c`v_©weÁvb
BDwbU 1 c„ôv 1
BDwbU-1
†fŠZivwk I cwigvc
Physical Quantity & Measurement f‚wgKv
wek¦ eªþv‡Û ARvbv in‡m¨i †kl †bB| wek¦ cÖK…wZi GB ARvbv welq m¤ú‡K© Rvbvi Rb¨ weÁvbxiv A‡bK M‡elYv
Ges wewfbœ cixÿv wbixÿv K‡i _v‡Kb| GB cixÿv wbixÿvi dj cÖKv‡ki Rb¨ wewfbœ GKK e¨envi Ki‡Z nq, hv
n‡e me©RbMÖvn¨| GRb¨ cwigv‡ci Ggb wKQz GKK D™¢veb Kiv n‡q‡Q hv AvšÍRv©wZKfv‡e ¯xK…Z| cwigv‡ci Rb¨
Avwe®‹vi Kiv n‡q‡Q wewfbœ hš¿, †hme h‡š¿i mvnv‡h¨ m~² †_‡K m~²Zi c`v‡_©i cwigvc Kiv †h‡Z cv‡i| hvi
d‡j weÁv‡bi mvwe©K cÖmvi n‡q‡Q m¤¢eci|
cvV-1: c`v_©weÁv‡bi µgweKvk (Evolution of Physics)
D‡Ïk¨
GB cvV †k‡l Avcwb-
c`v_©weÁvb cv‡Vi D‡Ïk¨ eY©bv Ki‡Z cvi‡eb|
c`v_©weÁv‡bi µgweKvk e¨vL¨v Ki‡Z cvi‡eb|
c`v_©weÁvb (Physics):
wek¦ cÖK…wZ‡Z hv †Kvb ¯’vb `Lj K‡i Ges ej cÖ‡qv‡M evav m„wó K‡i, Zv‡K c`v_© e‡j| Avi weÁv‡bi
†h kvLvq c`v_© Ges G‡`i cÖK…wZ I kw³ m¤ú‡K© Av‡jvPbv Kiv nq, †mB kvLv‡K c`v_©weÁvb ejv nq| wewfbœ
cÖKvi cixÿv-wbixÿv I we‡køl‡bi gva¨‡g e¯‘ I kw³i g‡a¨ m¤úK© ¯’vcb Ges cwigvYMZfv‡e djvdj cÖKvk
KivB n‡”Q c`v_©weÁv‡bi g~j jÿ¨|
c`v_©weÁv‡bi cwimi (Scope of Physics):
ejv †h‡Z cv‡i, weÁv‡bi g~j wfwËB n‡”Q c`v_©weÁvb| wek¦ eªþv‡Û hv wKQz msMwVZ nq Zvi cÖvq meB
c`v_©weÁv‡bi gva¨‡g e¨vL¨v Kiv m¤¢e| c`v_©weÁv‡bi bxwZ¸‡jv e¨envi K‡i weÁv‡bi Ab¨vb¨ kvLvmg~‡ni wfwË
ˆZix n‡q‡Q| myZivs c`v_©weÁvb‡K weÁv‡bi †gŠwjK kvLv ejv nq|
wPwKrmvweÁvb, †R¨vwZ©weÁvb, cÖ‡KŠkjkv¯¿, RxeweÁvb, g‡bvweÁvb me©Î c`v_©weÁv‡bi wewfbœ c×wZ e¨envi Kiv
n‡q _v‡K| wek`fv‡e Av‡jvPbv Kivi myweav‡_© c`v_©weÁvb‡K K‡qKwU fv‡M fvM Kiv n‡q‡Q| G¸‡jv n‡jv-
1. ejweÁvb; 2.Zvc weÁvb; 3. kã weÁvb; 4. Av‡jvKweÁvb; 5. Pz¤K weÁvb; 6. Zwor weÁvb; 7. †Kvqv›Uvg
c`v_©weÁvb; 8. wbDwK¬q c`v_©weÁvb BZ¨vw`|
c`v_©weÁv‡bi µgweKvk (Evolution of Physics) :
AvaywbK wek¦ weÁv‡bi Ae`vb| weÁv‡bi GB mdj cÖqvm ¯í mg‡q N‡Uwb| hyM hyM a‡i weÁvbx‡`i AK¬všÍ
cwikÖg, M‡elYv, Avwe®‹v‡ii ga¨ w`‡q GB mdjZv G‡m‡Q| weÁvbx‡`i GB Avwe®‹vi gvbe RvwZ‡K DbœZZi Rxeb
`vb K‡i‡Q| weÁv‡bi BwZnvm ch©v‡jvPbv Ki‡j †`Lv hvq †h, cÖvPxbKvj †_‡KB weÁvbxiv weÁv‡bi wewfbœ kvLvi
Dbœq‡b Ae`vb †i‡L Avm‡Qb|
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 2
weÁvbx †_wjm (wLªóc~e© 624-569) m~h©MÖnY I R¨vwgwZ m¤ú‡K© aviYv †`b, Zv‡K Father of Science ejv nZ|
wc_v‡Mvivm (wLªóc~e© 570-495) wQ‡jb GKvav‡i MwYZwe`, `vk©wbK I ˆeÁvwbK| wZwb wewfbœ R¨vwgwZK Dccv`¨
Ges m~Î Avwe®‹vi K‡ib| ev`¨hš¿ I msMxZ welqK †¯‹j m¤ú‡K© wZwb wKQzUv aviYv cÖ vb K‡ib|
MÖxK `vk©wbK †W‡gvwµUvm (wLªóc~e© 460-370) c`v‡_©i MVb m¤ú‡K© aviYv cÖ vb K‡ib| wZwb e‡jb †h, c`v‡_©i
AwefvR¨ GKK i‡q‡Q| cieZx©‡Z wZwb Gi bvg †`b GUg ev cigvYy| Z‡e †W‡gvwµUv‡mi c~‡e© weÁvbx jywmcvm
cigvYy m¤ú‡K© fwel¨Øvbx cÖ vb K‡i wQ‡jb|
weÁvbx AvwK©wgwWm (wLªóc~e© 287-212) R¨vwgwZ I AsKkv‡¯¿ AbyivMx wQ‡jb| GQvov wZwb avZzi weï×Zv wbY©‡q
mÿg nb Ges †Mvjxq `c©‡bi mv‡_ m~h©iwk¥ cÖwZdjb NwU‡q Av¸b aiv‡bvi †KŠkj Avwe®‹vi K‡ib|
weÁv‡b gymwjg weÁvbx‡`i Ae`vbI wQj ¸iæZ¡c~Y©| Avieiv MwYZ, †R¨vwZ©we`¨v, imvqb I wPwKrmv weÁv‡bi
cvi`kx© wQ‡jb| weÁvbx Rvwei Be‡bi nvBqvb (721-815 wLª.) imvqbkv‡¯¿ cvi`kx© Ges †LvqvwiRwb (770-
840wLª.) MwYZ wel‡qi M‡elK wQ‡jb| 'Algebra' kãwU Zvi weL¨vZ MÖš’ Avj wRei Iqvj gyKvwejv †_‡K DrcwË|
Be‡b Avj nvBqvg (965-1040) wQ‡jb GKvav‡i c`v_©we` I MwYZwe`| Av‡jvK weÁv‡b Zuvi Ae`vb i‡q‡Q|
cvim¨‡`kxq cwÐZ Avey ivBqvb Avj‡eiæbx (973-1048) c„w_exi cwiwa wbY©q K‡ib|
iRvi †eKb (1214-1294) cixÿv g~jK ˆeÁvwbK c×wZi aviYv cÖ vb K‡ib| wKfv‡e ch©‡eÿY I wePvi
we‡køl‡Yi gva¨‡g djvdj cÖKvk I Gi mZ¨Zv hvPvB Kiv hvq, †m m¤ú‡K© aviYv †`b|
wjIbv‡`v© `¨v wfw (1452-1519) wQ‡jb g~jZ GKRb cÖL¨vZ wPÎwkíx| wZwb D‡ovRvnv‡Ri g‡Wj ˆZix
K‡iwQ‡jb|
g~jZ Gi cieZx© mgq c`v_©weÁv‡bi Avwe¯‹v‡ii Rb¨ D‡jøL¨‡hvM¨| Wv. wMjevU© (1540-1603) Pz¤KZ¡ wb‡q
M‡elYv K‡ib| Rvgv©bxi weÁvbx †¯œj (1591-1626) cÖwZmi‡Yi m~Î Avwe®‹vi K‡ib| weÁvbx nvB‡Mbm
(Huygens) (1626-1695) Av‡jvi Zi½ Z‡Ë¡i e¨vL¨v cÖ vb K‡ib| ievU© ûK (1635-1703) c`v‡_©i
w¯’wZ¯’vcKZvi m~Î Avwe®‹vi K‡ib| GQvov ievU© e‡qj (1627-1691) M¨v‡mi m~Î Avwe¯‹vi K‡ib| †ivgvi
(1644-1710) e„n¯úwZi GKwU DcMÖ‡ni MÖnY ch©‡eÿY K‡i Av‡jvi †eM cwigvY K‡ib, hv ZLbKvi weÁvbx‡`i
wbKU MÖnY‡hvM¨ wQj bv|
wb‡Kvjvm †Kvcv©wbKvm (1473-1543) GKRb †R¨vwZ©weÁvbx wQ‡jb| wZwbB cÖ_g aviYv †`b †h, c„w_ex m~‡h©i
Pvwiw`‡K Ny‡i| cieZx©‡Z †Rvnvb †Kc&jvi (1571-1630) MÖ‡ni MwZ m¤úwK©Z m~Î Avwe¯‹vi K‡ib hv †Kcjv‡ii
m~Î bv‡g cwiwPZ| wZwb cÖPwjZ e„ËvKvi Kÿc‡_i aviYv cv‡ë Dce„ËvKvi Kÿc‡_i Kíbv K‡ib|
M¨vwjwjI M¨vwjwj (1564-1642) †K ˆeÁvwbK c×wZi RbK ejv nq|wZwbB cÖ_g cÖgvY K‡ib †h cixÿY Ges
wewfbœ ivwki g‡a¨ m¤úK© ¯’vcb ˆeÁvwbK c×wZi g~j wfwË| cixÿvjä djvdj Qvov KL‡bvB †Kvb NUbv
MvwYwZKfv‡e cÖgvY Kiv hvq bv|
AvBR¨vK wbDUb (1642-1727) wQ‡jb me©Kv‡ji †kÖô weÁvbx‡`i GKRb| wZwb gnvKl©m~Î, e¨eKjb
K¨vjKzjv‡mi bxwZ cÖeZ©b K‡ib| GQvov wZwb Av‡jvi KYvZË¡ Avwe®‹vi K‡ib| wZwb n‡”Qb K¬ vwmK¨vj †gKvwb·
Gi RbK|
Aóv`k †_‡K Ebwesk kZvãx ch©šÍ Avwe®‹vi BD‡iv‡c wkí wecøe NUvq| †Rgm& Iqv‡Ui (1736-1819) ev®úxq
BwÄb wkí wecø‡e AMÖYx f‚wgKv iv‡L|
n¨vÝ wµwðqvb I‡qi‡÷W (1777-1851) Zwor cÖev‡ni †PŠ¤K wµqv Avwe®‹vi K‡ib| cieZx©‡Z gvB‡Kj d¨viv‡W
(1791-1867), †nbix (1797-1879), †jÄ (1804-1865) cÖg~L weÁvbxMY †PŠ¤Kxq wµqvi gva¨‡g Zwor cÖevn
Drcv`b Kivi ZË¡ Avwe®‹vi K‡ib| GwU wQj hvwš¿K kw³‡K Zworkw³‡Z iƒcvšÍ‡ii †KŠkj|
c`v_©weÁvb
BDwbU 1 c„ôv 3
Ebwesk kZvãxi †k‡li w`‡K AvaywbK c`v_©weÁv‡bi Af‚Zc~e© DbœwZ N‡U| 1864 mv‡j weL¨vZ c`v_©weÁvbx
†Rgm K¬vK© g¨v·I‡qj (1831-1879) Av‡jvi Zwor Pz¤Kxq Z‡Ë¡i aviYv †`b| wZwb Zwor †ÿÎ Ges Pz¤K †ÿÎ
GKÎ K‡i Zwor Pz¤Kxq Z‡Ë¡i weKvk NUvb hv cieZx©‡Z Rvgv©b c`v_©weÁvbx †nb&wiL nv‡R©i (1857-1894)
cixÿv Øviv cÖgvwYZ nq| 1896 mv‡j weÁvbx gvK©bx (1874-1937) ZvwoZ‡PŠ¤K Zi½ e¨envi K‡i AwaK `~i‡Z¡
ms‡KZ cvVv‡bvi cš’v Avwe®‹vi K‡ib| ev½vjx weÁvbx RM`xk P›`ª emyI (1858-1937) GKB cÖKvi cixÿv
bxwiÿv Pvjvb| cieZx©‡Z †eZvi hš¿ Avwe®‹vi nq|
Ebwesk kZvãxi †k‡li w`‡K cvigvYweK c`v_©weÁv‡bi D™¢e N‡U| 1895 mv‡j ib&‡Rb (1845-1923) G·-‡i
Ges †eK&‡ij (1852-1908) Avwe®‹vi K‡ib †h, wKQz wKQz c`v_© †_‡K ¯Z:ùzZ© fv‡e iwk¥ wbM©g‡bi gva¨‡g
ÿqcÖvß nq| †gix Kzix (1867-1934) Ges wc‡q‡i Kzix (1859-1906) G NUbvi bvg †`b †ZRw¯ŒqZv| 1897
mv‡j †R.‡R. _gmb (1856-1940) B‡j±ªb Avwe®‹vi K‡ib hv †_‡K cigvYyi MVb m¤ú‡K© we¯ÍvwiZ Rvbv m¤¢eci
wQj|
wesk kZvwãx‡Z c`v_©weÁv‡b Av‡iv bZzb bZzb Avwe®‹vi hy³ nq| g¨v· cø¨vsK (1858-1947) wewKiY m¤úKx©Z
†Kvqv›Uvg ZË¡ Avwe®‹vi K‡ib| AvjevU© AvBb÷vBb (1871-1955) Av‡cwÿK ZË¡ cÖ vb K‡ib| GQvov wZwb
weL¨vZ fi-kw³i m~Î (E=mc2) Avwe®‹vi K‡ib|
1911 mv‡j Av‡b©÷ iv`vi‡dvW© (1871-1937) cigvYy welqK wbDwK¬q ZË¡ Ges bxjm& †evi (1885-1962)
nvB‡Wªv‡Rb cigvYy B‡jKUªb ¯Í‡ii aviYv cÖ vb K‡ib| cieZx©‡Z wbDwK¬q c`v_©weÁv‡b Av‡iv DbœwZ mvwaZ nq|
1938 mv‡j I‡Uv nvb (1879-1968) I †÷ªmg¨vb (1902-1980) cÖgvY K‡ib †h, wbDwK¬qvm wdkb‡hvM¨ | A_v©r
wdk‡bi d‡j GKwU eo fi msL¨v wewkó wbDwK¬qvm †f‡½ cÖvq mgvb fi wewkó `ywU wbDwK¬qv‡m cwiYZ nq Ges
cÖPzi kw³ Drcvw`Z nq| GB ZË¡ cÖ‡qvM K‡i wbDwK¬q †evgv I wbDwK¬q Pzjøxi D™¢veb nq| wbDwK¬qvm wefvRb †_‡K
†h kw³ Drcv`b nq, †mB kw³i cwigvY wecyj | GRb¨ eZ©gvb AvaywbK wek¦ wbDwK¬q kw³‡K kw³i GKwU cÖavb
Drm wn‡m‡e we‡ePbv Ki‡Q|
m‡Z¨›`ªbv_ emy (1894-1974) c`v_©weÁv‡b ¸iæZ¡c~Y© Ae`vb iv‡Lb| Zvi ZË¡ †evm-AvBb÷vBb ZË¡ bv‡g
cwiwPZ| Zvi bvgvbymv‡i we‡kl GK †kÖwYi ‡gŠwjK KYvi bvgKiY Kiv n‡q‡Q Ô†evmbÕ bv‡g|
fviZxq †bv‡ej weRqx weÁvbx P›`ª‡kLi †fsKUvigb (1888-1970) igb cÖfve Avwe®‹vi K‡ib| GQvov cvwK¯Ívbx
weÁvbx Avãym mvjvg (1926-1996) ZvwoZPz¤K ej I `ye©j cvigvYweK e‡ji AwfbœZv cÖ vb K‡ib|
wesk kZvãx‡Z c`v_©weÁv‡bi cvkvcvwk weÁv‡bi Ab¨me kvLvqI h‡_ô AMÖMwZ mvwaZ n‡q‡Q| Gme Dbœq‡bI
c`v_©weÁvb h‡_ó ¸iæZ¡c~Y© f‚wgKv cvjb K‡i Avm‡Q| †hgb wPwKrmv weÁv‡bi µgweKv‡k c`v_©weÁv‡bi f‚wgKv
Acwimxg|
†ZRw¯Œq AvB‡mv‡Uvc e¨envi K‡i wewfbœ RwUj †ivM wbivgq Kiv m¤¢e n‡”Q| c`v_©weÁv‡bi Avwe®‹v‡ii Øviv gvbyl
Rq K‡i‡Q cÖK…wZ‡K| gvbyl Pvu` †_‡K ïiæ K‡i g½j MÖ‡n c`vc©b K‡i‡Q| gnvk~‡b¨ †÷kb ¯’vcb K‡i w`‡bi ci
w`b gnvk~‡b¨ Ae¯’vb K‡i wewfbœ ¸iæZ¡c~Y© Z_¨vejx msMÖn Ki‡Z cvi‡Q hv M‡elYv‡Z f‚wgKv ivL‡Q| GQvov K„wÎg
DcMÖn ¯’vcb K‡i Zvi gva¨‡g AenvIqvi c~ev©fvm w`‡Z mÿg n‡”Q| Avgv‡`i ˆ`bw›`b Rxe‡b wewfbœ
B‡jKUªwb‡·i e¨envi Qvov Avgiv GKgyn~Z© wPšÍv Ki‡Z cvwi bv| Kw¤úDUvi, †iwWI, †Uwjwfkb, †gvevBj,
B›Uvi‡bU, wWwRUvj K¨v‡giv, AvB c¨vW, U¨ve BZ¨vw` Avgv‡`i Rxeb hvÎv‡KB cv‡ë w`‡q‡Q| AvR‡K we‡k¦i GK
cÖv‡šÍi msev` Ab¨ cÖv‡šÍ e‡m gyn~‡Z©B cvw”Q Zv GKgvÎ weÁv‡bi Ae`vb|
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 4
c`v_©weÁv‡bi D‡Ïk¨ (Objective of Physics) t
cÖK…wZi inm¨ D‡b¥vP‡b c`v_©weÁvb (Role of Physics to reveal the mystery of Nature) :
c`v_©weÁvb‡K weÁv‡bi †gŠwjK kvLv ejv nq| Gi bxwZ¸‡jvi mvnv‡h¨ Ab¨vb¨ kvLvmg~‡ni wfwË ˆZix n‡q‡Q|
D`vniY¯iƒc ejv hvq, kw³i msiÿYbxwZ c`v_©weÁv‡bi GKwU g~j bxwZ hv w`‡q cigvYyi Af¨šÍixb Ae¯’v †_‡K
cÖK…wZ ch©šÍ e¨vL¨v Kiv m¤¢e|
hw`I c`v_© I kw³i iƒcvšÍi wek`fv‡e Av‡jvPbv KivB c`v_©weÁv‡bi g~j KvR| wKš‘ c`v_©weÁv‡bi cÖavb D‡Ïk¨
n‡”Q cÖK…wZi inm¨ D`NvUb Kiv| wesk kZvãxi ïiæi w`‡K weÁvbxiv Avwe®‹vi Ki‡jb †h, cigvYyi †K‡›`ª
abvZœKfv‡e AvwnZ wbDwK¬qvm _v‡K| wbDwK¬qvm‡K †K›`ª K‡i wewfbœ kw³ ¯Í‡i B‡jKUªb¸‡jv Nyi‡Z _v‡K| Gi
cieZx© M‡elYvi djvdj n‡”Q wbDwK¬qvm †cÖvUb I wbDUªb Øviv MwVZ| eZ©gv‡b weÁvbxiv Avwe®‹vi Ki‡Qb †h,
†cÖvUb I wbDUªb ÿz`ª KYv Øviv MwVZ| A_v©r weÁvbxiv cÖwZwbqZ inm¨ D‡b¥vPb K‡iB P‡j‡Qb|
imvqb weÁvb, f‚-ZË¡ weÁvb, †R¨vwZ©weÁvb, AvenvIqv weÁvb, Rxe weÁvb, mgy`ª weÁvb, wPwKrmv weÁvb BZ¨vw`
m¤ú‡K© †gŠwjK e¨vL¨v I aviYv cÖ vb K‡i| GQvov c`v_©weÁv‡bi c×wZ I hš¿cvwZi cÖf‚Z e¨envi i‡q‡Q|
cÖK…wZi wbqg eY©bvq c`v_©weÁvb (Physics to describe the law of Nature):
gnvwek¦‡K Rq K‡i‡Q c`v_©weÁvb| Avgiv †h c„w_ex‡Z evm Kwi ZvI wKQz wbw`©ó wbqg †g‡b P‡j| GB
wbqg¸‡jv‡K c`v_©weÁv‡bi wKQz m~‡Îi mvnv‡h¨ eY©bv Kiv hvq| †hgb, wbDU‡bi gnvKl© m~Î, wbDU‡bi MwZm~Î,
kw³i msiÿYbxwZ BZ¨vw`| gvbyl wkïKvj †_‡K cÖK…wZ †_‡K Ávb AvniY K‡i cÖK…wZ‡K †gvKv‡ejv Kivi Rb¨
wewfbœ †KŠkj D™¢veb K‡ib|
cÖK…wZi DbœwZ mva‡b c`v_©weÁvb (Physics to develope the Nature) :
Avgiv Avgv‡`i Pvicv‡k A‡bK we¯§qKi Avwe®‹vi †`wL| †hgb- †Uwjwfkb, i‡KU, D‡ovRvnvR, K…wÎg DcMÖn,
B›Uvi‡bU, †gvevBj †dvb, mve‡gwib, gnvk~b¨hvb BZ¨vw`| GB hš¿cvwZ¸‡jv Avwe®‹vi Ki‡Z c`v_©weÁv‡bi †gŠwjK
m~θ‡jv cÖ‡qvM Kiv n‡q‡Q| GQvov G¸‡jvi Kvh©cÖYvjx eyS‡Z Avgv‡`i c`v_©weÁvb Rvb‡Z n‡e|
†gavi weKv‡k c`v_©weÁvb (Physics for development of intellect):
c`v_©weÁvb Aa¨qb K‡i Avgiv mg¨K Ávb AR©b Ki‡Z cvwi| wKfv‡e wPšÍv Ki‡Z nq, wPšÍv¸‡jv‡K wKfv‡e
cÖ‡qvM Ki‡Z n‡e Ges hyw³i gva¨‡g wKfv‡e ev¯Íe iƒc`vb Ki‡Z n‡e-c`v_©weÁvb Zv wkwL‡q †`q| GQvov
c`v_©weÁvb Avgv‡`i ch©‡eÿY ÿgZv evwo‡q †`q|
wKfv‡e mwVKfv‡e ch©‡eÿY K‡i Zvi djvdj cÖKvk Ki‡Z nq c`v_©weÁvb cvV †_‡K Avgiv Zv Rvb‡Z cv‡i|
¯’vb I Kvj (Space and time):
¯’vb I Kvj c`v_©weÁv‡bi AwZ ¸iæZ¡c~Y© GKwU welq| †Kvb NUbv eY©bv Kivi Rb¨ ¯’vb I Kv‡ji cÖ‡qvRbxqZv
i‡q‡Q| GKwU NUbv KLb, †Kv_vq N‡U‡Q Zv m¤ú‡K© aviYv cvIqvi Rb¨ GB `ywU welq Aek¨B Rvb‡Z n‡e| c`v_©
Z_v e¯‘ gvÎB RvqMv `Lj K‡i| e¯‘i Ae¯’vb †Kv_vq Ges wK cwigvY RvqMv `Lj K‡i Gme Z_¨vw` Rvbvi Rb¨
cÖvPxbKvj †_‡K ¯’vb m¤ú‡K© GKwU avibv cvIqv hvq| GQvov †Kvb NUbv KLb N‡U‡Q, †Kvb NUbvwU Av‡M N‡U‡Q
Ges †KvbwU c‡i Zv e¨vL¨v Ki‡Z mgq Rvbvi cª‡qvRb n‡q c‡o| cÖvPxbKvj †_‡K ¯’vb I Kvj m¤ú‡K© weÁvbxiv
aviYv w`‡q Avm‡Qb|
c`v_©weÁvb
BDwbU 1 c„ôv 5
BDwK¬‡Wi aviYv (Concept of Euclide):
me©cÖ_g BDwK¬W ¯’vb m¤ú‡K© R¨vwgwZK aviYv Dc¯’vcb K‡ib| Avgv‡`i Pvicv‡k hv Av‡Q meB ¯’vb|
M¨vwjwjI Gi aviYv (Concept of Gallileo):
M¨vwjwjI ¯’vb I Kvj‡K Zvi MwZ I Z¡i‡Yi m~‡Î e¨envi Ki‡Qb| d‡j c`v_©weÁv‡b ¯’vb I Kvj ¸iæZ¡c~Y© ivwk
wn‡m‡e MvwYwZK mgxKi‡Y cÖ‡ek Ki‡Q|
wbDU‡bi aviYv (Concept of Newton):
wbDU‡bi ejwe`¨vi gva¨‡g ¯’vb I Kv‡ji aviYv cwigvYMZ Ges my¯úó fv‡e e¨vL¨v Kiv hvq| wbDUbxq ev wPivqZ
c`v_©weÁv‡b ¯’vb n‡”Q wÎgvwÎK we¯Í…wZ| Gi †Kvb ïiæ ev †kl †bB| Gi we¯Í…wZ Amxg| ¯’vb‡K ÿz`ª ÿz`ª As‡k
fvM Kiv hvq| ¯’v‡bi †h‡Kvb GjvKv Ab¨ GjvKv †_‡K Awfbœ A_v©r ¯’vb mgmË¡| ¯’vb wbi‡cÿ| mg¯Í NUbv
¯’v‡bi g‡a¨ N‡U Ges mg¯Í e¯‘i Ae¯’vb I ¯’v‡bi we¯Í…wZi g‡a¨ _v‡K, wKš‘ ¯’vb †Kvb e¯‘ ev NUbv Øviv cÖfvweZ
nq bv A_v©r wbi‡cÿ| ¯’vb ïay e¯‘ I NUbv wbi‡cÿ bq, mgq wbi‡cÿI e‡U| GRb¨ Kv‡ji cÖevn ¯’vb‡K
cwieZ©b Ki‡Z cv‡i bv|
wbDU‡bi aviYv g‡Z mgq Zvi wbR¯ avivq cÖevwnZ nq| †Kvb e¯‘ ev NUbv Øviv mg‡qi cÖevn cÖfvweZ nq bv| Gi
†Kvb ïiæ ev †kl †bB| mgq‡K AwZ ÿz`ª ÿz`ª As‡k fvM Kiv hvq| Gi †h †Kvb Ask Ab¨ As‡ki Abyiƒc| GRb¨
†Kv‡bv cixÿv hLbB m¤úv`b Kiv †nvK bv †Kb Zv mgq wbev©P‡bi Dci wbf©ikxj bq| mgq ¯’vb wbi‡cÿ|
wbDU‡bi ¯’vb-Kv‡ji e¨vL¨v †_‡K Avgiv Dcjwä Ki‡Z cvwi †h, Avgv‡`i GB gnvwek¦ wÎgvwÎK ¯’vb I GKgvwÎK
mgq wb‡q MwVZ| wKš‘ AvaywbK c`v_©weÁv‡b wbDU‡bi aviYvi cwieZ©b n‡q‡Q| AvBb÷vB‡bi Av‡cwÿK ZË¡ Ges
cø vs‡Ki †Kvqv›Uvg ZË¡ †_‡K Gi bZzb aviYv cvIqv hvq|
mvi-ms‡ÿc:
c`v_©: cÖK…wZ‡Z hv †Kvb ¯’vb `Lj K‡i Ges ej cÖ‡qv‡M evav m„wó K‡i, Zv‡K c`v_© ejv nq|
¯’vb I Kvj: e¯‘i Ae¯’vb Rvbvi Rb¨ hv cÖ‡qvRb nq Zv‡K ¯’vb e‡j| Avevi †Kvb NUbv KLb NU‡Q ev
†KvbwU Av‡M NU‡Q A_ev †KvbwU c‡i N‡U‡Q Zv e¨vL¨v Ki‡Z mg‡qi cÖ‡qvRb nq|
cv‡VvËi g~j¨vqb-1
mwVK Dˇii cv‡k wUK () wPý w`b
1. cvigvYweK c`v_©weÁv‡bi D™¢e KLb N‡U?
K) Aóv`k kZvãx‡Z L) Ebwesk kZvãx‡Z
M) wesk kZvãx‡Z N) GKwesk kZvãx‡Z
2. ¯’vb I Kvj m¤ú‡K© aviYv cÖ vb K‡ib-
i) wbDUb I BDwK¬W ii) M¨vwjwjI I m‡Z¨›`ªbv_ emy
iii) BDwK¬W I M¨vwjwjI
wb‡Pi †KvbwU mwVK?
K) i I ii L) ii I iii M) i I iii N) i, ii I iii
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 6
cvV t 2 †fŠZ ivwk
D‡Ïk¨
GB cvV †k‡l Avcwb-
†fŠZ ivwk Kx Zv e¨vL¨v Ki‡Z cvi‡eb|
†gŠwjK ivwk Ges jä ivwk Kx Zv e¨vL¨v Ki‡Z cvi‡eb|
ivwki gvÎv wnmve Ki‡Z cvi‡eb|
†fŠZ ivwk:
GB wek¦ cÖK…wZi hv wKQz cwivgvc Kiv hvq Zv‡K ivwk ejv nq| †hgb GKwU †jvnvi e‡ji fi cwigv‡ci
Kiv hvq| fi GKwU ivwk| Avevi Kvc‡oi ˆ`N¨© cwivgvc Kiv hvq †hLv‡b ˆ`N¨© GKwU ivwk| cvwbi ZvcgvÎv
cwigvc Kiv hvq, Zvn‡j cvwbi ZvcgvÎvI GKwU ivwk| evwo †_‡K ¯‹z‡j †h‡Z KZ mgq jv‡M †mB mgqI GKwU
ivwk| GB †fŠZ RM‡Z Giƒc eû ivwk i‡q‡Q| G mKj ivwki g‡a¨ K‡qKwU ivwk i‡q‡Q †h¸‡jv cwigvc Kivi
Rb¨ Ab¨ †Kvb ivwki Dci wbf©i Kivi cÖ‡qvRb nq bv| G ivwk ¸‡jv‡K †gŠwjK ivwk ejv nq| †hgb mgq gvc‡Z
Ab¨ †Kvb ivwki Dci wbf©i Ki‡Z nq bv| myZivs mgq GKwU †gŠwjK ivwk|
Aciw`‡K, Ggb A‡bK ivwk Av‡Q †h¸‡jv gvcvi Rb¨ Ab¨ ivwki `iKvi nq| †hgb †eM cwigv‡ci Rb¨ `~iZ¡
Ges mgq GB ivwk `ywU Rvbvi cÖ‡qvRb nq| AZ:ci `~iZ¡‡K mgq w`‡q fvM K‡i †e‡Mi gvb †ei Ki‡Z nq| Gi
†_‡K eySv hvq †h, †eM GKwU jä ev †hŠwMK ivwk| AZGe GUv cÖZxqgvb nq †h, wKQz wKQz g~j ivwk Av‡Q,
†h¸‡jv Ab¨ ivwki Dci wbf©ikxj bq| Gme ivwk¸‡jv‡K †gŠwjK ivwk ejv nq|
Ávb weÁv‡bi mKj kvLvq weÁvbxiv cwigv‡ci †ÿ‡Î Giƒc mvZwU ivwk‡K †gŠwjK ivwk wn‡m‡e wPwýZ K‡i‡Qb|
G¸‡jv n‡jv ‰`N¨©, fi, mgq,ZvcgvÎv, ZworcÖevn, `xcb ZxeªZv Ges c`v‡_©i cwigvY|
†h mKj ivwk †gŠwjK ivwki Dci wbf©ikxj A_©vr †gŠwjK ivwk †_‡K cvIqv hvq, Zv‡`i‡K jä ivwk ejv nq|
†eM, Z¡iY, KvR, ej, Zvc, wefe BZ¨vw` jä ivwki D`vnviY| †h ¸‡jv †gŠwjK ivwk †_‡K MwVZ nq|
†hgb: KvR = ej × miY
= fi × Z¡iY × miY = fi ×2
mgq
miY ×miY = fi ×2
2
mgq
miY
myZivs KvR GKwU jä ivwk ev †hŠwMK ivwk|
gvÎv (Dimension) :
c~‡e©i Av‡jvPbv ‡_‡K Avgiv †R‡bwQ †h, †fŠZ ivwk¸‡jv GK ev GKvwaK †gŠwjK ivwk Øviv MwVZ nq| myZivs †h
†Kv‡bv †fŠZ ivwk‡K wewfbœ m~P‡Ki GK ev GKvwaK †gŠwjK ivwki ¸Ydj wn‡m‡e cÖKvk Kiv nq| †Kv‡bv †fŠZ
ivwk‡Z we`¨gvb †gŠwjK ivwk ¸‡jvi m~PK‡K ivwkwUi gvÎv e‡j| †gŠwjK ivwk ˆ`N¨©, fi I mgq‡K h_vµ‡g L, M I T Øviv cÖKvk Kiv nq| L †K ˆ`‡N¨©i gvÎv, M †K f‡ii gvÎv, T †K mg‡qi gvÎv e‡j|
†hgb, ej = fi × Z¡iY
= fi × †eM
mgq
= fi ׈`N¨©
mgq
2 = M× 2TL
= MLT-2
myZivs, e‡ji gvÎv MLT-2| A_©vr e‡ji i‡q‡Q f‡ii gvÎv (M), ˆ`‡N¨©i gvÎv (L) Ges mg‡qi gvÎv (T)|
c`v_©weÁvb
BDwbU 1 c„ôv 7
†h mgxKi‡Yi mvnv‡h¨ †Kvb ivwki gvÎv cÖKvk Kiv n‡q _v‡K Zv‡K gvÎv mgxKiY e‡j| gvÎv mgxKi‡Y gvÎv
wb‡`©k Ki‡Z Z…Zxq eÜbx [ ] e¨envi Kiv nq| †hgb, e‡ji gvÎv mgxKiY nj, [F] = [MLT-2]
2.3-3 mviYx‡Z wewfbœ ivwki gvÎv †`Lv‡bv nj| gvÎv mgxKi‡Yi mvnv‡h¨ Avgiv †Kvb †fŠZ ivwki GKK wbY©q
Ki‡Z Ges mgxKi‡Yi ï×Zv cixÿv Ki‡Z cvwi| D`vniY ¯iƒc Avgiv wb‡gœi mgxKiYwU we‡ePbv Ki‡Z cvwi|
s = ut + 21
at2
†KejgvÎ GKB RvZxq ivwki †hvM, we‡qvM ev mgZv m¤¢e| myZivs GKwU mgxKi‡Yi cÖwZwU c`‡K Aek¨B GKB
RvZxq ivwk‡K wb‡`©k Ki‡Z n‡e| Dc‡ii mgxKiYwU‡Z wZbwU c` Av‡Q| evgw`‡K GKwU Ges Wvbw`‡K `ywU| GB
mgxKi‡Y s nj miY|
myZivs, s Gi gvÎv nj L
u nj Avw`‡eM, Gi gvÎv=
TL
= LT-1
a nj Z¡iY, Gi gvÎv= 2TL
= LT-2
t nj mgq, Gi gvÎv= T
ut Gi gvÎv= LT-1× T= L
Ges at2 Gi gvÎv= LT-2
× T2= L
myZivs cÖZxqgvb n‡”Q †h, D³ mgxKiYwUi evgw`‡Ki c`wUi gvÎv L Ges Wvbw`‡Ki `ywU c‡`i gvÎvI L| myZivs
mgxKiYwU wm×|
mvi ms‡ÿc t
†gŠwjK ivwkt ˆ`N© , fi, mgq, ZvcgvÎv, ZworcÖevn, `xcb ZxeªZv, c`v‡_©i cwigvY- GB mvZwU ivwk‡K
†gŠwjK ivwk e‡j| ivwk¸‡jv‡K cwigvc Ki‡Z Ab¨ †Kvb GK‡Ki Dci wbf©i Ki‡Z nq bv|
jä ivwkt †h ivwk¸‡jv †gŠwjK ivwki Dci wbf©ikxj Zv‡`i‡K jä ivwk e‡j| †hgb- †eM, KvR, Z¡iY
BZ¨vw`|
cv‡VvËi g~j¨vqb-2
mwVK Dˇii cv‡k wUK () wPý w`b
1. †KvbwU jä ivwki D`vniY?
K) KvR L) fi M) mgq N) ZvcgvÎv
2. gvÎv mgxKi‡Yi mvnv‡h¨-
i) †fŠZ ivwki GKK wbY©q Kiv hvq ii) mgxKi‡Yi mZ¨Zv hvPvB Kiv hvq
iii) MvwYwZK mgm¨v mgvavb Kiv hvq
wb‡Pi †KvbwU mwVK?
K) i L) i I ii M) i I iii N) i, ii I iii
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 8
cvV t 3 cwigvc I GKK (Measurement and Unit)
D‡Ïk¨
GB cvV †k‡l Avcwb-
cwigvc I GK‡Ki cÖ‡qvRbxqZv e¨vL¨v Ki‡Z cvi‡eb|
GK‡Ki AvšÍR©vwZK c×wZ‡Z †gŠwjK GKK¸‡jv eY©bv Ki‡Z cvi‡eb|
GK‡Ki wewfbœ DcmM© e¨envi Ki‡Z cvi‡eb|
‰eÁvwbK ms‡KZ I GKK †jLvi wbqg eY©bv Ki‡Z cvi‡eb|
cwigv‡ci GKK :
cÖvPxbKvj †_‡KB gvbyl Zvi ˆ`bw›`b KvRKg© Ges e¨emv evwY‡R¨i Rb¨ gvc †Rv‡Li cÖ_v D™¢veb
K‡ib| A_v©r Avgv‡`i ˆ`bw›`b Rxe‡b cÖwZwU Kv‡Ri mv‡_ gvc †Rv‡Li e¨vcviwU RwoZ i‡q‡Q|
GQvov wewfbœ M‡elYvi Kv‡R m~ÿ¥ gvc †Rv‡Li cÖ‡qvRb nq| gvc †Rv‡Li GB welqwU‡K ejv nq cwigvc| A_v©r
cwigvc ej‡Z eySvq †Kv‡bv wKQzi cwigvY wbY©q Kiv| †hgb iæwe †`vKvb †_‡K 1wjUvi `ya wKbj| iæcg cÖwZw`b
mKv‡j 2 wK‡jvwgUvi †`Šouvq, cªxZ‡gi evmv †_‡K ¯‹z‡j †h‡Z 15 wgwbU mgq jv‡M| GLv‡b 1 wjUvi n‡jv `y‡ai
AvqZb Ges 2 wK‡jvwgUvi n‡j `~i‡Z¡i cwigvY Ges 15 wgwbU n‡jv mg‡qi cwigvY| A_v©r †Kv‡bv wKQz cwigvY
wbY©q Ki‡Z n‡j `ywU wRwb‡mi cÖ‡qvRb nq| GKwU n‡jv msL¨v Ab¨wU n‡jv GKK|
†h †Kvb †fŠZ ivwki cwigv‡ci Rb¨ Zvi GKwU wbw`ó cwigvY‡K Av`k© wn‡m‡e aiv nq Ges GB cwigv‡Yi
mv‡c‡ÿ mgMÖ †fŠZ ivwkwUi cwigvc Kiv nq| G Av`k© cwigvY‡K H ivwkwUi GKK ejv nq| g‡b Kiv hvK GKwU
†Uª‡bi ˆ`N¨© 100 wgUvi| GLv‡b, wgUvi nj ˆ`‡N¨©i GKK Ges †Uª‡bi ˆ`N¨© D³ GKK `~i‡Z¡i 100¸Y| wewfbœ
†fŠZ ivwk †hgb, †ÿÎdj, AvqZb, IRb, †KvY, mgq, ej, Zvc, kw³ BZ¨vw` cwigv‡ci Rb¨ wfbœ wfbœ GKK
i‡q‡Q Ges cwigv‡ci wewfbœ c×wZ‡Z G‡`i wfbœ wfbœ bvg i‡q‡Q| G GKK¸‡jv Avevi ci¯úi m¤úK©hy³|
myZivs †h Av`k© cwigv‡ci mv‡_ Zzjbv K‡i †fŠZ ivwk‡K cwigvc Kiv nq Zv‡K cwigv‡ci GKK ejv nq|
wgUvi, wK‡jvMÖvg, †m‡KÛ, wbDUb, Ryj BZ¨vw` cwigv‡ci GK‡Ki D`vniY|
Gm.AvB. (SI) Gi †gŠwjK GKK mg~n:
†h‡nZz †gŠwjK ivwki GKK mg~n Ab¨ †Kv‡bv GK‡Ki Dci wbf©i K‡i bv, ZvB †gŠwjK GKK B”QvgZ wbev©Pb Kiv
hvq| Z‡e wbev©wPZ GKK¸‡jvi AvšÍRv©wZK ¯xK…wZ _vK‡Z n‡e Ges GB GKK ¸‡jvi wKQz ˆewkó¨ _vK‡Z n‡e|
†hgb, GwU n‡e AcwieZ©bxq A_©vr ¯’vb, Kvj, cvÎ †f‡` †Kvb wKQzi Dci wbf©i Ki‡e bv| Kv‡ji weeZ©‡b ev Ab¨
†Kvb cÖvK…wZK cwieZ©‡bi d‡j Gi †Kvb cwieZ©b n‡e bv| mn‡R GKKwU c‚biærcv`b Kiv hv‡e| 1960 mv‡j
GK‡Ki AvšÍRv©wZK c×wZ Pvjyi mgq †gŠwjK GKK ¸‡jvi †h Av`k© ev ÷¨vÛvW© MÖnY Kiv n‡qwQj cieZ©xKv‡j
Dchy³ ‰ewk󨸇jv AR©‡bi j‡ÿ¨ G‡`i g‡a¨ A‡bK GK‡Ki Av`k© e`j Kiv n‡q‡Q wKš‘ Zv‡Z GKK¸‡jvi
gv‡bi †Kvbiƒc cwieZ©b nqwb| †hgb 1900 mv‡j UªwcK¨vj erm‡ii Dci wfwË K‡i mg‡qi GKK †m‡KÛ Gi
msÁv cÖ vb Kiv n‡qwQj| cieZx©‡Z wmwRqvg cigvYyi cvigvYweK cwie„wËi Dci wfwË K‡i †m‡K‡Ûi msÁv
cÖYqb Kiv n‡q‡Q| AvšÍRv©wZK c×wZ‡Z †gŠwjK GKK¸‡jvi Rb¨ me©‡kl M„nxZ Av`k© wb‡gœ eY©bv Kiv nj|
c`v_©weÁvb
BDwbU 1 c„ôv 9
ˆ`‡N© i GKK t wgUvi
evqyk~b¨ ¯’v‡b Av‡jv
458,792,2991
†m‡K‡Û †h `~iZ¡ AwZµg K‡i, †m `~i †K 1 wgUvi (m) ejv nq|
f‡ii GKK t wK‡jvMÖvg
dªv‡Ýi m¨v‡å‡Z B›Uvib¨vkbvj ey¨‡iv Ae I‡qU&m GÛ †gRvim& G msiwÿZ cøvwUbvg BwiwWqvg msKi avZzi ˆZwi
GKwU wmwjÛv‡ii fi‡K 1 wK‡jvMÖvg (kg) e‡j| GB wmwjÛviwUi D”PZv I e¨vm Df‡qB 3.9 cm|
mg‡qi GKK t †m‡KÛ
GKwU wmwRqvg cigvbyi ( Cs133) 9,192,631,770 wU ¯ú›`b m¤úbœ Ki‡Z †h mg‡qi cÖ‡qvRb nq Zv‡K 1 †m‡KÛ
(s) e‡j|
ZvcgvÎvi GKK t †Kjwfb
cvwbi ˆÎa we›`yi (triple point) ZvcgvÎvi
16.2731
fvM‡K 1 †Kjwfb (K) e‡j|
Zwor cÖev‡ni GKK : A¨vw¤úqvi t
k~b¨ gva¨‡g 1m `~i‡Z¡ Aew¯’Z Amxg ˆ`‡N© i Ges D‡cÿbxq cÖ ’‡”Q‡`i `ywU mgvšÍivj mij cwievnxi cÖ‡Z¨KwU‡Z
†h cwigvY ZworcÖevn Pj‡j ci¯ú‡ii g‡a¨ cÖwZ wgUvi ˆ`‡N© 2×10-7 N wbDUb ej Drcbœ nq Zv‡K 1 ampere
e‡j|
`xcb ZxeªZvi GKK t K¨v‡Ûjv
K¨v‡Ûjv n‡”Q †mB cwigvY `xcb ZxeªZv hv †Kv‡bv Av‡jvK Drm GKwU wbw`©ó w`‡K 540×1012 nvR© K¤úv‡¼i GK
eYx© wewKiY wbtmiY K‡i Ges H wbw`©ó w`‡K Zvi wewKiY ZxeªZv n‡”Q cÖwZ †÷‡ivwWqvb Nb‡Kv‡Y
1863 IqvU|
c`v‡_©i cwigv‡Yi GKK t †gvj
†h cwigvb c`v‡_© 0.012 wK‡jvMÖvg Kve©b-12 G Aew¯’Z cigvYyi mgvb msL¨K cÖv_wgK BDwbU (†hgb cigvYy,
AYy, Avqb, B‡jKUªb BZ¨vw` ev G¸‡jvi wbw`©ó †Kv‡bv MÖæc) _v‡K Zv‡K 1 †gvj e‡j|
mviwY: 3.1 : †gŠwjK ivwk I Zv‡`i GKK
µwgK bs ivwk ivwki cÖZxK Gm. AvB GKK GK‡Ki cÖZxK
1. ‰`N¨© (length) l wgUvi (meter) m
2. fi (mass) m wK‡jvMÖvg
(kilogram) kg
3. mgq (time) t ‡m‡KÛ(second) s 4. ZvcgvÎv (temperature) ,T ‡Kjwfb (kelvin) K
5. Zwor cÖevn (electrict current)
I A¨vw¤úqvi (ampere)
A
6. `xcbZxeªZv (luminious intensity)
Iv K¨v‡Ûjv
(candela) Cd
7. c`v‡_©i cwigvY (amount of substance)
n ‡gvj (mole)
mol
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 10
GK‡Ki ¸wYZK I Dc¸wYZK :
A‡bK mgq e¨envi I eySvi myweav‡_© †gŠwjK GKK¸‡jvi ¸wYZK I Dc¸wYZK e¨eüZ nq| weÁvbxiv Ggb
A‡bK ivwk e¨envi K‡i _v‡Kb †h¸‡jvi gvb Lye †QvU ev eo n‡q _v‡K| †hgb Av‡jvi `ªæwZ cÖvq 30,00,00,000 ms-1
| GB RvZxq ivwki msL¨v ¯vfvweKfv‡eB cov, †jLv, eySv Ges g‡b ivLv LyeB AmyweavRbK| Gme mgm¨v
mgvav‡bi Rb¨ 10 msL¨vwUi NvZ (power) e¨envi Kiv| Zvn‡j Av‡jvi `ªæwZ‡K †jLv hvq 3108ms-1| Avevi aiv
hvK `ywU KYvi ga¨Kvi `~iZ¡ 0.0000000001 m| wKš‘ GB msL¨vwU‡K hw` GKwU DcmM© e¨envi K‡i wjwL Zvn‡j
msL¨vwU n‡e 0.110-9m ev 0.1 nm|
mviYx : 3.2 : `‡ki m~PK mg~n
DcmM© Drcv`K ms‡KZ D`vniY
G·v (exa) 1018 E 1 G·v wgUvi =1 Em =1018m
‡cUv (peta) 1015 P 1 ‡cUv wgUvi =1 Pm =1015m
†Uiv (tera) 1012 T 1 †Uiv MÖvg =1 Tg =1012g
wMMv (giga) 109 G 1 wMMv Ryj =1 GJ =109J †gMv (mega) 106 M 1 †gMv IqvU =1 MW =106W
wK‡jv (kilo) 103 k 1 wK‡jv‡fvë =1 kV =103V
†n‡±v (hecto) 102 h 1 †n‡±v c¨vm‡Kj =1 hPa =102Pa ‡WKv (deca) 101 da 1 ‡WKv wbDUb =1 daN =101N
†Wwm (deci) 10-1 d 1 †Wwm Ing =1 d =10-1
†mw›U (centi) 10-2 c 1 †mw›UwgUvi =1 cm =10-2m
wgwj (milli) 10-3 m 1 wgwj A¨vw¤úqvi =1 mA =10-3A
gvB‡µv (micro) 10-6 1 gvB‡µv †fvë =1 V =10-6V
b¨v‡bv (nano) 10-9 n 1 b¨v‡bv †m‡KÛ =1 ns =10-9s wc‡Kv (pico) 10-12 p 1 wc‡Kv d¨vivW =1 pF =10-12F
†dg‡Uv (femto) 10-15 f 1 †dg‡Uv wgUvi = 1 fm =10-15m
A‡Uv (atto) 10-18 a 1 A‡Uv IqvU = 1 aW =10-18W
†Kv‡bv msL¨v‡K 10 Gi †h †Kvb NvZ Ges 1 †_‡K 10 Gi g‡a¨ Aew¯’Z Aci msL¨vi ¸Ydj wn‡m‡e cÖKvk Kiv
n‡j Zv‡K ˆeÁvwbK cÖZxK e‡j| †hgb,5800000 nj 5.8×106 Ges 0.0000000956 nj 9.56×10-8| Zvn‡j
cÖZxqgvb n‡”Q †h, G cÖZx‡K cÖKvwkZ msL¨vwUi 10 Gi abvZœK m~PK hZ, `kwgK we›`y‡K Wvb w`‡K ZZ Ni
miv‡j g~j msL¨vwU cvIqv hv‡e| AbyiƒcfA‡e 10 Gi FYvZœK m~PK hZ, `kwgK we›`y‡K evg w`‡K ZZ Ni miv‡j
g~j msL¨vwU cvIqv hv‡e|
ˆeÁvwbK cÖZx‡K cÖKvwkZ msL¨vi †ÿ‡Î ¸‡Yi wb‡gœv³ mvaviY wbqgwU cÖ‡hvR¨:
10m×10n=10m+n
GLv‡b m Ges n †h †Kvb msL¨v, hv abvZœK ev FYvZœK n‡Z cv‡i|
†hgb, 105×109 = 1014, 103×10-7 = 10-4
fv‡Mi †ÿ‡ÎI wbqgwU cÖ‡hvR¨ :
10m ÷10n=10m-n, 108÷105 = 108-5=103, 108÷10-12 = 108-(-12) = 1020
c`v_©weÁvb
BDwbU 1 c„ôv 11
‰eÁvwbK cÖZxK I ms‡KZt
c`v_©weÁvb‡K cÖKvk Kivi Rb¨ cÖ‡qvRb nq MwY‡Zi| MvwYwZK mgxKi‡Yi mvnv‡h¨ c`v_©weÁv‡bi m~θ‡jv‡K
Avgiv cÖKvk K‡i _vwK| c`v_©weÁvbxiv wewfbœ mgm¨v mgvav‡bi Rb¨ c`v_©weÁv‡bi m~Î ev mgxKiY¸‡jv e¨envi
K‡ib| GB m~Î ev mgxKiY ¸‡jv‡K cÖKvk Kivi Rb¨ wewfbœ ivwk Ges GKK e¨envi Kiv nq| Avevi ivwk ev
GKK¸‡jv‡K mswÿßiƒ‡c cÖKv‡ki Rb¨ wewfbœ ms‡KZ Ges cÖZxK e¨envi Kiv nq Ges Gi Rb¨ GK‡Ki
AvšÍRv©wZK c×wZ AbymiY Kiv n‡q _v‡K| ïay c`v_©weÁv‡bB bq, Ávb weÁv‡bi †h‡Kv‡bv kvLvq cwigvc Ki‡Z
n‡j AvRKvj GK‡Ki AvšÍRv©wZK ixwZ AbymiY Kiv nq|
GB eB‡qi GK‡Ki ms‡KZ I wewfbœ ivwki gvb cÖKvk Kivi Rb¨ wb‡¤œv³ c×wZ¸‡jv AbymiY Kiv n‡q‡Q-
1| †K‡bv ivwki gvb cÖKvk Kivi Rb¨ GKwU msL¨v wj‡L Zvici GKwU dvuK (space) †i‡L GK‡Ki ms‡KZ wjL‡Z
nq| †hgb '6.1 N', '5.5103 cm', '30 sec'| GKBfv‡e kZKiv wPý (%) I cÖKvk Kiv nq| wKš‘ wKQz wKQz †ÿ‡Î
e¨wZµg cwijwÿZ nq| †hgb †Kv‡bi GKK wWMÖx (0), wgwbU () ev †m‡KÛ ()| GB mKj †ÿ‡Î msL¨v †jLvi ci
†Kv‡bv dvuK (space) _v‡K bv| †hgb, 300
|
2| ¸Y‡b cÖvß jä GKK †jLvi mgq `yB GK‡Ki gvSLv‡b GKwU dvuK (space) w`‡Z nq| †hgb, J s
3| fvM Øviv MwVZ jä GKK‡K FYvZœK m~PK wn‡m‡e cÖKvk Kiv nq| †hgb,
wgUvi
‡m‡KÛ
= wgUvi/†m‡KÛ (m/s)
(meter per second) ev ms-1
4| †h‡nZz cÖZxK¸‡jv MvwYwZK cÖKvk, †K‡bv wKQzi mswÿß iƒc bq| ZvB G¸‡jvi †k‡l †Kvb hwZ wPý ev dzj
÷c (.) e¨eüZ nq bv|
5| GK‡Ki ms‡KZ †mvRv Aÿ‡i wjL‡Z nq| †hgb wgUv‡ii (meter) Rb¨ m, †m‡K‡Ûi (second) Rb¨ s, BZ¨vw`| Avevi †Kv‡bv ivwki ms‡KZ wjL‡Z nq evuKv (Italic) ni‡d †hgb, f‡ii (mass) Rb¨ m, miY‡K
(displacement) cÖKvk Ki‡Z nq s BZ¨vw`| GB mKj ivwki ms‡KZ I GK‡Ki d›U welqe¯‘i d‡›Ui (font) Gi
Dci wbf©i K‡i bv|
6| GK‡Ki ms‡KZ †QvU nv‡Zi ni‡d †jLv nq| †hgb, m, s, mol| Z‡e †hme GKK e¨w³i bvg ‡_‡K †bIqv
n‡q‡Q †m‡ÿ‡Î ms‡KZ †jLvi mgq (GK Aÿi n‡j) eo nv‡Zi ni‡d ev cÖ_g Aÿi (GKvwaK Aÿ‡ii n‡j) eo
nv‡Zi ni‡d n‡e| †hgb, Ry‡ji bvgvbymv‡i GKK Ryj †jLv nq J| Avevi weÁvbx c¨v¯‹v‡ji bvgvbymv‡i c¨v‡¯‹j
†jLv nq Pa| Z‡e cy‡iv bvg †jLvi mgq Aek¨B †QvU nv‡Zi ni‡d †jLv nq newton ev joule|
7| GK‡Ki ms‡KZ KL‡bv eûeP‡b cÖKvk Kiv nq bv| †hgb, 220 volt †K KL‡bv 220 volts †jLv nq bv|
8| †Kv‡bv msL¨v ev †hŠwMK GKK ev msL¨v I GKK `yB jvB‡b (line break) †jLv DwPZ bq| hw` Lye †ekx
cÖ‡qvRb nq Zvn‡j msL¨v I GKK yBfvM K‡i †jLv †h‡Z cv‡i|
9| GKvwaK DcmM© GKmv‡_ e¨envi Kiv hvq bv| †hgb, mmV †jLv hvq bv, V wjL‡Z nq| mvi ms‡ÿc t
GKK: GK‡Ki AvšÍRv©wZK c×wZ‡K ms‡ÿ‡c Gm AvB (SI) BDwbU ejv nq|
†gŠwjK ivwki GKK mg~n ¯’vb, Kvj, cvÎ †Kv‡bv wKQzi Dci wbf©i K‡i bv|
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 12
cv‡VvËi g~j¨vqb-3
mwVK Dˇii cv‡k wUK () wPý w`b
1. `xcb ZxeªZvi GKK †KvbwU?
K) A¨vw¤úqvi L) †gvj M) K¨v‡Ûjv N) wbDUb
2. wb‡gœi Z_¨¸‡jv jÿ¨ Kiæb|
i) 1 wgwjMÖvg = 10-3 MÖvg
ii) [F] = MLT-2
iii) am
an = a m-n
wb‡Pi †KvbwU mwVK?
K) i I ii L) ii I iii M) i I iii N) i, ii I iii
cvV- 4: cwigv‡ci hš¿cvwZ : ˆ`‡N© i cwigvc
D‡Ïk¨
GB cvV †k‡l Avcwb-
wgUvi †¯‹j I fvwY©qvi †¯‹‡ji MVb eY©bv Ki‡Z cvi‡eb Ges G‡`i mvnv‡h¨ †K‡bv e¯‘i ˆ`N¨© cwigv‡ci
c×wZ e¨vL¨v Ki‡Z cvi‡eb|
¯øvBW K¨vwjcv‡m©i MVb eY©bv Ki‡Z cvi‡eb Ges G‡`i mvnv‡h¨ †K‡bv e¯‘i ˆ`N¨© cwigv‡ci c×wZ e¨vL¨v
Ki‡Z cvi‡eb|
¯Œz M‡Ri MVb eY©bv Ki‡Z cvi‡eb Ges Gi mvnv‡h¨ †K‡bv e¯‘i ÿz`ª ˆ`N¨© cwigv‡ci c×wZ e¨vL¨v Ki‡Z
cvi‡eb|
cwigv‡ci hš¿vw` :
Avgiv cwigv‡ci Rb¨ wewfbœ cÖKvi hš¿ e¨envi K‡i _vwK| wewfbœ e¨envwiK Kv‡R AwZ ¶z`ª n‡Z Avi¤¢
K‡i e„nr `~iZ¡ cwigvc Ki‡Z nq| ZvB G †ÿ‡Î wbfz©jZv AR©‡bi Rb¨ cÖavbZ Gme h‡š¿i e¨envi n‡q _v‡K |
ˆeÁvwbK cwigv‡ci †ÿ‡Î †hme hš¿vw` mPivPi e¨envi Kiv nq, Zv‡`i g‡a¨ K‡qKwU hš¿ m¤‡Ü wb‡gœ Av‡jvPbv
Kiv nj|
K) wgUvi †¯‹j; L) fvwb©qvi †¯‹j; M) ¯øvBW K¨vwjcvm©; N) ¯Œ MR; O) Zzjv hš¿; P) _vgv Nwo
K) wgUvi †¯‹j :
‰`N© cwigv‡ci Rb¨ cixÿvMv‡i mvaviYZ †h mKj hš¿ e¨envi Kiv nq Zvi g‡a¨ me‡P‡q eo hš¿ n‡jv wgUvi
†¯‹j| †¯‹jwUi ˆ`N¨© mvaviYZ 1 wgUvi ev 100 †mw›UwgUvi _v‡K e‡j G‡K wgUvi †¯‹j ejv nq| †¯‹jwUi GK avi
†mw›UwgUv‡i Ges Aci avi Bw‡Z `vM KvUv _v‡K| cÖ‡Z¨K †mw›UwgUvi Ges cÖ‡Z¨K Bw mgvb `k fv‡M fvM Kiv
_v‡K| cÖ‡Z¨K †mw›UwgUv‡ii cÖ‡Z¨KwU fvM‡K 1 wgwjwgUvi ev 0.1 †mw›UwgUvi ejv nq| †Kv‡bv †Kv‡bv †¯‹‡j
cÖ‡Z¨K Bw‡K AvU fvM ev †lvj fv‡M wef³ Kiv nq|
c`v_©weÁvb
BDwbU 1 c„ôv 13
cwigvc c×wZ :
wgUvi †¯‹‡ji mvnv‡h¨ †Kv‡bv mij e¯‘i ˆ`N¨© AwZ mn‡RB cwigvc Kiv hvq| †h `Û ev KvwVi ˆ`N¨© gvc‡Z n‡e
Zvi GK cÖvšÍ wgUvi †¯‹‡ji k~b¨ (0) `v‡M ev Ab¨ †Kv‡bv myweavRbK ¯’v‡b ¯’vcb Ki‡Z n‡e| `‡Ûi Aci cÖvšÍ
†¯‹‡ji †h `v‡Mi mv‡_ wg‡j hv‡e Zvi cvV wb‡Z n‡e| AZ:ci `‡Ûi `ywU cÖvšÍ cv‡Vi cv_©K¨ n‡jv `‡Ûi ˆ`N¨©|
mvaviYfv‡e ejv hvq, †h `‡Ûi ˆ`N¨© gvc‡Z n‡e Zvi GK cÖvšÍ hw` X `v‡M ¯’vcb Kiv nq Ges `‡Ûi Aci cÖvšÍ
Y `v‡Mi mv‡_ wg‡j hvq Zvn‡j `‡Ûi ˆ`N¨© L n‡e X I Y Gi we‡qvMdj| A_©vr L= Y- X | GB †¯‹‡ji mvnv‡h¨
wgwjwgUvi ch©šÍ ˆ`N© mwVKfv‡e cwigvc Kiv hvq| hw` Gi †P‡q m~² cwigvc Ki‡Z nq, Zvn‡j fvwb©qvi †¯‹j
e¨envi Kiv nq|
L) fvwb©qvi †¯‹j :
wgUvi †¯‹‡j Avgiv mvaviYZ wgwjwgUvi ch©šÍ ˆ`N¨© gvc‡Z cvwi| wgwjwgUv‡ii fMœvsk †hgb, 0.2 wgwg, 0.5 wgwg ev
0.9 wgwg BZ¨vw` gvcvi Rb¨ Avgv‡`i fvwb©qvi †¯‹j e¨envi Ki‡Z nq| divmx MwYZ kv¯¿¿we` wc‡q‡i fvwb©qvi GB
†¯‹j D™¢veb K‡ib| GRb¨ Zvui bvgvbymv‡i G †¯‹‡ji bvgKiY Kiv nq fvwb©qvi †¯‹j|
g~j ‡¯‹‡ji ÿy`ªZg fv‡Mi fMœvs‡ki gvb wbLyuZfv‡e wbY©q Kivi Rb¨ g~j †¯‹‡ji cv‡k †QvU Avi GKwU †¯‹j
e¨envi Kiv nq| †mB †QvU †¯‹jwUi bvg fvwb©qvi †¯‹j| wgUvi †¯‹‡ji mv‡_ fvwb©qvi †¯‹j mshy³ K‡i wgwjwgUv‡ii
fMœvsk wbfz©jfv‡e wbY©q Kiv hvq|
wPÎ: 1.1 fvwb©qvi ‡¯‹j
fvwb©qvi †¯‹j AvKv‡i g~j †¯‹j A‡cÿv †QvU nq| GB †¯‹jwU g~j †¯‹j ev cªavb †¯‹‡ji cv‡k mshy³ _v‡K,
fvwb©qvi †¯‹j‡K cÖavb †¯‹‡ji cvk w`‡q mvg‡b ev †cQ‡b miv‡bv hvq| aiv hvK, GKwU fvwb©qvi †¯‹‡j `kwU fvM
Av‡Q| fvwb©qvi †¯‹‡ji `k fvM cÖavb †¯‹‡ji bqwU ¶z`ªZg fv‡Mi mgvb| cÖavb †¯‹‡ji bqwU ¶z`ªZg fv‡Mi gvb 9
wgwjwgUvi ev 0.9 †mw›UwgUvi| †h‡nZz fvwb©qvi †¯‹‡ji 10 fvM cÖavb †¯‹‡ji 9 ¶z`ªZg fv‡Mi mgvb †m‡nZz
fvwb©qvi †¯‹‡ji fvM¸‡jv cÖavb †¯‹‡ji ÿy`ªZg fv‡Mi †P‡q mvgvb¨ †QvU| cÖavb †¯‹‡ji GK fv‡Mi ‰`N¨© Ges
fvwb©qvi †¯‹‡ji GK fv‡Mi ˆ`‡N© i cv_©K¨‡K fvwb©qvi aªæeK (Vernier constant) V.C ejv nq|
wb‡gœi m~‡Îi mvnv‡h¨ fvwb©qvi aªæeK wbY©q Kiv hvq|
fvwb©qvi aªæeK =
ns
†hLv‡b, s nj cÖavb †¯‹‡ji GK ¶z`ªZg fv‡Mi ˆ`N¨© Ges n nj fvwb©qv‡ii fv‡Mi msL¨v|
Zvn‡j, s = 1 wgwg Ges n = 10 fvM
fvwb©qvi aªæeK, V.C =
ns
=
1 wgwg
10 = 0.1 wgwg = 0.01 †mwg
†Kv‡bv †Kv‡bv mgq fvwb©qvi †¯‹‡ji 20 fvM cÖavb †¯‹‡ji 19 ¶z`ªªZg fv‡Mi mgvb _v‡K Ges cÖavb †¯‹‡ji GK
¶z`ªZg fv‡Mi gvb 1 wgwg Gi †P‡q Kg nq| ZLb fvwb©qvi aªæeK cwieZ©b n‡q hvq| g~jZ: fvwb©qvi aªæe‡Ki gvb
wbf©i K‡i cÖavb †¯‹j I fvwb©qvi †¯‹‡ji `vM KvUvi Dci|
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 14
M) ¯øvBW K¨vwjcvm© :
fvwb©qv‡ii cwigvc c×wZ Aej¤b K‡i ¯øvBW K¨vwjcvm© ˆZwi Kiv nq e‡j G‡K fvwb©qvi K¨vwjcvm©I ejv nq|
¯øvBW K¨vwjcv‡m©i g~j ev cÖavb †¯‹j mvaviYZ B¯úvZ Øviv wbg©vY Kiv nq| hvi GK cv‡k¦© Bw I Aci cv‡k¦©
†mw›UwgUvi Ges wgwjwgUv‡i `vM KvUv _v‡K| cÖavb †¯‹‡ji †h cªvšÍ †_‡K †¯‹‡ji m~Pbv nq A_©vr k~b¨ `vM KvUv
_v‡K †m cÖvšÍwU avZe †Pvqvj hy³ _v‡K (wPÎ 1.2)| †Pvqvjhy³ GKwU fvwb©qvi †¯‹j cÖavb †¯‹‡ji mv‡_ mgvšÍivj
fv‡e Ae¯’vb K‡i| GB †Pvqvjhy³ fvwb©qvi †¯‹jwU cªavb †¯‹‡ji Dci mvg‡b ev wcQ‡b miv‡bv hvq| GB †¯‹‡ji
mv‡_ GKwU ¯Œz mshy³ _v‡K|
wPÎ: 1.2 øvBW K¨vwjcvm©
GB ¯Œzi mvnv‡h¨ fvwb©qvi †¯‹j‡K cÖavb †¯‹‡ji mv‡_ †h‡Kv‡bv RvqMvq AvUKv‡bv hvq| g~j †¯‹‡ji †Pvqvj Ges
fvwb©qvi †¯‹‡ji †Pvqvj c¯ú‡ii mv‡_ †j‡M _v‡K, ZLb mvaviYZ fvwb©qvi †¯‹‡ji k~b¨ `vM cÖavb †¯‹‡ji k~b¨
`v‡Mi mv‡_ wg‡j hvq| Avevi A‡bK h‡š¿ wg‡j bv|
¯øvBW K¨vwjcv‡m©i mvnv‡h¨ cwigvc :
aiv hvK, XY `‡Ûi ˆ`N¨© cwigvc Ki‡Z n‡e| `ÛwUi X cÖvšÍ cÖavb †¯‹‡ji k~b¨ (0) `v‡Mi mv‡_ wgwj‡q fvwb©qvi
†¯‹jwU mvg‡b ev wcQ‡b mwi‡q Y cÖv‡šÍi mv‡_ wgjv‡bv nq| g‡b Kiv hvK, `‡Ûi Y cÖvšÍ †¯‹‡ji M wgwg `vM
AwZµg K‡i‡Q| Zvn‡j, Gi ˆ`N¨© M I (M+1) wgwg Gi gvSvgvwS n‡e| G M wgwg Gi †P‡q evowZ ˆ`N¨© †ei
Ki‡Z fvwb©qvi ‡¯‹j e¨envi Ki‡Z nq Ges Gi ˆ`N¨© UzKz n‡e fvwb©qvi †¯‹j cvV|
AZ:ci fvwb©qv‡ii †Kvb `vMwU cÖavb †¯‹‡ji †Kvb `v‡Mi mv‡_ wgj‡Q Zv ch©‡eÿY Ki‡Z n‡e| hw` †Kv‡bv `vM
bv wg‡j Zvn‡j fvwb©qv‡ii †Kvb `vMwU cÖavb †¯‹‡ji †Kv‡bv GKwU `v‡Mi me‡P‡q KvQvKvwQ n‡q‡Q Zv †`L‡Z
n‡e| fvwb©qvi †¯‹‡ji GB `vMB n‡e fvwb©qvi mgcvZb|
aiv hvK, fvwb©qv‡ii V b¤i `vMwU cÖavb †¯‹‡ji †h‡Kv‡bv GKwU `v‡Mi mv‡_ wg‡j‡Q ev KvQvKvwQ n‡q‡Q| hw`
h‡š¿i fvwb©qvi aªyeK V.C nq , Zvn‡j
`‡Ûi ˆ`N¨© = cÖavb †¯‹j cvV + fvwb©qvi †¯‹j cvV
=cÖavb †¯‹j cvV + fvwb©qvi mgcvZb × fvwb©qvi aªæeK
A_©vr, L = M+ V× V. C
c`v_©weÁvb
BDwbU 1 c„ôv 15
D`vniYt
g‡b Kiv hvK, `‡Ûi Y cÖvšÍ cÖavb †¯‹‡ji 15 wgwg `vM AwZµg K‡i‡Q Ges cÖavb †¯‹‡ji GKwU `v‡Mi mv‡_
fvwb©qv‡ii 5 b¤i `vMwU wg‡j‡Q|
Zvn‡j `‡Ûi ˆ`N¨© n‡e,
L = 15 wgwg + 5×0.1 wgwg [ fvwb©qvi aªæeK=0.1 wgwg] = 15 wgwg + 0.5 wgwg
=15.5 wgwg
=1.55 †mwg
cÖavb †¯‹‡ji †Pvqvj Ges fvwb©qvi †¯‹‡ji †Pvqvj hLb †j‡M _v‡K ZLb mvaviYZ fvwb©qvi †¯‹‡ji k~b¨ `vM cÖavb
†¯‹‡ji k~b¨ `v‡Mi mv‡_ wg‡j hvq| Avi hw` bv wg‡j ZLb ey‡S wb‡Z n‡e hš¿wU‡Z hvwš¿K ÎæwU Av‡Q| ZvB GB
ÎæwUi Rb¨ cvV ms‡kva‡bi cÖ‡qvRb Av‡Q|
N) ¯yŒ MR :
¯Œy MR‡K gvB‡µvwgUvi ¯Œz MRI ejv nq| GwU B¯úvZ Øviv wbwg©Z nq| GB h‡š¿i mvnv‡h¨ ¶z`ª e¯‘i ˆ`N¨©, miæ
Zv‡ii e¨vm, miæ †Pv‡Oi e¨vmva© BZ¨vw` cwigvc Kiv hvq| GB h‡š¿ U AvK…wZi GKwU KvVv‡gv _v‡K (wPÎ 1.3)|
GB U AvK…wZ wewkó KvVv‡gvi `yB evûi cÖv‡šÍ `ywU bj mshy³ _v‡K| GKwU b‡ji ga¨ w`‡q KxjK ev `Û A
¯’vqxfv‡e AvUKv‡bv _v‡K Ges Aci evû‡Z i‡q‡Q GKwU duvcv bj C, hvi ga¨ w`‡q GKwU `Û B mshy³ _v‡K hv
mvg‡b †cQ‡b miv‡bv hvq| C b‡j wgwjwgUv‡i `vMvw¼Z GKwU ˆiwLK †¯‹j _v‡K| C b‡ji evB‡ii Ask Aci
GKwU dvucv bj Øviv †ewóZ _v‡K hvi ewn:cÖv‡šÍ GKwU †ejbvK…wZi Uzwc T _v‡K| T Gi wKbvi‡K mvaviYZ 50 ev
100 fvM Kiv nq| hLb B ¯’vqx KxjK ev mgZj cÖvšÍ wewkó `Û A †K ¯úk© K‡i ZLb e„ËvKvi †¯‹j k~b¨ `vM I
ˆiwLK †¯‹‡ji k~b¨ `vM wg‡j hvq| hw` `ywU †¯‹‡ji k~b¨ `vM wg‡j bv hvq Zvn‡j eyS‡Z n‡e hš¿wU‡Z hvwš¿K ÎæwU
i‡q‡Q|
wPÎ : 1.3 ¯Œz MR
Uywc T GKevi Nyiv‡j hZUzKz miY N‡U Ges ˆiwLK †¯‹j eive‡i †h ˆ`N© AwZµg K‡i Zv‡K ¯Œzi wcP (pitch) ejv
nq| e„ËvKvi †¯‹‡ji gvÎ GKfvM Nyiv‡j, Gi cÖvšÍ hZUzKz m‡i Av‡m Zv‡K h‡š¿i jwNó MYb (Least count) L.C ejv nq| ®úóZ: h‡š¿i wcP‡K e„ËvKvi †¯‹‡ji †gvU fvM msL¨v w`‡q fvM Ki‡j h‡š¿i jwNô MYb cvIqv hvq|
myZivs
jwNô MYb =
wcP
e„ËvKvi †¯‹‡ji fv‡Mi msL¨v
mvaviYZ e„ËvKvi †¯‹‡j 100 fvM _v‡K Ges GB h‡š¿ wcP _v‡K 1 mm
jwNô MYb, L.C =
1 mm 100
=0.01 mm
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 16
e¨envi c×wZ :
†h Zv‡ii e¨vm cwigvc Ki‡Z n‡e ev †h cv‡Zi cyiæZ¡ wbY©q Ki‡Z n‡e †m e¯‘‡K A I B [wPÎ : 1.3] Gi gv‡S
¯’vcb Ki‡Z n‡e| Zvi ev cvZwU A I B Gi gvSLv‡b Ggb fv‡e ¯’vcb Ki‡Z n‡e hv‡Z Gi GK cvk A †K Ges
Aci cvk B †K ¯úk© K‡i| Gevi T Gi mvnv‡h¨ `„pfv‡e e¯‘wU‡K AvUKv‡Z n‡e| GLb e„ËKvi Ges ˆiwLK †¯‹j
cvV wb‡Z n‡e| aiv hvK, ‰iwLK †¯‹j cvV L wgwg Ges e„ËvKvi †¯‹‡ji fvM msL¨v C| myZivs Zv‡ii e¨vm ev
cyiæZ¡ n‡e,
e¨vm ev cyiæZ¡= ‰iwLK †¯‹j cvV + e„ËvKvi †¯‹‡ji fvM msL¨v×jwNô MYb
= L wgwg + C × L. C = L wgwg + C×0.01 wgwg
= (L + 0.01C) wgwg
D`vnib ¯iƒc, ˆiwLK †¯‹‡ji cvV 3 wgwg Ges e„ËvKvi †¯‹‡ji fvM msL¨v 25, Zvn‡j
Zv‡ii e¨vm = 3 wgwg + 25×0.01 wgwg
= (3+0.25) wgwg
= 3.25 wgwg
¯Œz M‡Ri mvnv‡h¨ Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj wbY©q:
e„ËvKvi cÖ ’‡”Q` wewkó †Kv‡bv Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj hw` A nq, Zvn‡j
A = r2 = (2d
)2 =41d2
†hLv‡b, r =Zv‡ii e¨vmva©©
Ges d = Zv‡ii e¨vm
¯Œz M‡Ri mvnv‡h¨ Zv‡ii e¨vm wbY©q K‡i DcwiD³ m~Î e¨envi K‡i Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj cwigvc Kiv hvq|
mvi-ms‡ÿc:
wgUvi †¯‹‡ji ˆ`N© 1 wgUvi ev 100 †mw›UwgUvi|
wgwjwgUv‡ii †P‡q ÿz`ª ˆ`N© gvcvi Rb¨ fvwb©qvi †¯‹j e¨envi Kiv nq|
ÿz`ª e¯‘ †hgb miæ Zv‡ii e¨vm gvcvi Rb¨ ¯Œz MR e¨envi Kiv nq|
cv‡VvËi g~j¨vqb-4
mwVK Dˇii cv‡k wUK () wPý w`b
1. ¯øvBW K¨vwjcv‡m©i mvnv‡h¨-
i) †ej‡bi AvqZb wbY©q Kiv nq
ii) Zv‡ii e¨vm wbY©q Kiv nq
iii) dvucv b‡ji AšÍ:e¨vm wbY©q Kiv nq
wb‡Pi †KvbwU mwVK?
K) i L) i I ii M) ii I iii N) i I iii
c`v_©weÁvb
BDwbU 1 c„ôv 17
wb‡Pi Aby‡”Q`wU co–b Ges 2 I 3 bs cÖ‡kœi DËi w`b|
j¨ve‡iUix‡Z GKRb wkÿv_x© ¯ŒzM‡Ri mvnv‡h¨ GKwU miæ Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj †cj 45.3610-6 m2 2. Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj wbY©‡qi m~Î †KvbwU?
K) A = ( 2r
)2 m2 L) A = 2
2r m2
M) A = (2d
)2 m2 N) A = 2
2d m2
3. e¨eüZ Zv‡ii e¨vmva© KZ?
K) 3.2 cm L) 3.1416 cm
M) 3.8 cm N) 3.2 mm
cvV- 5 : cwigv‡ci hš¿cvwZ : fi I mg‡qi cwigvc
D‡Ïk¨
GB cvV †k‡l Avcwb-
Zzjv h‡š¿i MVb eY©bv Ki‡Z cvi‡eb Ges G‡`i mvnv‡h¨ †K‡bv e¯‘i fi cwigv‡ci c×wZ e¨vL¨v Ki‡Z
cvi‡eb|
_vgv Nwoi MVb eY©bv Ki‡Z cvi‡eb Ges Gi mvnv‡h¨ †K‡bv NUbvi mgq cwigv‡ci c×wZ e¨vL¨v Ki‡Z
cvi‡eb|
Zzjv hš¿ :
c`v_©weÁvb ev imvq‡b Lye Aí cwigvY wRwb‡mi fi m~²fv‡e gvcvi cÖ‡qvRb nq| ZLb mvaviY
wbw³i mvnv‡h¨ Zv cwigvc Kiv m¤¢e nq bv| e¯‘ ev c`v‡_©i fi hZ Kg n‡e, Zvi fi cwigv‡ci Rb¨ ZZ my²
wbw³i cÖ‡qvRb n‡e| GB iKg GKwU wbw³ nj Zzjv hš¿| c`v_©weÁvb ev imvq‡bi j¨ve‡iUix‡Z Lye Aí cwigvY
bgybvi fi cwigvc Ki‡Z GB hš¿ e¨eüZ nq| KviY j¨ve‡iUix‡Z †Kvb wRwb‡mi fi mwVKfv‡e cwigvc Ki‡Z bv
cvi‡j H cixÿ‡Yi djvdj fzj Avm‡Z cv‡i Ges cixÿ‡Yi D‡Ïk¨ mdj n‡Z cv‡i bv|
wPÎ : 1.4 Zzjv hš¿
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 18
MVb cÖYvjx:
wbw³i `yB cÖv‡šÍ mvaviY wbw³i gZ `ywU mgvb IR‡bi cvjøv ev ZzjvcvÎ (Scale pan) P1 I P2 _v‡K (wPÎ 1.4)|
GKwU avZe `Û ev weg AB Gi `yB cÖv‡šÍ `ywU Lvu‡Ri g‡a¨ Dëv‡bv Qzwii dv‡ji Dci `ywU mgvb IR‡bi †d«‡gi
mvnv‡h¨ cvjøv `ywU Szjv‡bv _v‡K| GKwU Qzwi AB we‡gi †K‡›`ª AvUwK‡q †`qv nq, hv wb‡Pi w`‡K gyL K‡i _v‡K|
AB wegwU‡K GKwU Dj¤ dvucv _vg P-Gi Dci ¯’vcb Kiv nq hv‡Z Kv‡Vi wfZ ev cvUvZb BB Gi gvSLv‡b
`„pfv‡e AvUKv‡bv _v‡K| GB cvUvZ‡bi mv‡_ wZbwU †j‡fwjs ¯Œz _v‡K| GB ¯Œz¸‡jvi mvnv‡h¨ hš¿wU‡K †j‡fwjs
Kiv nq| dvucv _vgwUi g‡a¨ GKwU wb‡iU avZe `Û _v‡K hv cvUvZ‡bi msjMœ nvZj H Nywi‡q DVv‡bv ev bvgv‡bv
hvq|
GKwU w·KvYvKvi A¨v‡MU cv_‡ii †gvUv w`K weg Gi wVK ga¨¯’‡j AvUwK‡q miæ aviwU _vgwUi wb‡iU `‡Ûi Dci
Aew¯’Z GKwU A¨v‡MU †cø‡Ui Dci emv‡bv nq| wb‡iU `ÛwU‡K Dc‡i Zzj‡j weg AB A¨v‡MU cv_‡ii miæ
w`KUv‡K dvjµv‡g K‡i `yj‡Z _v‡K|
Zzjv`‡Ûi ga¨¯’‡j GKwU j¤v m~P‡Ki (PO) PIov w`KUv AvUwK‡q w`‡q Gi wb‡Pi miæ cÖvšÍwU‡K GKwU †¯‹‡ji
Dci gy³ ivLv nq| hLb Zzjv`Û Abyf‚wgK Ae¯’vq _v‡K ZLb m~P‡Ki miæ cÖvšÍ †¯‹‡ji k~b¨(0) `v‡Mi Dci
_v‡K| Ijb`wo (PL) Ges cvUvZ‡bi wb‡Pi ¯Œz Gi mvnv‡h¨ `ÛwU‡K Abyf‚wgK Kiv nq| mgMÖ hš¿wU‡K GKwU
Kv‡Pi ev‡· ivLv nq|
Zzjvhš¿wU e¨envi Kivi mgq nvZj H Nywi‡q _vgwU‡K Dc‡i DVv‡bv nq| G‡Z AB wegwU Dc‡i D‡V Ges Qzwii
wKbvivi Dci gy³fv‡e `yj‡Z _v‡K| `‡Ûi mv‡_ cvjøv `ywUI Dc‡i wb‡P `yj‡Z _v‡K| nvZj H †K D‡ëv w`‡K
Nyiv‡j _vg wb‡P †b‡g hvq Ges weg AB I cvjøvi †`vjb †_‡g hvq|
hLb AB weg `yj‡Z _v‡K ZLb m~PK KvuUvwU wb‡Pi †¯‹‡ji Dci Wv‡b ev‡g `yj‡Z _v‡K| cvjøvq †Kvb wRwbm bv
_vK‡j m~PKwUi †`vj‡bi we¯Ívi k~b¨ `v‡Mi ycv‡k mgvb n‡e| Avi hw` †`vjb k~b¨ `v‡Mi ycv‡k mgvb bv nq
Zvn‡j AB we‡gi `ycv‡k mgšq ¯Œy (BS) Øviv Ggbfv‡e mgšq K‡i wb‡Z n‡e hv‡Z m~P‡Ki †`vjb ycv‡k mgvb
nq| Ijb †iLv PL Øviv _vg P Dj¤ nj wKÕbv Zv †`‡L wb‡Z n‡e|
†Kvb e¯‘ ev wRwb‡mi fi gvc‡Z n‡j e ‘wU‡K evgw`‡Ki cvjøvq †i‡L Wvbw`‡Ki cvjøvq ax‡i ax‡i GKUv GKUv
K‡i evULviv ivL‡Z nq hZÿb ch©šÍ bv m~PKwU k~b¨ `v‡Mi `ycv‡k mgvb †`vjb w`‡Z _v‡K| Gfv‡e Rvbv
evULvivi mvnv‡h¨ ARvbv e¯‘i fi Zzjvh‡š¿i mvnv‡h¨ wbY©q Kiv hvq|
_vgv Nwo :
ÿz`ª mg‡qi e¨eavb cwigvc Kivi Rb¨ _vgv Nwo (stopwatch) e¨envi Kiv nq| _vgv Nwo `yB cÖKvi| h_v:
wWwRUvj _vgv Nwo Ges GbvjM _vgv Nwo| wWwRUvj _vgv Nwo GbvjM _vgv Nwoi †P‡q wbf©yj cvV w`‡Z cv‡i|
GRb¨ wWwRUvj _vgvNwoi e¨envi †ekx n‡q _v‡K| †hLv‡b GKwU GbvjM _vgvNwo 0.1s ch©šÍ wbf©yj cvV w`‡Z
cv‡i †mLv‡b GKwU wWwRUvj _vgv Nwo 0.01s ch©šÍ mwVK cvV w`‡Z cv‡i| AvRKvj wWwRUvj Nwo Ges †gvevB‡j
_vgv Nwo _v‡K|
mgq cwigvc Kivi Rb¨ _vgv NwowU nvZ w`‡q Pvjy Ki‡Z nq, Avevi eÜI Ki‡Z nq| †h‡nZz KvRwU nvZ w`‡q
cwiPvjbv Ki‡Z nq, myZivs mgq e¨eav‡bi cv‡V wKQzUv ÎæwU P‡j Av‡m|
c`v_©weÁvb
BDwbU 1 c„ôv 19
cwigv‡c ÎæwU I wbfy©jZv :
cwigv‡ci mgq wewfbœ Kvi‡Y cwigv‡c ÎæwU †`Lv w`‡Z cv‡i| e¨eüZ hš¿cvwZi Ges cixÿK‡`i `ÿZvi Dci
cwigv‡ci wbf©yjZv wbf©i K‡i A_v©r cwigv‡c ÎæwUi cwigvY Kg n‡Z cv‡i| aiv hvK, GKwU wgUvi †¯‹j †bq nj|
†¯‹jwU‡Z †mw›UwgUvi I wgwjwgUv‡i `vM KvUv Av‡Q| GB wgUvi †¯‹jwUi mvnv‡h¨ GKwU eB‡qi ‰`N¨© gvcv n‡j
cwigvcwU wbfz©j a‡i †bqv †h‡Z cv‡i| Avevi GB †¯‹‡ji mvnv‡h¨ hw` †Kvb N‡ii ‰`N¨© gvcv nq Zvn‡j ÎæwUi
cwigvb e„w×i m¤¢vebv _v‡K| Kvib GB †ÿ‡Î †¯‹jwU cici K‡qKevi ewm‡q ˆ`N¨© gvc‡Z n‡e|
cwigv‡ci wbfz©jZv LyeB ¸iæZ¡c~Y©| ZvB me cixÿ‡Ki cixÿvi mgq mZK©Zv Aej¤b Kiv DwPZ|
†hgb, GKwU Zv‡ii ˆ`N¨© hw` nq 20cm Zvn‡j Zv‡ii ˆ`N© 20cm 0.1cm †jLv †h‡Z cv‡i| GLv‡b Øviv
eySv‡bv n‡q‡Q †h, Zv‡ii cÖK…Z ‰`N© 19.9cm Ges 20.1cm Gi g‡a¨ n‡e| myZivs 0.1cm n‡jv cwigv‡ci
AwbðqZv ev ÎæwU|
cwigv‡ci †ÿ‡Î mvaviYZ wZb ai‡Yi ÎæwU cwijwÿZ nq| G¸‡jv n‡jv
K) ˆ`e ÎæwU
L) hvwš¿K ÎæwU
M) e¨w³MZ ÎæwU
K) ˆ`e ÎæwUt aªæe ivwki gvb me mgq wbw`©ó| †Kv‡bv aªæe ivwk‡K K‡qKevi cwigvc Ki‡j †h ÎæwUi Kvi‡Y
cwigvcK…Z gv‡bi AmvgÄm¨ †`Lv hvq, †mB ÎæwU‡K ˆ`e ÎæwU ejv nq| cwigvcK…Z gvb¸‡jv mwVK gv‡bi wKQzUv
Kg‡ekx cvIqv †h‡Z cv‡i Ges GKB hš¿ w`‡q GKB ivwki gvb evievi cwigvc K‡i Mo gvb wb‡j GB ÎæwUi gvb
k~b¨ nIqv DwPZ| †hgb iv¯Ívi ˆ`N¨© gvcvi Rb¨ wgUvi †¯‹j hZeviB emv‡bv nq ZZeviB ˆ`e ÎæwUi m¤¢vebv †_‡K
hvq| KviY †¯‹jwU GKevi ewm‡q DVv‡bvi mgq †¯‹‡ji m¤§yL wPwýZ Kivi Rb¨ †h `vM †`Iqv nq A‡bK mgq
mvg‡b ev wcQ‡b n‡q hvq| ˆ`e ÎæwUi d‡j P~ovšÍ djvdj AZ¨šÍ ‡ekx ev Kg cvIqv †h‡Z cv‡i| wKš‘ mZK©Zv
Aej¤b Ki‡j GB ÎæwUi cwigvY Kwg‡q Avbv m¤¢e|
L) hvwš¿K ÎæwUt c`v_©weÁv‡b wewfbœ cixÿv bxwiÿvi Rb¨ Avgv‡`i wewfbœ h‡š¿i e¨envi Ki‡Z nq| †mBme h‡š¿
hw` †Kvb ÎæwU _v‡K Zv‡K hvwš¿K ÎæwU ejv nq| †hgb cixÿvMv‡i ¯øvBW K¨vwjcvm© e¨envi K‡i _vwK| ¯øvBW
K¨vwjcv‡m© hw` cÖavb †¯‹‡ji k~b¨ `vM fvwY©qvi †¯‹‡ji k~b¨ `v‡Mi mv‡_ wg‡j bv hvq Zvn‡j a‡i wb‡Z n‡e GB
h‡š¿ hvwš¿K ÎæwU i‡q‡Q| ZvB cixÿY ïiæi Av‡M GwU fvjfv‡e †`‡L wb‡Z n‡e| hw` cy‡ivcywi wg‡j bv hvq Zvn‡j
ÎæwUi cwigvY wnmve K‡i wb‡Z n‡e|
M) e¨w³MZ ÎæwUt cixÿ‡Yi mgq Avgv‡`i wewfbœ cvV wb‡Z nq| GB mgq ch©‡eÿ‡Ki Kvi‡b cv‡V †h me ÎæwU
Av‡m Zv‡K e¨w³MZ ÎæwU ejv nq| †hgb- †`vj‡Ki †`vjbKvj wbY©‡qi mgq hw` †`vjb msL¨v wbY©q Ki‡Z fzj
nq Zvn‡j mwVK †`vjbKvj cvIqv hv‡e bv| GB mKj e¨w³MZ ÎæwU ~i Kivi mgq h_vm¤¢e mveavbZv Aej¤b
Kiv DwPZ|
mvi-ms‡ÿc:
Lye Aí cwigvY c`v‡_©i fi mylgfv‡e gvcvi Rb¨ cixÿvMv‡i Zzjv hš¿ e¨eüZ nq|
ÿz`ª mg‡qi e¨eavb cwigv‡ci Rb¨ _vgv Nwo e¨eüZ nq|
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 20
cv‡VvËi g~j¨vqb-5
mwVK Dˇii cv‡k wUK () wPý w`b
1. hw` ¯Œz M‡Ri e„ËvKvi †¯‹‡j 100 fvM Ges GB h‡š¿ wcP _v‡K 1 wgwg ZLb jwNô MYb KZ n‡e?
K) 0.1 wgwg L) 0.01 wgwg M) 0.001 wgwg N) 1 wgwg
2. N‡ii ˆ`N¨© cwigv‡ci mgq †Kvb ai‡bi ÎæwU nIqvi m¤¢vebv i‡q‡Q?
i) ‰`e ÎæwU
ii) hvwš¿K ÎæwU
iii) hvwš¿K ÎæwU I e¨w³MZ ÎæwU
wb‡Pi †KvbwU mwVK?
K) i I ii L) i M) i I iii N) i, ii I iii
cvV t 6
e¨envwiK -1: øvBW K¨vwjcv‡m©i mvnv‡h¨ AvqZvKvi e ‘i AvqZb wbY©q
D‡Ïk¨
GB cvV †k‡l Avcwb-
¯øvBW K¨vwjcv‡m©i mvnv‡h¨ GKwU AvqZvKvi e¯‘i †Kv‡bv c„‡ôi ˆ`N© , †Kv‡bv c„‡ôi †ÿÎdj I e¯‘i
AvqZb wbY©q Ki‡Z cvi‡eb|
e¨envwiK t 1: GKwU AvqZvKvi e ‘i GKwU c„‡ôi †ÿÎdj I e¯‘i AvqZb wbY©q|
D‡Ïk¨ t ¯øvBW K¨vwjcvm© e¨envi K‡i e¯‘i ˆ`N¨© wbY©q|
m~Î t †ÿÎdj n‡jv †Kv‡bv e¯‘i c„‡ôi cwigvY| Avi †Kv‡bv e¯‘ †h ¯’vb `Lj K‡i Zv‡K m‡B e¯‘i AvqZb e‡j|
†Kv‡bv AvqZvKvi e¯‘i †Kv‡bv c„‡ôi †ÿÎdj A Ges AvqZb V n‡j,
V = L A... ... ... ... ... ... ... ... ... (i)
Ges V = L B H ... ... ... ... ... ... ... ... ... (ii)
GLv‡b, L = e¯‘i ˆ`N©
B = e¯‘i cÖ ’
H = e¯‘i D”PZv
¯øvBW K¨vwjcv‡m©i mvnv‡h¨ †h †Kv‡bv ˆ`‡N© i cvV wbY©‡qi m~Î:
ˆ`N¨= cÖavb †¯‹j cvV (M) + fvwY©qvi mgcvZb (V ) fvwY©qvi aªæeK (VC )
A_v©r L ev B ev H = M + V VC
hš¿cvwZt ¯øvBW K¨vwjcvm©, AvqZvKvi e¯‘|
c`v_©weÁvb
BDwbU 1 c„ôv 21
Kv‡Ri aviv:
1| ¯øvBW K¨vwjcvm©wU wb‡q Gi cÖavb †¯‹‡ji ÿz`ªZg GK fv‡Mi gvb Ges fvwb©qvi †¯‹‡ji †gvU fvM msL¨v KZ Zv
jÿ¨ Kiæb| Gici hš¿wUi fvwb©qvi aªæeK wbY©q Kiæb|
2| Gevi AvqZvKvi e¯‘wU‡K ˆ`N© eivei ¯øvBW K¨vwjcv‡m©i g‡a¨ ¯’vcb Kivi ci †Pvqvj `ywU‡K `ycÖv‡šÍi mv‡_
¯úk© Kiæb| GB Ae¯’vq fvwb©qv‡ii k~b¨ `vM cÖavb †¯‹‡ji †h `vM AwZµg Ki‡e †mB `v‡Mi cvVB n‡jv cÖavb
†¯‹j cvV|
3| GB Ae¯’vq fvwb©qvi †¯‹‡ji †Kvb `vMwU cÖavb †¯‹‡ji †h‡Kv‡bv GKwU `v‡Mi mv‡_ wg‡j hvq Zv wbY©q Kiæb|
GwU n‡e fvwb©qvi mgcvZb|
4| Gfv‡e e¯‘wU‡K ˆ`N© eivei ewm‡q 2 I 3 bs cÖwµqvwU‡K cybive„wË K‡i cvV wbb Ges cÖvß gvb¸‡jv Q‡K
wjwce× Kiæb|
5| Gici e¯‘wU‡K cÖ ’ eivei ¯øvBW K¨vwjcv‡m©i †Pvqv‡ji g‡a¨ ¯’vcb K‡i 2 I 3 bs cÖwµqvi mvnv‡h¨ K‡qKevi
cvV wbb Ges Q‡K ¯’vcb Kiæb|
6| Avevi e¯‘wU‡K D”PZv eivei ¯øvBW K¨vwjcv‡m©i †Pvqv‡ji g‡a¨ ¯’vcb K‡i 2 I 3 bs cÖwµqv Abyhvqx
K‡qKevi cvV wbb Ges Q‡K ¯’vcb Kiæb|
7| Gici e¯‘wUi ˆ`N¨©, cÖ ’ I D”PZv wnmve K‡i gvb¸‡jv (i) I (ii) bs mgxKi‡Y ewm‡q AvqZvKvi e¯‘wUi GKwU
c„‡ôi †ÿÎdj I AvqZb wbY©q Kiæb|
ch©‡eÿY
K. fvwb©qvi aªæeK wbY©q:
cÖavb †¯‹‡ji ÿz`ªZg GK N‡ii gvb, s =............ cm
fvwb©qvi ‡¯‹‡ji †gvU fvM msL¨v, n =............ cm
fvwb©qvi aªæeK, VC = sn =............ cm
L. AvqZvKvi e¯‘i ˆ`N© , cª ’ I D”PZv wbY©‡qi QK
AvqZvKvi
e¯‘i
ch©‡eÿY
msL¨vcÖavb †¯‹j
cvV, M (cm)
fvwb©qvi
mgcvZb
V
fvwb©qvi
aªæeK
VC (cm)
cvV
M+VVC (cm)
Mo cvV
(cm)
‰`N©
L
1.
2.
3.
cÖ ’
B
1.
2.
3.
D”PZv
H
1.
2.
3.
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 22
M. wnmve I djvdj:
AvqZvKvi e¯‘i GK c„‡ôi †ÿÎdj, A = L B =............ cm2 =............ 10-4 m2
Ges AvqZb, V = L B H =............ cm3 =............ 10-6 m3
cvV t 7
e¨envwiK-2: ¯Œz M‡Ri mvnv‡h¨ GKwU e„ËvKvi cÖ ’‡”Q`wewkó Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj wbY©q
D‡Ïk¨
GB cvV †k‡l Avcwb-
¯ŒzMR e¨envi K‡i GKwU e„ËvKvi cÖ ’‡”Q`wewkó Zv‡ii e¨vm, e¨vmva© I cÖ ’‡”Q‡`i †ÿÎdj wbY©q Ki‡Z
cvi‡eb|
m~Î t †ÿÎdj n‡jv †Kv‡bv e¯‘i c„‡ôi cwigvY| †Kv‡bv Zv‡ii cÖ ’ eivei ‰`‡N¨©i mv‡_ j¤fv‡e †Q` Ki‡j †h
Zj cvIqv hvq Zvi cwigvYB n‡”Q cÖ ’‡”Q‡`i †ÿÎdj| †Kvb e„ËvKvi cÖ ’‡”Q` wewkó Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj
A n‡j,
A= r2
GLv‡b, r = Zv‡ii e¨vmva©
= 3.14; aªæe msL¨v
GLb Zv‡ii e¨vm d n‡j r = d2 , myZivs
A=
d2 2
A= 14 d2 ... ... ... ... ... ... ... ... ... (i)
¯ŒzM‡Ri mvnv‡h¨ †h †Kvb ˆ`‡N¨©i cvV wbY©‡qi m~Î:
‰`N¨© = ‰iwLK †¯‹j cvV (L) + e„ËvKvi †¯‹‡ji fvM msL¨v (L) jwNó MYb (LC)
A_v©r d = L + C LC
hš¿cvwZ: ¯ŒzMR, Zvi|
Kv‡Ri aviv:
1| cÖ_‡g ˆiwLK †¯‹‡ji ÿz`ªZg N‡ii gvb I e„ËvKvi †¯‹‡ji †gvU fvM msL¨v †`‡L wbb|
2| Gici h‡š¿i wcP wbY©q Kiæb| e„ËvKvi †¯‹j m¤ú~Y© GKevi Nyiv‡j GwU ˆiwLK †¯‹j eivei †h ˆ`N© AwZµg
K‡i Zv‡K h‡š¿i wcP ejv nq| wcP †K e„ËKvi †¯‹‡ji †gvU fvM msL¨v Øviv fvM K‡i jwNó MYb (LC) †ei Kiæb|
3| GLb cixÿYxq ZviwU‡K ¯ŒzM‡Ri ¯’vqx `Û I ¯Œzi gvSLv‡b ¯’vcb K‡i ¯ŒzwU‡K GKw`K eivei Nywi‡q KxjK I
¯Œz‡K Avj‡Zvfv‡e Zv‡ii Mv‡q ¯úk© Ki‡Z n‡e|
c`v_©weÁvb
BDwbU 1 c„ôv 23
4| GB Ae¯’vq ˆiwLK †¯‹‡ji †h `vMwU e„ËvKvi †¯‹‡ji evgw`‡K †`Lv hvq †mB `vMwUi cvV wbb| GwUB n‡jv
‰iwLK †¯‹j cvV (L)| Gevi e„ËvKvi †¯‹‡ji †h `vMwU ˆiwLK †¯‹‡ji `v‡Mi mv‡_ wg‡j hvq †m `vMwUi cvV wbb|
GwU n‡jv e„ËvKvi †¯‹‡ji fvM msL¨v (C)|
5| Gfv‡e ZviwUi wewfbœ ¯’v‡b K‡qKevi cvV wb‡q Q‡K wjwce× Kiæb|
6| Gici cÖ‡qvRbxq wnmv‡ei mvnv‡h¨ Zv‡ii e¨vm †ei K‡i (i) bs mgxKi‡Y ewm‡q Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj
wbY©q Kiæb|
ch©‡eÿY
K. jwNô MYb wbY©q:
‰iwLK †¯‹‡ji GK fv‡Mi gvb, s =............ mm
e„ËvKvi †¯‹‡ji †gvU fvM msL¨v, n =............
wcP (e„ËvKvi †¯‹j m¤ú~Y© GKevi Nyiv‡j ˆiwLK †¯‹‡j †h ˆ`N© AwÎKg K‡i), p =............ mm
jwNô MYb, LC= pn =............ mm
L. Zv‡ii e¨vm wbY©‡qi QK
ch©‡eÿY
msL¨v‰iwLK †¯‹j
cvV, L(mm) e„ËvKvi ‡¯‹‡ji
fvM msL¨v, C
jwNô MYb
LC (mm) e¨vm, d = L+C LC
(mm) Mo e¨vm
(mm) 1.
2.
3.
4.
5.
M. wnmve I djvdj:
Zv‡ii cÖ ’‡”Q‡`i †ÿÎdj, A = 14 d2 =............ mm2 =............ 10-6 m2
Gm.Gm.wm †cÖvMÖvg
BDwbU 1 c„ôv 24
P‚ovšÍ g~j¨vqb
m„Rbkxj cÖkœ
mRxe beg †kªYxi QvÎ| †m c`v_©weÁvb eB wK‡b eB‡Z gvÎv mgxKiY †`‡L welqwU eyS‡Z cvij bv| G Rb¨ †m
Zvi wkÿ‡Ki Kv‡Q G wel‡q Rvb‡Z PvBj| Zvi wkÿK Zv‡K ivwk, wewfbœ ivwki g‡a¨ m¤úK©, gvÎv mgxKiY Ges
Gi mvnv‡h¨ mgxKi‡Yi mZ¨Zv hvPvB BZ¨vw` welq m¤ú‡K© wek` Av‡jvPbv Ki‡jv| d‡j †m welqwU m¤ú‡K©
Rvb‡Z cvij Ges wb‡R wb‡R cÖ‡qvM Kivi †Póv Kij|
K) gvÎv mgxKi‡Yi msÁv wjLyb| 1
L) †gŠwjK ivwk Ges jä ivwki g‡a¨ cv_©K¨ D‡jøL Kiæb| 2
M) Kv‡Ri gvÎv mgxKiY we‡køl‡Yi gva¨‡g †ei Kiæb| 3
N) gvÎv mgxKi‡Yi mvnv‡h¨ mRxe wKfv‡e wb‡gœvwjøwLZ mgxKi‡Yi mZ¨Zv hvPvB Kij| mgxKiYwU n‡jv-
4
s= ut + 21
at2
DËigvjv
cv‡VvËi g~j¨vqb-1 t 1. L 2. M
cv‡VvËi g~j¨vqb-2 t 1. K 2. L cv‡VvËi g~j¨vqb-3 t 1. M 2. N
cv‡VvËi g~j¨vqb-4 t 1. M 2. M 3. N
cv‡VvËi g~j¨vqb-5 t 1. K 2. L
