ZZxq Aavq

ej (Force)

MvwjwjI Mvwjwj

GalileoGalilei(15641642)

MvwjwjI wQjb GKRb BZvwjI c`v_wevbx, MwYZwe`, RvwZwe Ges `vkwbK| ZuvK AvaywbK wevbi RbK ejv nq| wZwb c_g Uwjvc eenvi Ki eenvwiK RvwZwevbi m~Pbv KiwQjb| KvcvwbKvmi m~hKw K mi RMZi evLvwU wZwb c_g mwZKvi A_ evwbK RMZ cwiwPZ Kib| G KviY wZwb Kv_wjK PvPi ivlvbj cob, Zuviv ZuvK `vlx mve Ki Ges ZuvK evwK Rxeb Mnew` nq KvUvZ nq| Zuvi gZzi 366 eQi ci 2008 mvj ivgvb Kv_wjK PvP wbR`i `vl ^xKvi Ki wbq ZuvK gv Ki!

3.1 RoZv, ej I fi (Inertia,ForceandMass) Gi AvMi Aavq Avgiv eM, wZ, ZiY (Ges g`b), AwZv `~iZ Ges Zv`i fZiKvi mKjv wkLwQ, mgxKiYjv ei KiwQ Ges eenvi KiwQ| GB Aavq Avgiv c_gevi mwZKvii wKQz c`v_wevb wkLe| i Kiv hvK wbDUbi c_g m~ w`q:

wbDUbi c_g m~ : ej cqvM bv Kij wi e wi _vKe Ges mgeM PjZ _vKv e mgeM PjZ _vKe| (eySZB cviQ eM hnZy fi ZvB mgeM PjZ nj w`K cwieZb KiZ cvie bv mvRv mij iLvq mgvb `wZZ hZ ne|)

wbDUbi c_g m~i c_g Ask wbq Kviv mgmv nq bv KviY Avgiv me mgqB `wL wi eK avvavw bv Kiv ch mUv bo bv wi _K hvq| wZxq AskUv wbq mgmv, KviY Avgiv KLbvB Kvbv Pj eK AbKvj PjZ `wL bv, avv w`q Kvbv eK Qo w`jI `Lv hvq Kvbv ej cqvM bv KijI kl ch e Uv _g hvq| Avgv`i `bw`b Rxebi

52 ej

AwfZv _K gb nq h Kvbv wKQzK mgeM Pvwjq wbZ nj gvMZ eywS mUvZ ej cqvM Ki hZ nq| wbDUbi c_g m~ _K Avgiv RvbZ ciwQ mUv mwZ bq mgeM PjZ _vKv Kvbv e hw` _g hvq Zvnj eySZ ne mLvb Kvbv bv Kvbvfve ej cqvM Kiv nqQ| NlY, evZvmi evav G iKg AbK wKQz Avmj Dvw`K _K ej cqvM Ki Pjgvb GKUv e K _vwgq `q hw` mwZ mwZ me ej e Ki `qv hZ Zvnj Avgiv mwZB `LZ cZvg mgeM PjZ _vKv GKUv e AbKvj ai PjQ| wbDUbi c_g m~ c_gevi ej kUv eenvi Kiv nqQ wK gRvi evcvi nQ ej ejZ Avgiv Kx evSvB mUv GLbv ejv nqwb GUv hw` c`v_ wevbi eB bv nq Ab Kvbv eB nZv Zvnj ej cqvM -Gi RvqMvq kw cqvM K_vUv eenvi KijI evKUvq A_i Kvbv Dwbk-wek nZv bv| wK hnZz GUv c`v_wevbi eB ZvB Avgiv GLvb kw K_vUv eenvi KiZ cvie bv c`v_wevbi fvlvq kw m~Y wfb GKUv ivwk! GLvb Avgv`i ej K_vUvB eenvi KiZ ne! wK ej gvb Kx? Avgiv Zv GLb ch eji Kvbv msv w`Bwb! Avmj wbDUbi c_g m~UvB eji msv nZ cvi! h KviY wi e PjZ i Ki Avi mgeM PjZ _vKv ei eMi cwieZb nq mUvB nQ ej| wbDUbi c_g m~ _K ejUv Kx, mUv eySZ cvwi wK cwigvc KiZ cvwi bv| wZxq m~ _K Avgiv ej cwigvc Kiv wkLe| ej cqvM bv Kiv ch wi e h wi _vKZ Pvq wKsev MwZkxj e h MwZkxj _vKZ Pvq mUvB nQ RoZv| nVvr Mvwo PjZ i Kij Avgiv hfve cQbi w`K GKUv SuvKzwb LvB mUv nQ RoZvi D`vniY| kixii wbPi Ask Mvwoi mv_ jM AvQ Mvwoi mv_ mv_ mUv PjZ i KiQ wK kixii Dcii Ask GLbv wi Ges wi _vKZ PvBQ! ZvB kixii Dcii Ask cQbi w`K SuvKzwb LvQ| hnZy GUv wi _vKvq RoZv ZvB GUvK ej wwZ RoZv| MwZ RoZvi KviY Avgiv gvbylRbK Pj evm Ub _K bvgZ wMq AvQvo LZ `wL| Pj evm Ubi gvbylwUi cyiv kixiUvB MwZkxj, m hLb gvwUZ cv w`qQ ZLb wbPi Ask _g wMqQ, Dcii Ask MwZ RoZvi KviY ZLbv QyUQ ZvB m gwo Lq coQ! RoZvi welqwU hw` aygv GKUv msv nZv Zvnj GUvK GZ iZ w`q kLvbv nZv bv Avmj GUv c`v_wevbi `wKvY _K Lye iZc~Y GKUv welq| Avgiv GLb ch fi wbq GKwU K_vI ewjwb wK Kvbv wKQzi MwZ mK RvbZ PvBj Avgv`i mwUi fi mK RvbZ nq| GKB MwZZ QzU Avmv GKUv nvjKv mvBKj Avi GKUv fvix UvKK Avgiv GK wZ `wL bv, Zvi KviYUv nQ fii cv_K| wK fiUv Avmj Kx? Avgiv AbK mgqB ewj fi nQ KZUv e AvQ Zvi GKUv cwigvc! Gi PvBZ AbK wevbmZ Di nQ fi nQ RoZvi cwigvc| (Zvgiv welqUv fvjv Ki j Kiv Lye iZc~Y GKUv K_v ejv nqQ!) Kvbv wKQzi RoZv hw` ewk nq Zvnj eySZ ne Zvi fiI wbqB ewk! RoZv hw` Kg nq Zvnj fiI Kg| Zvgiv wbqB GUv j KiQ mgvb cwigvY ej cqvM Kiv nj hvi fi ewk mUvK ewk wePzZ Kiv hvq bv| wK hvi fi Kg mUvK ewk wePzr Kiv hvq| wKsev Abfve ejv hvq fi Kg nj RoZvi cfveUv Zzjbvg~jKfve Kg nq|

ej53

D`vnib 3.1: D`vniY 3.1: Qwe 3.1 Gi Mvd ywUZ mgqi mv_ miY Ges eMi gvb `Lvbv nqQ, Kv_vq KZY ej cqvM Kiv nqQ evLv Kiv|

Qwe 3.1 Aevb mgq I eM mgqi ywU jLwP|

Di: ywU MvdB `LZ KB iKg wK G`i gvS m~Y wfb Z_ iqQ| G

(i) c_g Mvd 0 _K wKsev _K kl ch mgq ywUZ Aevbi cwieZb nQ bv, hvi A_ Kvb eM bB, KvRB eMi cwieZbi ckB Avm bv hvi A_ G `yUv mgq wbqB Kvbv ej cqvM Kiv nQ bv| _K mgq Aevbi cwieZb nQ wK hnZz mg nvi cwieZb (iLvwU hnZz mij iLv) nQ Zvi A_ mgeM A_vr eMi Kvbv cwieZb bB KvRB _K mgqI Kvbv ej cqvM Kiv nQ bv| aygv gyn~Z Kvbvfve ej cqvM Ki w i e wUK mgeM MwZkxj Kiv nqQ| Avevi wVK gyn~Z ej cqvM Ki MwZk g Ab v vbv ej cqvM Kiv nqwb|

xj e wUK _vw q `qv nqQ, K _vI K

A_vr 0 , Ges Z Kvbv ej bB|

aygv Ges Z n~Zi Rb ej cqvM Kiv nqQ| gy

(ii) wZxq Mvd 0 _K Ges _K kl ch ewU mgeM hvQ, KvRB Kvbv ej cqvM Kiv nqwb| _K mgq eMwU mgnvi cwiewZZ nQ KvRB GLvb wbqB ej cqvM

Kiv nQ|

Ges Kvbv ej bB| A_vr 0

Z ej cqvM Kiv nqQ|

54 ej

3.2 eji cKvi f` (DifferentkindsofForces) cw_exZ KZ aibi ej AvQ wRm Kiv nj Zvgiv wbqB eje AbK aibi! Kvbv wKQzK hw` avv w`B mUv GKUv ej, UvK hLb evSv Ub wbq hvq mUv GKUv ej, So hLb MvQ Dco co mUv GKUv ej, Pz^K hLb jvnvK AvKlY Ki mUv GKUv ej, evgv weviY hLb Ni evwo Dwoq `q mUv GKUv ej, b hLb Kvbv wKQzK Ub Zzj mUv GKUv ej GKUzLvwb mgq w`jB G iKg bvbv aibi eji Zvgiv GKUv wekvj ZvwjKv Zwi KiZ cvie| wK PgKc` evcviwU Kx Rvb? cKwZZ gv Pvi iKgi ej iqQ, Dci h ZvwjKv `qv nqQ mjvK weklY Kiv nj `Lv hve Gjv Nyi-wdi GB Pvi iKgi evBi KvbvUv bq! Avmj gwjK ej gv PviwU! mjv nQ : 3.2.1 gnvKl ej (Gravitation) GB mwRMZi mKj e Zv`i fii KviY GK AciK h ej w`q AvKlY Ki mUvB nQ gnvKl ej| GB gnvKl eji KviY Mvjvwi fZi biv NyicvK Lvq wKsev m~hK wNi cw_ex Nyi, cw_exK wNi Puv` Nyi! cw_exi gnvKl ej hLb Avgv`i Ici KvR Ki Avgiv mUvK ewj gvavKlY| GB gvavKlY ej Avgv`iK wbPi w`K Ub iLQ Ges Gi KviYB Avgiv wbR`i IRbi Abyf~wZ cvB| 3.2.2 Zwor P^K ej ev we yr PKxq ej (ElectroMagneticForce) wPiwb w`q Pzj AvPo mUv w`q KvMRi UzKivK AvKlY Kiv ev Pz^K w`q Ab PzKK AvKlY-weKlY Avgv`i AbKB KLbv bv KLbv KiwQ| hw`I Zwor ev we`yr Ges Pz^Ki ejK Avjv`v aibi ej gb nq Avmj `ywU GKB ej aygv yBfve `Lv hvq| ay gv GB ejUv AvKlY Ges weKlY yUvB KiZ cvi Abjv ay AvKlY KiZ cvi weKlY KiZ cvi bv| gvavKlY kwi Zzjbvq GUv AbK kwkvjx (10 Y ev wUwjIb wUwjIb wUwjIb Y kwkvjx!) K_vUv h mwZ mUv wbqB Zvgiv Abygvb KiZ cvie KviY hLb GKUv wPiwb w`q Pzj AvPo GKUv KvMRK AvKlY Ki Zyj bvI ZLb wK mB KvMRUvK cyiv cw_ex Zvi mg fi w`q Zwi gvavKlY ej w`q Ub ivLvi Pv Ki ZeyI Zvgvi wPiwbi A GKUz we yr mB wekvj cw_exi cyiv gvavKlYK nvwiq `q| 3.2.3 yej wbDKxq ej (WeakForce) GUvK yej ejv nq KviY GUv Zwor P^K ej _K `yej (cvq wUwjIb Y) wK gvUI gnvKl eji gZv GZv yej bq| gnvKl Ges Zwor P^K ej h Kvbv `~iZ _K KvR KiZ cvi wK GB ejUv LyeB A ~iZ (10 ) KvR Ki! ZRwq wbDwKqvm _K h eUv () iwk ev BjKUb ei nq mUvi KviY GB yej wbDKxq ej|

ej55

3.2.4 mej wbDKxq ej (Stro Nu arForce) ng cleGwU nQ mw RMZi mePq kwkvjx ej, Zwor P^K ej _KI GKkY ewk kwkvjx wK GUvI LyeB A ~iZ (10 ) KvR Ki| cigvYyi K` h wbDwKqvm iqQ Zvi fZiKvi cvUb Ges wbDUbi wbR`i gvS GB cP kwkvjx ej KvR Ki wbR`i AvUK ivL| cP ej AvUK _vKvi KviY Gi gvS AbK kw Rgv _vK ZvB eo wbDwKqvmK f wKsev QvU wbDwKqvmK Rvov w`q AbK kw Zwi Kiv me| wbDwKqvi evgv m Rb GZ kwkvjx| m~h _K Avjv ZvcI GB ej _K Zwi nq|

wevbxiv aviYv Kib GB Pvi aibi eji g~j GK RvqMvq Ges Zviv mejvK GK m~ w`q evLv Kivi Pv KiQb| Zwor PK (we yr P^Kxq) Ges yej wbDwKqvi ejK Gi gvS GKB m~ w`q evLv Kiv me nqQ Ges mwU ZvwK c`v_wevbi GKwU AvKvkQuvqv mvdj! (KvRB Zzwg BQ Kij ejZ cvi ej wZb aibi: gnvKl, BjKUv DBK (Electroweak) Ges wbDwKqvi KD GUvK fzj ejZ cvie b!) AbjvKI GK m~ Muv_vi Rb wevbxiv KvR Ki hvQb| Zvgiv hLb Zvgv`i `bw`b Rxeb bvbv KvR ej eenvi Kiv ZLb Zvgv`i gb nZ cvi Kvbv Kvbv ej cqvM KiZ nj k KiZ nq (b w`q fvix wRwbm Zvjv, Kvbv wKQzK avv `Iqv, wKsev PjZ PjZ NlYi Rb Pj e i _g hvIhv) Avevi Zvgiv j KiQ Kvbv Kvbv ej cqvMi Rb k KiZ nq bv Kvbv wKQz Qo w`j gvavKlY eji Rb wbP cov, Pz^Ki AvKlY!) KvRB Avgiv ejK k Ges Ak `yB aibi ej fvM KiZ cvwi| wK Zvgiv wbqB eySZ cviQ Avgiv hLvb k KiwQ ej aviYv KiwQ, mLvb wK ciii AYy-cigvYy, Zv`i wNi N~Yvqgvb BjKUb mivmwi k w`q bq Zv`i Zwor PK ej w`q GK Abi mv_ KvR KiQ! Ab K_vq ejv hvq Avgiv hw` cvigvYweK chvq Pj hvB Zvnj me ejB AkK! GK cigvYy Ab cigvYyK AvKlY-weKlY Ki `~i _K, Zv`iK AvwiK A_ k KiZ nq bv! 3.3 wbDUbi wZxq m~ (NewtonsSecondLaw) Avgv`i Pvicvk Avgiv hv wKQz `wL mwU Mn-b nvK Avi Mvwo Ub-wegvb nvK wKsev Kvigi wU nvK Zvi me wKQzB wbDUbi wZxq m~ w`q evLv Kiv hvq| wbDUbi wZxq m~ c`v_wevbi RMZ h Ac~e wece mw KiwQj Zvi Kvbv Zzjbv bB| Avjvi eMi KvQvKvwQ hvIqvi mgq wKsev AYy-cigvYyi z` RMZ hvIqvi AvM ch wbDUbi wZxq m~i evBi wKQz cqvRb nq bv| GB AmvaviY m~wU LyeB mnR, GUv G iKg :

56 ej

wbDUbi wZxq m~: ei fieMi cwieZbi nvi Zvi Dci chy eji mvgvbycvwZK Ges h w`K ej cqvM Kiv nq fieMi cwieZbUvI NU mw`K|

m~UvZ eMi cwieZbi nvi bv ej fieMi cwieZbi nvi K_vUv ejv nqQ| fi eM mnR fve fi Ges eMi YdjK ejv nq| A_vr fi hw` nq , eM hw` nq Zvnj fieM nQ evSvB hvQ hnZz nQ fi ZvB I GKwU fi| Zvgiv aviYv KiZ cvi h mvaviYfve hLb Kvbv wKQz MwZkxj nq ZLb Zvi fii Kvbv cwieZb nq bv, ZvB fieMi cwieZbUzKz Avme eMi cwieZb _K| LyeB wekl Kvbv nqZv Avgiv `Le eMi cwieZb nqwb wK fii cwieZb nqQ ej fi eMi cwieZb nq MQ! fieM bvg GKUv b~Zb ivwk Avwevi bv Ki fi Ges eMi Ydj K_vUv ejj Kx mgmv wQj? eo Kvbv mgmv bB wK Zvgiv Rb ivLv AvjvK hLb KYv wnme `Lv nq ZLb Zvi wK fi _vK bv wK fieM _vK! KvRB fi Ges eMi _K fieM ewk gwjK GKwU ivwk!

D`vniY 3.2: Zywg GKwU Uwbm ej 10 / eM GKUv `qvj Qzo `qvi ci GUv GKB wZZ wVK Zvgvi w`K wdi GmQ| ejUvi fi 100 nj fieMi cwieZb KZ?

Di: ejwU Qzo `qvi mgq fieM , `qvj AvNvZ Ki wVK Dv w`K wdi Avmvi mgq fieM nQ KvRB fieMi cwieZb:

2

GB cwieZbi Rb Uwbm ejUvi Dci `qvjUv Lye A mgqi Rb ej cqvM KiQ| wKU Ljvi mgq evUmgvbiv Gfve evU w`q Lye A mgqi Rb wKU ejK AvNvZ Ki mUvi fieMi cwieZb Ki dj| Avgiv hjvK evDvwi wKsev Qv ewj!

Gevi Avgiv wbDUbi wZxq m~ wdi hvB| aiv hvK Kvbv GKUv e i Avw`eM wQj

Ges mB eM cwiewZZ nq (eo wKsev Kg) nqQ , KvRB fi eMi cwieZb nQ :

mgq ci

KvRB fieMi cwieZbi n vi :

ej57

hnZy GLvb ai wbqwQ fii Kvbv c vB Gfve wjLZ cvwi Avi Avgiv Rvwb ZiY nQ

wieZb nqwb Z

m Kiv ej hw` nq Zvnj Avgiv wbDUbi wZxq m~K wjLZ cvwi: yZivs cqvM

wK Avgiv m~UvK mgvbycvwZKfve wjLZ PvB bv, mgxKiY wnme wjLZ PvB!

Zvgiv mevB Rvb mgvb Ges mgvbycvwZK K_v ywUi A_ Kx| GKwU ivwk h nvi evo ev Kg AbwUI hw` mB nvi evo ev Kg Zvnj Avgiv ewj ivwk `ywU mgvbycvwZK| h Kvbv GKwU ivwkK mwVK GKUv mvgvbycvwZK aeK w`q Y ywU mgvbycvwZK ivwkK mgvb K djv hvq|

Ki i

A_vr hw` , Gi mgvbycvwZK nq, A_vr nq Zvnj GKUv mgvbycvwZK ae LyuR ei Kiv me hLb Avgiv wjLZ cvie

wbDUbi wZxq m~wUi ejvq Gevi GKUv PgKc` evcvi NUvbv me| hnZy ej

welqUvB Gi AvM Kv_vI evLv Kiv nqwb, (wbDUbi c_g m~ w`q ay mUvi GKUv aviYv `Iqv nqQ) wZxq m~ w`q mUvK c_gevi cwigvc Kiv ne ZvB Avgiv ejZ cvwi wbDUbi wZxq m~ cqvM Kivi mgq mgvbycvwZK aeKK 1 aiv nj hUv cve mUvB nQ eji cwigvc! Kx mnR mgvbycvwZK mKK mgxKiY evwbq djv hvq|

myZivs Avgiv wbDUbi wZxq m~UvK GKUv mgxKiY wnme wjLZ cvwi| ej hw` F nq Ges aeKK hw` 1 ai bB Zv nj mgvbycvwZK

GB QvU Ges mnR mgxKiYwU h c`v_wevbi RMZ Kx wece Ki w`Z cvi mwU wekvm Kiv KwVb|

eji gvv:

D`vniY 3.3: 3.2QweZ `Lvbv Dcvq GKwU fii yB cvk ywU KwcKj eenvi Ki 10 Ges 5 fii ywU IRb Szwjq `qv nqQ| fiwUi Dci KZ ej KvR KiQ?

58 ej

Di: 10 Ges 5 fi Kvbv ej bq, Gjv fi KvRB GjvK c_g w`q Y w`q ej cwiYZ K i wbZ ne|

10 9.8 /

98 5 9.8 /

9 4

KvRB fiwUi Dci evg w`K 98 w`q Ges Wvb w`K 49 w`q Uvbv nQ

|

yUv hvM nq ejv hvq evg w`K 49 KvR KiQ| ( fiwUi Dci AviKwU ej mvRv bPi w`K KvR KiQ, wK mwU Uweji cwZwqv ej w`q KvUvKvwU nq AvQ)

Qwe3.2:KwcKj w`q GKwU fiK ycvk _K ywU IRbi gvag ej cqvM Kiv nQ

D`vniY 3.4: 1 fii GKUv e K Qwe 3.3 G `Lvbv Dcvq Szwjq ivLv nqQ|

Ges eji gvb KZ?

Qwe3.3: yUv myZv w`q Svjvbv GKwU fi

Di: hnZz GLvb me wKQz w i Ae vq AvQ ZvB evSv hvQ we yZ gvU eji wigvY k~b| 1 fiK c_g w`q Y

`q e i Z Z cw

j cw Y Ki wb ne:

1 9. 9.8 8 /

wbPi w`Ki GB 9.8 ejwU Dci w`Ki ywU ej Ges w`q mvg Ae vq ivLv

Kiv AvQ| A_vr: Dci wbP Kvbv ej bB, Wvb evgI Kvbv ej bB| Wvb ev e L

q ji Rb wj Z cvwi:

sin 45 sin 45 Kv

RB

Dci wbP eji Rb w 4 cos 45

wjLZ cv i 9.8 cos 5

c_g mgxKiY _K 9.8 2 cos 245 2 /

9.82

6.93

ej59

1 2 K 2 6.93 vRB

D`vniY 3.5: 5 fii GKwU w i e i Ici 100 ej 10 ch cqvM Kiv njv| (a) ej cqvM Kivi KviY ZiY KZ? (b) 10 ci eM KZ? (c) 20 ci eM KZ? (d) 20 mgq KZUzKz ~iZ AwZg KiQ? (e) eM Ges AwZv ~iZ Mvd GuK `LvI|

100 5 20 /

Di: (a) ZiY

(b) 10 ci eM

0 20 10 / 200 /

(c) 10 ch ej cqvM Kiv nqQ Gici hnZy Avi ej cqvM Kiv nqwb KvRB 200 eM cuQvbv ci eM AcwiewZZ _vKe| A_ ci eM 200 /

Qwe3.4:eM mgq Ges Aevb mgqi ywU Mvd ev jLwP

/ vr 20

(d) 20 G AwZ ~iZ:

G AwZv `~iZ yBevi ei KiZ ne| c_g 10 v

20 10 1000

wZxq 10 G AwZv ` 3~iZ (Qwe .4)

200 10 2000

gvU AwZv ~iZ 1000 2000 3000 (e)3.4 QweZ `Lvbv nqQ|

60 ej

D`vniY 3.6: w i Ae v _K i Ki 10 GKUv e 100 ~iZ AwZg KivZ 20 ej w`Z nqQ| ewUi fi KZ?

Di: 0

2 2 10010 / 2 /

202 10

D`vniY 3.7: Zvgiv mevB AvBbvBbi mB weLvZ m~wUi K_v Rvb GLvb nQ kw (Avgiv cii Aavq coe Q Ges nQ Avjvi eM| AvBbvBbi AvcwK m~ _K Avgiv Rvwb

) n fi

1

hLvb nQ MwZkxj Ae vi fi Avi nQ w i Ae vi fi, A_vr AvBbvBbi AvcwK Z Abyhvqx w i Ae vi fi _K MwZkxj Aevi fi ewk! `LvI h AvjvK KYv wnme weePbv Kij Gi fi k~b njI Gi fi eM k~b bq! Di: fieM nQ KvRB

1

yB cvkB eM Kwi:

1

w`q Y Kwi:

1

yB cvk hvM Kwi:

1

ej61

1 1

yBcvk eMg~j bB

1

Avgiv Rvwb

KvRBhw` 0 nq

KvRB / A_vr fi k~b njI fieM k~b bq! KZ mnR KZ wewP welq `Lvbv hvq!

3.4 gnvKl ej (GravitationalForce)Avgiv ej Kx mUv ejwQ (hUv ZiYi Rb `q) mUv Kgb Ki cwigvc KiZ nq mUvI ejwQ (fi Avi ZiYi Ydj) wK GLbv Zvgv`iK mwZKvi Kvbv eji mv_ cwiPq Kwiq w`Bwb| c`v_wevbi GKwU PgKc` ej nQ gnvKl ej, fi AvQ m iKg h Kvbv e Ab eK gnvKl ej w`q AvKlY Ki| aiv hvK `ywU fi Ges Zv`i gvS ~iZ

gvS h ej mw ne mUvK hw` Avgiv ewj Zvnj Zvnj Zv`i

GLvb nQ gnvKlxq aeK Ge Q :s Zvi gvb n

6.67 10

gvv:

62 ej

GLvb gb ivLZ ne fiwU K wbRi w`K ej AvKlY Ki Avevi fiwU K wbRi w`K AvKlY Ki|

GB yUv fii GKUv hw` Avgv`i cw_ex nq Ges Avgiv hw` ai wbB Zvi fi , Ges cw_exi Dci fii Ab GKUv wRwbm ivLv nq Zvnj cw_ex fiK Zvi K`i w`K ej AvKKie

lY

Qwe3.5: ywU fii fZi gvavKlY ej

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D`vniY 3.8: m kbi DPZv cw_exc _K AvbygvwbK 100 . mLvb Gi gvb KZ?

Di: m kb gvavKlYRwbZ ZiY nj

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1 / 1 /

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mLvb gnvKvkPvixiv IRbnxb (Qwe 3.6) Kb? D`vniY 3.9: cw_exi K _K Puv`i ~iZ 3.8 10 . Puv`i GKevi

cw_exK c`wY KiZ KZ mgq jvMe? Qwe3.6: gnvKvkhvb fvmgvb GvbU| Di: Puv`K cw_ex gvavKlY ej UvbQ| mwU nj

cw_ex _K Puv`i ~iZ

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m~Uv Avgiv cw_exK wNi NyiZ _vKv h Kvbv DcMni RbI eenvi KiZ cvie| D`vniY 3.10: m~h _K wewfb Mni ~iZjv nQ (cw_exi ~iZi Zzjbvq)

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Mn eya cw_ex gj enwZ kwb BDibvm bcPzb ~iZ 0.387 0.723 1 1.524 5.203 9.539 19.18 30.06

Kvb Mn KZ mgq m~hK GKevi Nyi Avm? Di: Mni fi Ges m~hi fi nj, GKwU MnK m~h Zvi w`K h ej UvbQ:

GB ej Uvbvi KviY mB Mni ZiY:

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GLvb GKevi Nyi Avmvi mgq| nQ m~hKhnZz

4

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m~h _K cw_exi ~iZ nj ne m~hK GKevi Nyi AvmZ cw_exi h

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Zvgiv BUvibU eBc NuvUvNuvwU Ki wgwjq `L Zvgvi wnmve wK mwZ wK bv! KZ A Rb Kvb MnK m~hK wNi AvmZ eQi jvMe ei KiZ cviQ fe `LQ?

3.4.1 cw_exi K g Gi gvb Avgiv `LwQ cw_exi c Gi gvb

hw` cw_exi K i Gi gvb ei Kivi Rb GB mgxKiY 0 ewmq w`B Zvnj gvUI mwVK Di cve bv, KvRB wVK Ki GUv ei KiZ ne|

aiv hvK cw_exi evmva Ges Avgiv cw_exi c _K MZ Ki cw_exi Mfxi XyK MwQ Ges mLvb cw_exi K _K `~iZ | Avgiv K emva ai AviKUv MvjK Kbv Ki wbB| GLb Avgiv cw_exUvK yB fvM fvM Ki wbZ cvwi, evmvai MvjK Ges Zvi evBii AskUzKz| (Qwe 3.8)

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cw_exi Mfxi K _K ~iZ hw` Kvbv fi _vK Zvnj Zvi Ici gvavKlY ejwUK Avgiv ywU wfb eji hvMdj wnme ei KiZ cvwi| evmvai MvjKi KviY gvavKlY ej Ges evBii AskUzKzi KviY gvavKlY ej| Qwe `LB Zvgiv eySZ cviQ evBii Aski KviY h gvavKlY ej Zwi nq mUv hgb wbPi w`K AvQ wVK m iKg Icii w`KI AvQ| Avgiv hw` wVK Ki wnme Kwi Zvnj `Le evmvai c h Kvbv we yZ wbPi wcQi w`K h gvavKlY ej UvbQ mUvK KvUvKvwU Ki djQ Dci w`K _K Uvbv gvavKlY ej Ges me wgwjq GB gvavKlY eji gvb nQ k~b! KvRB K` _K ~iZ _vKv fii Ici gvavKlY ej Avme aygv MvjKi fZiKvi fiUzKzi Rb evBi

_K wKQz Avme bv|

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cw_exi fi Ges AvqvZb

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43

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3

myZivs cw_exi fZi K Z vLv fii Ici gvavKlY ej nQ K _ ~i i

nQ cw_exi c gvavKlYRwbZ ZiY| myZivs cw_exi fZi K _K ~iZ

gvavKlYRwbZ ZiY nj gvavKlY ej KvRB ne ,

68 ej

KvRB GKevi K` ( 0) Gi gvb k~b| A_vr cw_exi K h Kvbv e IRbnxb|

D`vniY 3.11: cw_exi Afi K _K Ki i cw_ex _K evBi Gi gvb ~iZi mv_ wKfve cwiewZZ nq `LvI| Di: cw_exi Afi K _K r ~iZ:

cw_exi evBi K _K r ~iZ:

Qwe3.9:cw_exi K` _K evBii w`K gGi gvb|

g Gi gvb 3.9 QweZ `Lvbv nqQ 3.5 wsqi ej aiv hvK ^vfvweK Aevq GKUv wsqi `N GB wsUvK Uwej Bq ivLv nqQ Ges aiv hvK GB wsqi GK gv_v GKwU `qvj jvMvbv Ab gv_vq GKUv fi jvMvbv AvQ| ^fvweK Aevq fiwUi Ici wsqi KviY Kvbv ej bB| wsqi cyiv `N Rvbvi Pq Zvi msKvPb wKsev cmviY RvbZ Avgiv ewk AvMnx ZvB wsqi ^vfvweK `N we ywUK Ai K`we y wnme Kbv Ki wbqwQ| (Qwe3.10)

KvRB hw` Avgiv fiwUK Avyj w`q wsqi w`K Pc awi, A_vr ej cqvM Kwi Zvnj wsUv msKzwPZ nq hve| Avgiv hw` Pvc w`q ai ivwL A_vr ej cqvM Kwi Zvnj wbDUbi wZxq m~ Abyhvqx ZiY nIqvi K_v| wK hnZy fiwU wi Kvbv ZiY nQ bv Zvi gvb wbqB Ab GKwU ej wecixZ w`K _K KvR KiQ Ges ywU eji hvMdj k~b nq hvIqvi KviY e wUi gvU ej k~b Ges ewUi ZiY bB| Zvgiv wbqB eySZ cviQ wecixZ w`K _K ejwU AvmQ ws _K hvi A_ ws hw` msKzwPZ nq Zvnj mwU ej cqvM

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Ki| cZKUv wsqiB GKUv ws aeK _vK Ges `Lv MQ wsK Zvi ^vfvweK Aev _K wePzZ Kiv nj msKvPb A_ev cmv c`vb Ki| wePzwZi cwigvY nj iY GKUv ej

GLvb GKwU bMwUf wP iqQ hvi A_ eji w`KwU wePywZi wecixZ w`K| A_vr

ws hw` msKzwPZ nq Zvnj Gi gvb bMwUf Ges m KviY cwRwUf A_vr Gi w`K nQ Ai cwRwUf w`K QweZ hgb `Lvbv nqQ| Avevi hw` fiwUK Ub aiv nq Zvnj wsUvi wePzwZ ne cwRwUf KvRB Gi gvb ne bMwUf A_vr ejUv ne Ai wbMwUf

w`K, QweZ hgb `Lvbv nqQ|

Qwe3.10:^vfvweK Aev, msKzwPZ Ges cmvwiZ xs|

wsqi GB ejwU c`v_wevbi Lye iZc~Y GKwU ej| Avgiv fiwUK Qo w`Bwb, ZvB eji jw k~b Ges fiwUZ Kvbv ZiY nqwb| wK wswUK msKzwPZ wKsev cmvwiZ Ki Avgiv QoI w`Z cviZvg Zvnj ws _K cqvM Kiv eji KviY fiUvi ZiY nZv, eM eoZv Ges fiUv boZ i KiZ| GLvb ejwUi gvb me mgq mgvb _vKe bv, eo hvIqv, Kg hvIqv, cwRwUf wKsev bMwUf nIqvi KviY ejwUI evoe Kge GgbwK w`KI cwieZb Kie, KvRB ZiYUv ne ewPgq Ges fiwUi MwZ Aviv ewk ewPgq| wsqi KviY fiwUi eM Kgb nq mwU Avgiv Avgv`i AwfZv _K Rvwb, mwU mvgb wcQb KiZ _vKe Ges NlYi KviY GK mgq _g hve| hw` NlY bv _vKZ fiwU Zvnj AbKvj mvgb wcQb KiZ _vKZ|

D`vniY 3.12: 3.10 QweZ h fve `Lvbv nqQ mfve GKUv (NlYnxb) Uwej GKUv fi ivLv AvQ| Kvbv wKQz Kiv bv nj wsUvi `N GLb wsUvK hw` ~iZ Ub wbq Qo w`B Zvnj Kx ne?

Di: wsUv fiUvK ej Uvbe A_vr ejUv fiUvK evg w`K Uvbe| GB eji Rb fii ZiY ne Ges ZiYi Rb eM evoZ i Kie| eMi KviY fiUv evg w`K boZ i Kie Ges Gi gvb KgZ _vKe A_vr ejUvI KgZ _vKe KvRB ZiYI

70 ej

KgZ _vKe| GUv nQ mgZiY bv Pjvi GKUv D`vniY| ZiY KgZ _vKjI hnZz ZiY AvQ ZvB eM wK evoZ _vKe| hLb fiUv wsqi Avmj `N G cuQve ZLb

0 KvRB ej 0 Ges ZiY 0 A_vvr eM Avi ew cve bv| wK ew bv cjI Gi gvS wK eM mevP gvb eo MQ KvRB GUvi _g hvevi Kvbv myhvM bB| GUv wsUvK msKzwPZ KiB PjZ _vKe| hLb wsUvK msKvPb Kie ZLb wsUv Dvw`K ej cqvM Ki fiUvK _vgvbvi Pv Kie| Abfve ejv hvq Gevi Dvw`K ZiY (ev g`b) nZ i Kie Ges fiUvi MwZ KgZ i Kie| hLb Avevi ~iZ wsUvK msKvPb Kie ZLb eM KgZ KgZ k~b nq hve|

Qwe 3.11:xsqi MwZ|

wsUv hnZy msKywPZ nq AvQ mUv wK fiUvK Wvb w`K ej cqvM KiB hvQ, KvRB ZiY Zwi ne Ges Avevi eM evoZ _vKe, Ze Gevi Dv w`K| Gfve cyiv cwqvUv evievi NUZB _vKe| QweZ hiKg `Lvbv nqQ|

D`vniY 3.13: cw_exi gvSLvb w`q hw` GKUv dzUv Ki Zzwg Svc `vI (Qwe 3.12) Zvnj Kx ne? Di: wVK wsqi gZv GLvbI GKB evcvi ne, iZ Zvgvi eM k~b Av Av mUv evoZ _vKe K mePq ewk, Zvici mUv KgZ _vKe Ab cvk cuQvZ cuQvZ eM k~b nq hve| Zvici w`Ki cwieZb ne, Avevi GKB evcvi| Zvi gvb Zzwg GK w`K _K Abw`K hZ AvmZ _vKe| Zvgiv `LZB cvQ wsqi ejvq ejUv wQj

GLvb hLvb / 3.5 wbDUbi ZZxq m~ (NewtonsThirdLaw) Kvb ej cqvM bv Kij Kx nq mwU Avgiv RvbZ ciwQ wbDUbi c_g m~ _K| ej cqvM Kij Kx nq mUv Avgiv RbwQ wbDUbi wZxq m~ _K| hLb GKwU e Ab e i Ici ej cqvM Ki ZLb e `ywUi gvS Kx aibi cwZwqv nq, mwU Avgiv RvbZ cvie wbDUbi ZZxq m~ _K| m~wU GiKg :

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wbDUbi ZZxq m~ : hLb GKwU e Ab GKwU ei Ici ej cqvM Ki ZLb mB ewUI c_g ewUi Ici wecixZ w`K mgvb ej cqvM Ki|

c`v_wevbi eBq mvaviYZ hfve wbDUbi ZZxq m~ jLv nq, cZKwU wqvi (action) GKUv mgvb Ges wecixZ cwZwqv (reaction) _vK, Avgiv GLvb mfve wjwLwb| Avgv`i GZY ej mK LvwbKUv aviYv nqQ nVvr Ki ejK wqv wKsev cwZwqv ejj wevw nZ cvi! Zvi PvBZ eo K_v hviv b~Zb c`v_wevb kL Zv`i c_g ckB nq h hw` mKj wqvi (Kvbv GKwU ej) GKwU wecixZ cwZwqv (AviKwU ej) _vK Zvnj wqv-cwZwqv GK AciK KvUvKvwU Ki k~b nq hvq bv Kb! GRb ZZxq m~wUZ Lye Ki wjL `qv `iKvi h ZZxq m~ ejQ h hw` ywU e Ges _vK Zvnj hLb eji Dci ej cqvM Ki ZLb ej cqvM Ki Gi Ici! wecixZ `ywU ej wfb wfb eZ KvR Ki KLbvB GK eZ bq| hw` GKB eZ ywU ej cqvM Kiv nZv ay ZvnjB GK AbK KvUvKvwU KiZ cviZ| GLvb KvUvKvwUi Kvbv myhvM bB|

Qwe3.12:cw_exi gvSLvb w`q Qo `qv GKRb gvbyl Dci wbP KiZ _vKe|

KqKUv D`vniY w`j welqUv cwivi ne| aiv hvK Ici _K Avgiv fii GKUv

e Qo w`qwQ (Qwe3.13)| Avgiv Rvwb cw_exi gvavKlY eji Rb fi cw_exi w`K GKUv ej Abyfe Kie:

Avgiv AvMB `LwQ GB ejUvK wnme jLv hvq| wbDUbi ZZxq m~ kLvi ci Avgiv Rvwb fiwUI wekvj cyiv cw_exUvK wbRi w`K AvKlY KiQ! mB ejwUI aygv wecixZ w`K! Avgiv GB ejwUK wbq gv_v NvgvBbv, Zvi KviY GB ejUvi KviY cw_exi KZUzK Q mUv BQ Kij ei KiZ cvwi : z ZiY n

72 ej

GLvb nQ cw_exi fi Ges nQ cw_exi ZiY

KvRB

hw` cw_exi fi 5.98 10 nq Zvnj Avgiv hw` 1 fii GKUv ei Dci _K Qo w`B Zvi Rb cw_exi ZiY ne 1.6 10 / GwU GZ z` h KD GUv wbq gv_v Nvgvq bv! Zywg hLb cii evi Kvbv RvqMvq jvd `e ZLb gb iLv wbP covi mgq cyiv cw_exUvK Zzwg AvKlY Ki wbRi w`K Ub wbqwQj! (hZ KgB nvK Zzwg mviv cw_exK wbRi w`K UbwQj, mUv wbq GKUz Me KiZ cvi|) wbDUbi ZZxq m~ evSvi mePq mvRv Dcvq nQ Avgiv Kxfve nuvwU mUv evSv| Avgiv mevB nuvUZ cvwi Gi cQb wK c`v_wevb AvQ mUv bv RbB mevB nuvU| wK Zvgiv hnZz c`v_wevb wkLZ i KiQ Zvgv`i Lye mnR GKUv ck Kiv hvq| Zzwg hnZy w i Ae v _K nuvUZ cvi KvRB Avmj Zvgvi GKwU ZiY nQ, hvi A_ Zvgvi Dci ej cqvM Kiv nQ| wK Avgiv mevB Rvwb KD Avgv`i Dci ej cqvM Ki bv| Avgiv wbRivB nuvwU| Kgb Ki mUv me?

Qwe3.13:GKwU fiK cw_ex hgb AvKlY Ki fiwU cw_exKI mfve AvKlY Ki|

wbDUbi ZZxq m~ bv Rvbv _vKj Avgiv KLbvB nuvUvi welqUv evLv KiZ cviZvg bv| Avgiv hLb nuvwU ZLb Avgiv cv w`q gvwUZ avv w`B (A_r ej cqvM Kwi) ZLb gvwUUv wbDUbi ZZxq m~ Abyhvqx Avgv`i kixi mgvb Ges wecixZ ej cqvM KI (Qwe3.14)| GB mgvb Ges wecixZ ejUv w`qB Avgv`i ZiY nq, Avgiv nuvwU!

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welqUv hv`i eySZ GKUz mgmv nQ Zv`iK gb Kwiq `qv hvq, k gvwUZ nuvUv mvRv wK SziSzi evjyi Dci nuvUv mvRv bv Zvi KviY evjyi Ici ej cqvM Kiv hvq bv, evjy mi hvq ZvB wbDUbi ZZxq m~i cvv ejUvI wVK fve cvIqv hvq bv| evcviUv Aviv AbK Ki `qv hvq hw` KvDK Ame gmY GKUv gSZ mvevb cvwb wKsev Zj w`q wcwQj Ki nuvUZ `qv nq! mLvb NlY Lye Kg, ZvB Avgiv wcQb ej cqvM KiZB cvie bv, Ges m Rb Zvi cwZwqv wnme Avgv`i Ici Kvbv ejI cve bv! Avi ZvB nuvUZI cvie bv (wekvm bv nj Pv Ki `LZ cvi)| ej cqvM Kij wecixZ Ges mgvb ej cvIqv hvq, hw` cqvM KiZB bv cvwi Zvnj Zvi cwZwqv ej cve Kgb Ki? Avi nuvUe Kgb Ki?

wbDUbi ZZxq m~ eySZ wMq AbKB c_g

c_g GKUv fzj Ki| mUv nQ Avgiv hw` gvwUZ GKUv cv_i ivwL ZLb Kx nq mUv mwVKfve evLv KiZ cvi bv. cv_iwU hnZz boQ bv KvRB Zvi ZiY bB KvRB Gi Dci wbqB Kvbv ej KvR KiQ bv A_vr gvU eji cwigvY k~b wKsev ejjv GKUv AviKUvK KvUvKvwU KiQ| welqUv evLv KiZ wMq Avgiv cvqB ej dwj cv_iUv gvwUK Zvi IRbi mgvb ej cqvM KiQ wbDUbi ZZxq m~ Abyhvqx gvwUUvI Zvi wecixZ cv_iUvK mgvb Ges wecixZ ej cqvM KiQ Ges GB yUv ej GKUv AviKUvK KvUvKvwU Ki djQ| wK Zvgiv wbqB eySZ cviQ GB evLvUv mwVK bv KviY ZZxq m~ ej w`qQ GKwU e AbwUi Ici ej cqvM Kie| KvRB KvUvKvwU KiZ nj GKB e i Ici ywU ej cqvM KiZ ne wbDUbi ZZxq m~ hUv wbwl Ki w`qQ!

Qwe3.14:GKRb gvbyl nuvUvi mgq cv w`q hLb gvwUK avv `q ZLb gvwUI gvbylwUK cvv avv `q|

Qwe3.15:gvwUi Ici ivLv cv_iK GKUv wsqi Ici iqQ Kbv Kiv hvq|

Gi mwVK Di ei Kivi Rb Avgiv c_g cv_i Ges gvwUi gvSLvb GKUv ws Kbv Ki wbB (Qwe3.15)| cv_ii IRbi Rb sUv GKUz msKzwPZ nq cv_iUvi Ici wecixZ w`K ej cqvM

74 ej

Kie Ges cv_iUvZ ywU mgvb Ges wecixZ ej GK AbK KvUvKvwU Ki jw k~b Ki `e| wVK GKBfve wsUvi Ab AskI gvwUK ej cqvM Kie, gvwUI wecixZ w`K ej cqvM Kie! KvRB cZKUv eZB yUv wecixZ ej GK AbK KvUvKvwU Ki wi Aevq _vKe| vfvweK fveB Zvgiv ck KiZ cvi, Avgiv hLb gvwUZ GKUv cv_i ivwL wKsev hLb GKUv Pqvi ewm ZLb Zv Avmj gvSLvb Kvbv ws _vK bv ZLb Kx nq? ws bv _vKjI ws h `vwqZUv cvjb Ki KwVb e cqvRb GKUz weKZ, wePzZ, evuKv (deform) nq mB KvRUzKz Ki dj! KvRB KwVb e wsqi gZvB cvv GKUv ej mieivn Ki|

D`vniY 3.14: (a) aiv hvK Zywg m~Y NlYnxb GKUv mgZj uvwoq AvQ| Zvgvi IRb 50 Ges Zvgvi mvgb GKUv 100 fii cv_i| Zzwg wVK Kij Zzwg cv_iUvK 50 ej w`q avv w`q GK gv_v _K Ab gv_vq wbq hve| 10 ci cv_iUvi eM KZ ne? (Qwe 3.16) Di: Zzwg hLb cv_iUvK 50 ej w`q avv `e cv_iUvI wK wbDUbi ZZxq m~ Abyhvqx ZvgvK 50 ej w`q avv `e| cv_iUvi ZiY ne W w`Kvb

50

100 /0.5

/ wVK m iKg ZvgviI ZiY ne evg w`K

5050 / 1 /

Qwe3.16:GKRb gvbyl hLb GKUv cv_iK avv `qv ZLb cv_iwUI gvbylwUK cvv avv `q|

KvRB Zzwg Ges cv_i ywU yw`K mi hve! cv_iUvK avv w`q GK gv_v _K Ab gv_vq Zzwg wbq hZ cvie bv! KviY cv_i Avi Zvgvi fZi GKUv ~iZ Zwi nq hve KvRB Uvbv 10 cv_iUvK avv `qv me bv! (b) aiv hvK Zzwg 2 cv_iUvK avv w`Z ciQ ZLb Kx ne? Di : 2 G cv_iUvi eM eo ne:

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ci c_iUv 1 / mgeM hZ _vKe| 0 0.5 2 / 1 /

Gi 2 G Zvgvi e : eM n

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Qwe3.17:GKwU fii Dci ej cqvM Kij NlYi Rb wecixZ w`K GKwU ej Zix nZ cvi|

Qwe3.18:NlY cKZc yUv Geov _eov ci KviY Zix nq|

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