf£nuh v© : xU nkhš msîŸs bghUËš cŸs
_y¡TWfË‹ v©Â¡if mtf£nuh v© vd¥gL«.
mid¤J¥ bghUŸfS¡F« khwhj v©zhd ïj‹
kâ¥ò 6.023 × 1023 MF«.
2. XuyFgUk‹bfh©lthíÉ‹ne®¡nfh£Lïa¡f¤â‹
ruhrÇïa¡fM‰wšv›tsî?
XuyF gUk‹ bfh©l thíÉ‹ neu¡nfh£L ïa¡f¤â‹
ruhrÇ ïa¡f M‰wš
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 87
E C= 12
2r
PE
C
C= =
1312
23
2
2
r
r
∴ P = 13 rC2
~ P = 23 E
3. XuQ_y¡TWv¤jidcÇik¥gofis¡bfh©LŸsJ?
vL¤J¡fh£LjUf.
XuQ _y¡TW : XuQ _y¡TW x‹W òŸË Ãiw
bfh©l XuQit k£Lnk bfh©oU¥gjhš mJ
ne®¡nfh£L ïa¡f¤â‰fhd _‹W cÇik¥gofis
x, y, z âir¡TWfËš bfh©LŸsJ (gl«)
XuQ _y¡TW
vL¤J¡fh£LfŸ : ëÈa«. M®fh‹ ngh‹w kªj
thí¡fË‹ _y¡TWfŸ.
4. <uQ_y¡TWv¤jidcÇik¥gofis¡bfh©LŸsJ?
<uQ_y¡TWfS¡FvL¤J¡fh£LjUf.
<uQ _y¡TW : vªjbthU m¢ir¥ bghU¤J«
RHy¡Toa <uQ _y¡TW x‹W mj‹ m¢R¡F¢
br§F¤jhf mikªj m¢Rfis¥ bghU¤J RHyKoí«.
vdnt mJ RHš ïa¡f¤â‹ ïU cÇik¥gofisí«
ne®¡nfh£L ïa¡f¤â‹ _‹W cÇik¥gofisí«
bg‰WŸsJ. vdnt xU <uQ _y¡TW IªJ
cÇik¥gofis¥ bg‰WŸsJ (gl«).
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96 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
9. fâ® xËÆaš
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. xËvâbuhË¥òÉâfis¡TWf.
� gLfâ®, vâbuhË¥ò¡ fâ® k‰W« vâbuhË¥ò¤
js¤âF tiua¥g£l ne®¡F¤J¡nfhL M»ait
xnu js¤âš mikí«.
� gLnfhz«, vâbuhË¥ò¡ nfhz¤â‰F¢ rkkhf
ïU¡F«. mjhtJ i = r.2. by‹á‹âw‹v‹whšv‹d?xUilah¥g®v‹gJv‹d?
� FÉa¤ bjhiyÉ‹ jiyÑÊ by‹á‹ âw‹ vd
tiuaW¡fyh«. P = 1f
� âwÅ‹ myF xU ilah¥l® (D) MF«.
∴ 1D = 1m-1.
3. NÇa¡ f©zhofË‹gu¥òfŸtisthfïU¥ãD«
mt‰¿‹âw‹RÊahf¡TL«V‹?
NÇa¡ f©zhofË‹ gu¥òfŸ tisthf ïU¡F« nghJ
mt‰¿‹ FÉa¤öu§fŸ KoÉÈahf mik¡»‹wd.
nfhsf MoÆ‹ âw‹ v‹gJ FÉa¤öu¤â‹ jiyÑÊ
MF«.
P = 1f = 1
∞ = 0.
4. cŸçl‰wK¥g£lf«x‹¿DŸbtŸbshË¡ fh‰iw
Ãw¥ãÇifmilíkh?
milahJ. VbdÅš cŸçl‰w K¥g£lf« x‹¿DŸ
fh‰W ïU¡F«. vdnt cŸçl‰w K¥g£lf« x‹¿DŸ
fh‰¿ÈUªJ bršY« xË¡fâ® f©zho _y«
fh‰¿DŸ Éyfš milªJ, Û©L« f©zho tÊna
fh‰¿DŸ ÉL fâuhf btËnaW« nghJ gLfâU¡F
ïizahf btËnaW«. vdnt Ãw¥ãÇif milahJ.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 97
5. Mo q nfhz« RH‹whš vâbuhË¡f¥g£l fâ® 2q
nfhz«RHY«v‹gijbkŒ¥ã¡fî«.
MoÆ‹ RH‰áahš xËÆ‹ âirkh‰w« :
AO v‹w xË¡fâ® XY v‹w rkjs MoÆš O v‹w
òŸËÆš ÉGtjhf¡ bfhŸnth«. ï¡fâ® OBahf
vâbuhË¥ò mil»wJ. OA-íl‹ xË¡fâ® V‰gL¤J«
bjhLnfhz« a v‹f (gl«)
nkY« âirkh‰w¡ nfhz« COB = 2aMoia k£L« q nfhz« RH‰¿ v‹w Ãiyia
mila¢ brŒf. ïªj¥ gLfâ® AO j‰nghJ OPahf
vâbuhË¥ò mil»wJ. ï§F XY-íl‹ bjhLnfhz«
(a+q) MF«. vdnt òâa âirkh‰w¡ nfhz« COP = 2(a+q). ï›thwhf X® Mo q nfhz« RHY« nghJ
vâbuhË¡f¥g£l xËí« BOP v‹w nfhz« RHY»wJ.
BOP COP COB= -
BOP = 2(a+q) – 2a = 2qgLfâ® x‹¿‰F, Moia F¿¥ã£l nfhz¤â‰F
RH‰¿dhš, vâbuhË¡f¥g£l fâuhdJ m¡nfhz¤ij¥
nghš ïUkl§F nfhz« RHY«.
6. rkjsMofËšã«g«njh‹WtijÉs¡Ff.
rkjs MoÆš ã«g« : rkjs Mo¡F K‹ghf
bghUbsh‹W òŸË A -Æš it¡f¥g£LŸsjhf¡
fUjî«.
bghUËÈUªJ btËtU« AO v‹w xË¡fâ® MoÆš
g£L OB tÊahf vâbuhË¥ò mil»wJ. O òŸËÆš
rkjs Mo¡F ON v‹w F¤J¡nfhL tiuaî«.
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98 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
gLnfhz« AON = vâbuhË¥ò nfhz« BON.
AD v‹w k‰bwhU fâ® MoÆš òŸË D -Æš
ne®¡F¤jhf¥ g£L vâbuhË¡f¥g£L DAahf ÛŸ»wJ.
BO-k‰W« AD-ia ã‹òw« Ú£odhš mit I-Æš
rªâ¡F«. ï›thW Mo M-š vâbuhË¥ò milí«
fâ®fŸ Mo¡F¥ ã‹dhš I v‹w òŸËÆÈUªJ
btËtUtjhf¤ njh‹W«.
gl¤âÈUªJ,
AON DAO= v‹gd x‹WÉ£l nfhz§fŸ k‰W«
BON DIO= v‹gd x¤j nfhz§fŸ.
vdnt, DAO DIO=
K¡nfhz§fŸ ODA k‰W« ODI KGbjh¤jit.
∴ AD = ID bghUË‹ xU F¿¥ã£l Ãiy¡F A k‰W« D v‹gd
Ãiyahd òŸËfŸ MF«. AD = ID vd ïU¥gjhš
I-í« ÃiyahdJ. vdnt AO = OI. Mfnt rkjs
MoÆš, MoÆÈUªJ bghUŸ ïU¡F« mnj br§F¤J¤
bjhiyÉš Mo¡F¥ ã‹dhš ã«g« njh‹W«.
7. (i)rkjsMo(ii)FÊMo(iii)FÉMongh‹wt‰¿š
cUthF«khaã«g§fË‹ntWghLv‹d?
rkjs Mo FÊ Mo FÉ Mo
1. cUthF«
ã«g« ïlty
kh‰w«
cilaJ
ïlty kh‰w«
ïšyhjJ
ïlty kh‰w«
ïšyhjJ
2. bghUŸ, ã«g«
ït‰¿‹ msî
rk«
bghUisÉl
ã«g¤â‹
msî
bgÇajhf
ïU¡F«
bghUisÉl
ã«g¤â‹
msî á¿ajhf
ïU¡F«
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100 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
ïiz fâuhf cŸsJ. RD fâ® âU«gî« DE âirÆš
(f©zho¢ RtÇš) Éyfyil»wJ. ãwF fh‰¿š
QD fâuhf btËnaW»wJ. Mdhš EF fâ® RD
mšyJ PQ-¡F ïizahdJ. vdnt xU btŸis xË
cŸçl‰w g£lf¤â‹ _y« bršY«nghJ Ãw¥ãÇif
miltâšiy.
10. ÃwkhiykhÅia¡bfh©LK¥g£lfbkh‹¿‹áWk¤
âirkh‰w¡nfhz¤ijv›thWf©l¿aKoí«v‹gij
És¡Ff.
áWk¤ âir kh‰w¡ nfhz« (D) : ïizah¡»ÆÈUªJ tU« xËahdJ xU Éy¡F
Kf¤âDŸ br‹W ÉyfyilªJ, mL¤j Éy¡F Kf¤âš
bjhiyneh¡»Æš gh®¡f¡ ToathW K¥g£lf« K¥g£lf
nkirÆ‹ ÛJ it¡f¥gl nt©L«. âir kh‰w¡
nfhz« FiwíkhW K¥g£lf nkiria RH‰w nt©L«.
xU f£l¤âš (Stage) ã«g« fz neu¤â‰F ËW
v⮤âirÆš efu¤ bjhl§F«. mjhtJ, âirkh‰w¡
nfhz« mâfÇ¡F«. ãsÉ‹ ã«g« ËW, âU«ò«
ïl¤âš bjhiyneh¡»ia¥ bghU¤â, ã«gkhdJ
br§F¤J¡ f«ãíl‹ x‹¿ÆU¡FkhW¢ brŒa nt©L«.
ïªj Ãiy K¥g£lf¤â‹ áWk¤ âirkh‰w ÃiyahF«.
bt®Åa® msåLfŸ F¿¡f¥gl nt©L«. j‰nghJ,
K¥g£lf¤ij mf‰¿, bjhiyneh¡»ia¢ RH‰¿
ne®¡fâiu¡ fhz nt©L«. ne®¡ fâU« br§F¤J¡
f«ãí« x‹¿ÆU¡FkhW brŒJ, bt®Åa® msåLfis¡
F¿¡f nt©L«. ïU msåLfS¡F« ïilnaahd
ntWghL áWk¤ âirkh‰w¡ nfhzkhF« (D).
j‹ kâ¥ÕL-fz¡FfŸ
1. ik¡fšr‹rHyho¢nrhjidÆšv©KfMoÆšïU
ïl§fËšV‰gL«vâbuhË¥òfS¡»ilÆšxËfl¡F«
bjhiyî4.8km vÅšã«g«Û©L«cUthfv©Kf
MoÆ‹áWk¢RH‰ántf«v‹d?
RHyhoÆš Kf§fË‹ v©Â¡if N = 8 xË fl¡F« bjhiyî D = 4.8km = 4.8 × 10–3
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 101
xËÆ‹ âirntf« C = NnD
RH‰á ntf« N = cND
= 3×108× 4.8×10
= 10128
= 781.2
= 7.8×10 r
8
3
6
3
pps
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ
1. KGmfvâbuhË¥òv‹whšv‹d?
gLnfhz«, khWÃiy¡nfhz¤ij Él ( i >c ) m â f Ç ¡ f ¥ g £ l h š x Ë ¡ f â ® É y f y i l a h k š
KGtJkhf vâbuhË¡f¥g£L ml®ÄF Clf¤ânyna
bršY«. ïªÃfœî KGmf vâbuhË¥ò vd¥gL«.
X
A B
Y
ml®Fiw
ml®ÄF
O
i > c
2. itu¤â‹ xËÉyfš v© ahJ? mâš xË¡ fâ®
v›thWKGmfvâbuhË¥òmil»wJ?[mšyJ] itu«
b#hÈ¡f¡K¡»a¡fhuzkhdÃfœîahJ?És¡Ff
fh‰iw¢ rh®ªJ itu¤â‹ xËÉyfš v©.2.42 .
itu§fŸ ÄDÄD¡f K¡»a fhuz« KGmf
vâbuhË¥ò. itu¤â‹ khWÃiy¡nfhz« 24.41°.
itu¤â‹ vªjbthU g¡f¤â‹ tÊnaí« 24.41°¡F«
mâfkhd nfhz¤âš xË¡fâ® bršY« nghJ
KGmf vâbuhË¥ò mil»wJ. jFªj msɉF g£il
Ô£Ltjhš g‰gy mf vâbuhË¥òfŸ V‰gL«.
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110 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
10. fhªjÉaš
j‹ kâ¥ÕL
2-3 kâ¥bg©fŸ
1. TY«v⮤jfîïUkoÉâia¡TWf.
ïU fhªj KidfS¡»ilnaíŸs ft®¢á mšyJ
Éy¡F ÉirahdJ Kid tÈikfË‹ bgU¡F¤
bjhif¡F ne®¤jfÉY« mt‰¿‰F ïilnaíŸs
bjhiyÉ‹ ïUko¡F v⮤jfÉY« ïU¡F«.
F a m md1 2
2
2. Óuhdfhªj¥òy¤âšfhªjCáÆ‹ÛJbra‰gL«âU¥ò
Éir¡fhd¤bjhl®ãid¥bgWf.
Óuhd fhªj¥ òy¤âYŸs r£l¡ fhªj¤â‹ Ûjhd
âU¥òÉir:
fhªj¤ ö©lš (M) bfh©l xU Óuhd fhªj¥ òy¤â‹
âir¡F q nfhz¤âš it¡f¥g£LŸs 2l ÚsK« ‘m’
Kid tÈikí« cŸs r£l¡fhªj« NS x‹iw¡
fUjî«.
fhªj¥òy« B-Mš tlKid ÛJ brašgL« Éir mB.
ïJ fhªj¥òy¤â‹ âirÆš brašgL»wJ. bj‹Kid
ÛJ brašgL« Éir mB. ïJ fhªj¥òy¤â‹ âir¡F
v⮤âirÆš brašgL»wJ.
ïªj ïu©L ÉirfS« rkkhfî«. v⮤âirfËY«
miktjhš ïit ïu£ilia cUth¡F»‹wd.
ïªj ïu£il¡fhd âU¥ò Éir,
τ xU ÉirÆ‹ kâ¥ò ÉirfS¡F ïil¥g£l
br§F¤J¤ bjhiyî
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 111
τ = F × NA = mB × NA ... (1) = mB × 2l sinq∴ τ = MB sinq ... (2)τ= M B
→ →× v‹W bt¡l® F¿p£lhš F¿¡f¥gL«.
τ→
ï‹ âirahdJ, M→
k‰W« B→
ïitfis¡ bfh©l
js¤â‰F¢ br§F¤jhf mikªJŸsJ.
B = 1 vdî«, q = 90° vÅš, rk‹ghL (2)ÈUªJ ‚ τ = M.
vdnt fhªj¤ âU¥ò¤ âw‹ M v‹gJ XuyF fhªj¤
ö©lš bfh©l fhªj¥ òy¤âš mj‰F¢ br§F¤jhf
xU fhªj¤ij it¡f¤ njitahd âU¥ò Éir¡F¢
rk«.
3. nl‹AÃiyv‹gJahJ?ÉyFfhªjkhÅianl‹A
ÃiyÆšv›Éj«mik¥ghŒ?
r£l¡ fhªj¤â‹ m¢R¡nfh£oš cŸs xU òŸËÆš
fhªj¥òykhdJ, òÉ¡fhªj¥ òy¤â‹ »il¤js¡
TW¡F¢ br§F¤jhf mikí«. ÉyFfhªjkhÅí«
r£l¡ fhªjK« ïªj Ãgªjid¡F V‰g it¡f¥g£lhš
ïªÃiy nl‹ A Ãiy vd¥gL«.
nl‹ A ÃiyÆš it¥gj‰F ÉyFfhªjkhÅÆ‹
òa§fŸ »H¡F-nk‰F âirÆš mjhtJ fhªj¥òy¤
js¤â‰F br§F¤jhf it¡f¥gL»wJ. r£l¡ fhªjkhJ
»H¡F - nk‰FâirÆš ÉyFfhªjkhÅÆ‹ òa§fS¡F
ïizahf it¡f¥gL»wJ.
4. tiuaW:(i)fhªjc£òFâw‹(ii)fhªjkh¡F«br¿î
k‰W«(iii)fhªjV‰ò¤âw‹.
(i) fhªj c£òFâw‹ :
xU Clf¤â‹ fhªj c£òFâw‹ m vd¥gLtJ Clf¤âDŸns fhªj¤ö©lš B-¡F«, mnj Clf¤âYŸs fhªj¥òy¢br¿î H-¡F« cŸs É»j«
MF«.
∴ =m BH
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112 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
(ii) fhªjkh¡F« br¿î :
fhªjkh¡F« òy¤â‹ (H) _y« xU bghUŸ vªj msɉF¡ fhªjkh¡f¥ gL»wnjh mjid, fhªjkh¡f¢ br¿î F¿¡»wJ.
xU fhªj¥ bghUË‹ fhªjkh¡f¢ br¿î v‹gJ XuyF gUkD¡fhd bghUË‹ fhªj¤ âU¥ò¤ âw‹ MF«.
I = MV ïj‹ myF Am–1 MF«.
(iii) fhªj V‰ò¤ âw‹ :
fhªj V‰ò¤ âw‹ v‹w g©ò xU bghUŸ v›tsî vËâš k‰W« v›tsî tYîl‹ fhªjkh¡f¥gL»wJ v‹gij¤ Ô®khÅ¡»wJ.
xU bghUË‹ fhªj V‰ò¤ âw‹ cm v‹gJ bghUËš
ö©l¥g£l fhªjkh¡f¢ br¿É‰F« (I) mJ it¡f¥g£LŸs fhªjkh¡F« òy¤â‹, fhªj òy¢brî¡F« (H) cŸs jfthF«.
cm = IH
I k‰W« H ïit xnu gÇkhz§fis¡ bfh©LsŸjhš
cm -¡F myF ïšiy. cm gÇkhzk‰wJ.
5. fhªj¤ja¡f¡f©Âg‰¿És¡Ff.
fhªj¤ja¡f«(Hysteresis):xU fhªjkh¡F« òy¢ br¿î H _y« bkJthf fhªjkilí« ïU«ò¤ j©L x‹iw¡ fUjî«. fhªjkh¡F« òy¢ br¿î H kh‰w¥gl¡ ToaJ. fhªjkh¡F« òy¢ br¿î H mâfÇ¡F«nghJ ïU«ò¤ j©oYŸs fhªj¤ ö©lš B mâfǤJ, ã‹d® xU bjÉ£L Ãiyia mil»wJ. ïJ ghij OP-‹ _y« fh£l¥gL»wJ. (gl«).
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 113
fhªjkh¡F« òy« bkJthf Fiw¡f¥gL«nghJ fhªj¤
ö©lš Fiw»wJ. Mdhš fhªj ö©lš B, PO
tÊahf¤ âU«òtâšiy. khwhf H = 0 MF«nghJ B-‹
kâ¥ò RÊ Mfhkš kâ¥ò ·OQ-I¥ bgW»wJ. ïU«ò¤
j©oš fhªj¥ g©ò Ûj« ïU¥gij ïJ fh£L»wJ.
fhªjkh¡F« òy« RÊahf¡ Fiw¡f¥g£l ã‹ò« xU
bghUËYŸs fhªj¤ ö©lÈ‹ kâ¥ò mj‹ ÛJ
fhªj¤ ö©lš (residual magnetic induction) vd¥gL«.
gl¤âš ·OQ bghUË‹ Ûj¡ fhªj¥g©ig¡ fh£L»wJ.
ï¥nghJ fhªjkh¡F« òy¢ br¿Éid v⮤âirÆš
mË¡F«nghJ fhªj¤ ö©lš QR tÊna FiwªJ
R-š RÊ kâ¥ig milí«. ï›thW Ûj¡ fhªj¤âid
RÊah¡Ftj‰F fhªjkh¡F« òy¢ br¿î ·OR-I v⮤
âirÆš mË¡f nt©oíŸsJ.
xU fhªj¥ bghUËš cŸs Ûj¡ fhªj¤ ö©liy¡
Fiw¤J RÊah¡Ftj‰F mj‰F mË¡f¥gl nt©oa
v⮤âir fhªjkh¡F« òy¢br¿É‹ kâ¥ò fhªjÚ¡f¢
br¿î (Coercivity) vd¥gL«.
fhªjkh¡F« òy« H-I, v⮤ âirÆš nkY«
mâfÇ¡F«nghJ fhªj¤ ö©lš RS mâfǤJ òŸË
S-š bjÉ£L Ãiyia mil»wJ. (Pk‰W« S rk¢Ó®
òŸËfshF«). j‰nghJ, Û©L« fhªj¥òy¤â‹
âiria kh‰W«nghJ fhªj¤ ö©lš STUP v‹w ghij
tÊna brš»wJ. ïªj _oa tistiu¡nfhL PQRSTUP
fhªj¤ ja¡f¡ f©Â (hysteresis loop) vd¥gL«. ïJ
xU fhªjkh¡F¢ R‰¿id¡ F¿¡»wJ. fhªj¤ ja¡f«
v‹w brhš ã‹ j§Fjš v‹w bghUis¡ bfh©LŸsJ.
xU fhªjkh¡f¢ R‰¿‹nghJ fhªj¤ ö©lš B,
fhªjkh¡F« òy¢ br¿î H-¡F¥ ã‹j§»íŸsJ vd
m¿»nwh«. fhªjkh¡F« òy¤â‰F, fhªj¤ ö©lš
ã‹ j§F« Ãfœî fhªj¤ ja¡f« vd¥gL«.
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114 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
j‹ kâ¥ÕL-fz¡FfŸ
1. 72g Ãiwí«7200kgm–3 ml®¤âí«cŸsïU«ò¤j©o‹
fhªjkh¡f¢br¿î0.72Am–1 vÅšmj‹fhªj¤âU¥ò¤
âw‹kâ¥ãid¡fz¡»Lf?
ïU«ò¤ j©o‹ Ãiw m = 72g = 72 × 10–3kgïU«ò¤ j©o‹ fhªjkh¡f¢ br¿î I = 0.72ïU«ò¤ j©o‹ ml®¤â d = 7200kgm–3
d = mv
(mšyJ) gUk‹ V = md
( )
= 72×107200
= 1×10 m M = v×1
= 0.72×1×10
3
5 3
5
-
-
-
~fhªj¤ âU¥ò¤âw‹ m = 7.2 × 10–6Am2.2. 25cm3 gUkDŸs fhªj¤â‹ fhªj¤ âU¥ò¤ âw‹
12.5×10–4 Am2 vÅšfhªjkh¡f¢br¿É‹kâ¥ãid¡
fz¡»Lf?
fhªj¤â‹ gUk‹ V =25Cm3
fhªj¤ âU¥ò¤âw‹ M =12.5 × 10–4Am2
fhªjkh¡f¢ br¿î I = MV
= 12.5×1025×10
= 125025
= 50Am
4
6
1
-
-
-
~fhªjkh¡f¢ br¿î = 50Am–1
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 115
TLjš Édh¡fŸ
ïu©L kâ¥bg© Édh¡fŸ :
1. òÉfhªj¡TWfŸv‹whšv‹d?
òÉÆ‹ ÛJŸs xU òŸËÆš òÉ¡fhªj¥òy¤âid
KGtJ« tiuaW¡f¥ga‹gL« ïa‰ãaš msîfŸ
òÉ¡fhªj¡ TWfŸ vd¥gL»‹wd. mit,
(i) fhªj xJ¡f« (q)(ii) fhªj¢ rÇî (d)(iii) òÉ¡fhªj¥ òy¤â‹ »il¤js¡ TW (Bh)
2. »ôÇbt¥gÃiyv‹whšv‹d?vL¤J¡fh£LjUf.
fhªj V‰ò¤âw‹ bfšÉ‹ bt¥gÃiy¡F v⮤fÉy
mikí«. cma 1T
bt¥gÃiy caU«nghJ fhªj
V‰ò¤âw‹ Fiw»wJ. xU F¿¥ã£l bt¥g ÃiyÆš
~bg®nuh fhªj¥ bghUŸfŸ ghuh fhªj¥ bghUŸfshf
khW»‹wd. ïªj bga®î bt¥gÃiy¡F »ôÇ (curie)bt¥gÃiy v‹W bga®.
(v.fh) ïU«ò¡fhd »ôÇ bt¥gÃiy Rkhuhf 1000K
3. òÉ¡fhªj¥g©ã‰fhdfhuÂfŸahit?
(i) òÉÆ‹ fhªj¥ g©ò Ãiwªj¥ gFâfŸ
(ii) òÉÆš cŸs Ä‹ndh£l§fŸ
(iii) òÉÆ‹ tËk©ly¤â‹ nk‰gFâÆš fhz¥gL«
Ä‹ndh£l«.
(iv) NÇaÅÈUªJ tU« fâ® å¢RfŸ.
(v) ÃyÉ‹ brašghL.
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122 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
_‹W kâ¥bg© Édh¡fŸ :
1. fhªj§fË‹mo¥gil¥g©òfŸahit?(VnjD«_‹W)
fhªj§fË‹ mo¥gil¥ g©òfŸ :
(i) fhªj¤âid ïU«ò¤ JUtšfËš mÄœ¤â
vL¡F« nghJ mit fhªj¤â‹ KidfËš x£o¡
bfhŸ»‹wd. fhªj¤â‹ ïU KidfËY« ft®¢á
bgUkkhF«. ïªj KidfŸ fhªj KidfŸ vd
miH¡f¥gL»‹wd.
(ii) xU fhªj« jilÆ‹¿ bjh§fÉl¥gL«nghJ,
v¥nghJ« tl¡Fbj‰F¤ âirÆš ÉF«. òÉÆaš
tlJUt¤ij neh¡» ÉF« fhªj¤â‹ Kid fhªj
tlKid N vdî« òÉÆaš bj‹ JUt¤ij neh¡»
ÉF« fhªj¤â‹ Kid fhªj bj‹Kid (S) vdî«
miH¡f¥gL«.
(iii) fhªj KidfŸ v¥nghJ« nrhofshf k£Lnk
ïU¡F«. mjhtJ jÅik¥gL¤j¥g£l fhªjKid
ïU¥gâšiy.
(iv) fhªj¤â‹ Ús« v¥nghJ« mj‹ toÉaš Ús¤âid
(geometric length) Él¡ Fiwthf ïU¡F«. VbdÅš
fhªj§fË‹ ïašò KidfËÈUªJ (free ends) r‰W c£òwkhfnt fhªj KidfŸ mikªJŸsd.
(Mdhš fz¡Ñ£L neh¡f§fËš toÉaš
Úsnk v¥nghJ« fhªj¤â‹ Úskhf vL¤J¡
bfhŸs¥gL»wJ).
(v) x¤j KidfŸ x‹iwbah‹W Éy¡F»‹wd.
nt¿d KidfŸ x‹iwbah‹W ftU»‹wd.
xU fhªj¤â‹ tlKidia k‰bwhU fhªj¤â‹
tlKid¡fU»š bfh©L tªjhš Éy¡F
Éiria¡ fhzyh«. Mdhš, xU fhªj¤â‹ tl
Kidia k‰bwhU fhªj¤â‹ bj‹Kid¡fU»š
bfh©L tªjhš ft®¢á Éiria¡ fhzyh«.
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RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£ 123
(vi) ïU fhªj KidfS¡»ilna cŸs ft®¢á mšyJ
Éy¡F Éir TY« v⮤jfî ïUko Éâ _y«
bgw¥gL»wJ.
2. fhªjÉir¡nfhLg‰¿Úm¿tJahJ?mt‰¿‹g©òfŸ
ahit?(VnjD«_‹W)
xU jŤj tlKid fhªj¥ òy¤âš it¡f¥gL«nghJ
mJ efU« ghijia¡ F¿¡F« nfhL fhªjÉir¡
nfhL vd¥gL«.
(i) fhªj Éir¡nfhLfŸ, fhªj¥ bghUË‹ tÊahf
bršY« _oa bjhl®¢áahd tis nfhLfŸ MF«.
(ii) fhªj¤â‰F btËna fhªjÉir¡ nfhLfË‹
âir tlKidÆÈUªJ bj‹Kidia neh¡»í«,
f h ª j ¤ â ‰ F c Ÿ n s b j ‹ K i d Æ È U ª J
tlKidia neh¡»í« mikí«.
(iii) fhªj Éir¡ nfh£o‹ ÛJŸs vªj òŸËÆÈUªJ«,
m¡nfh£o‰F tiua¥g£l bjhLnfhL, m¥òŸËÆš
cŸs fhªj¥ òy¤â‹ âiria¡ F¿¡F«. (mjhtJ)
m¥òŸËÆš fhªj¤ ö©lÈ‹ âiria mJ
jU»wJ.
(iv) mit x‹iw x‹W bt£o¡bfhŸtâšiy.
(v) m i t f h ª j ¥ ò y t È i k Ä F ª j ï l ¤ â š
beU¡fkhfî« tÈik F‹¿a ïl¤âš gutyhfî«
mikí«.
3. TY«v⮤jfî«ïUkoÉâiavGâbkŒ¥ã¡fî«.
TY« v⮤jfî« ïUko Éâ:
TY« v⮤ jfî ïUko ÉâÆ‹go, ïU fhªj
KidfS¡»ilnaíŸs ft®¢á mšyJ Éy¡F
ÉirahdJ Kid tÈikfË‹ bgU¡F¤ bjhif¡F
ne®¤jfÉY«, mt‰¿‰F ïilnaíŸs bjhiyÉ‹
ïUko¡F v⮤jfÉY« ïU¡F«.
xU Clf¤âš m1, m2 v‹w KidtÈikíila fhªj
KidfË‹ ïil¤bjhiyî d vÅš,
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124 RuhÉ‹ ïa‰ãaš 11 - M« tF¥ò áfu« bjhLnth« lh®bf£
F a m1 m2 k‰W« F a1
2d
∴F m md
a 1 22
F k m md
= 1 22
ï§F k v‹gJ É»jkh¿È. k‰W« k = mp4
ïâš m v‹gJ Clf¤â‹ c£òFâw‹.
Mdhš m= m0× mr
∴ =m mmr
0
mr - Clf¤â‹ x¥òik c£òFâw‹
m0-bt‰¿l¤â‹ c£òFâw‹
m1= m2 = 1 nkY« d = 1m vÅš,
k 0=mp4
bt‰¿l¤âš m0=4p×10–7Hm–1
∴ =× ×-
F 10 71 2
2
m md
F = × ×-10 1 11
7
2 Þ F = 10–7N
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