cvv-3.1 rozv i ej t wbdu‡bi mwzi c g m~Îgk cv‡k nv‡zi avozj w`‡q †uvkv w`b| wk †`l‡z...

c`v_©weÁvb

BDwbU 3 c„ôv # 47

BDwbU 3

ej

Force

f‚wgKv

BDwbU 2 G Avgiv MwZ wb‡q Av‡jvPbv K‡iwQ| wKš‘ †R‡bwQ wK G MwZi KviY? Avgv‡ì Pvicv‡k ZvKv‡j wewfbœ

e¯‘ †`L‡Z cvB, mvB‡Kj Pj‡Q, Mvwo Pj‡Q, cvLv Nyi‡Q| G mewKQzB MwZkxj| G BDwb‡U Avgiv w¯’wZ, MwZ

KviY Av‡jvPbv Kie| Avi G Av‡jvPbvi Av‡jv‡K wbDU‡bi MwZi wZbwU m~Î eY©bv Kie| wbDU‡bi MwZi wZbwU

m~Î Av‡jvPbv Ki‡Z wM‡q RoZv, ej, fi‡eM, fi‡e‡Mi msiÿY m~Î, Nl©Y, wbivc` ågY wb‡q wek` Av‡jvPbv

Kie|

cvV-3.1 RoZv I ej t wbDU‡bi MwZi cÖ_g m~Î

Inertia and force : Newton’s first law

D‡Ïk¨

GB cvV †k‡l AvcwbÑ

RoZv e¨vL¨v Ki‡Z cvi‡eb;

ej Kx eY©bv Ki‡Z cvi‡eb;

wbDU‡bi MwZi cÖ_g m~ÎwU e¨vL¨v Ki‡Z cvi‡eb|

3.1.1 RoZv (Inertia)

cÖ‡Z¨K e¯‘B Zvi wb‡Ri Ae¯’vq _vK‡Z Pvq| w¯’i e¯‘ w¯’i, MwZkxj e¯‘ MwZkxj _vK‡Z Pvq| N‡ii

g‡a¨ †Uwej, LvU, †Uwjwfkb, †mvdv‡mU hv †`wL meB w¯’i A_©vr w¯’i e¯‘| N‡ii g‡aï G †Uwej, LvU,

†Uwjwfkb, †mvdv‡mU e¯‘ wj wK wbR †_‡K ¯’vb cwieZ©b K‡i? ev¯ÍeZvi Av‡jv‡K ejv hvq w¯’i e¯‘‡K GK¯’vb

†_‡K Ab¨ ¯’v‡b bv wb‡q †M‡j, e ‘ wj wbR †_‡K KL‡bvB ¯’vb cwieZ©b K‡i bv|

Avgiv Rvwb, c„w_ex m~‡h©i Pvwiw`‡K Nyi‡Q, Nyi‡Q †Zv Nyi‡QB A_©vr MwZkxj Ae¯’vq Av‡Q| c„w_exi G N~Y©‡b †Kv‡bv

evav bv _vKvq c„w_ex MwZkxj|

GKwU ej‡K Avgiv GKwU iv¯Ívi Dci Mwo‡q †`B| wK †`L‡Z cve Avgiv? ejwU Mwo‡q Mvwo‡q wKQz `~i hvIqvi

ci Av‡¯Í Av‡¯Í †_‡g hv‡e| G †_‡g hvIqvi KviY wK? iv¯Ívi mv‡_ e‡ji Nl©Y, evqyi evav? G evav bv _vK‡j

ejwU wK AbšÍKvj a‡i MovZ?

Avgv‡ì Pvicv‡ki G NUbv¸‡jv †_‡K Avgiv wK eyS‡Z cvwi? cÖ‡Z¨K e ‘B Zvi wb‡Ri Ae¯’vq _vK‡Z Pvq A_©vr

†Kvb e¯‘ hw` w¯’i _v‡K Z‡e GwU wPiKvj w¯’i _vK‡Z Pvq, Avevi †h e¯‘ MwZkxj, †m e¯‘ wPiKvj MwZkxj _vK‡Z

Pvq| e¯‘i G wbR¯ Ae¯’vq _vKvi cÖeYZv ev ag©‡K RoZv e‡j| wb‡¤œv³fv‡e RoZvi msÁv †`qv hvq-

RoZv: RoZv e ‘i GKwU ag© †h a‡g©i Kvi‡Y †Kvb w¯’i e¯‘ w¯’i _vK‡Z Pvq Ges MwZkxj e¯‘ MwZkxj _vK‡Z

Pvq| G w¯’i Avi MwZkxj a‡g©i Dci wfwË K‡i ejv hvq, RoZv yÕcÖKvi|

GmGmwm †cÖvMÖvg


wPÎ- 3.2: w ’wZ RoZv

wPÎ- 3.3: MwZ RoZv

wPÎ-3.4 : MwZ RoZv

(i) w¯’wZ RoZv (Inertia of rest) Ges

(ii) MwZ RoZv (Inertia of motion)

(i) w¯’wZ RoZv : w ’i e¯‘ wPiKvj w¯’i _vK‡Z Pvq, e ‘i G cÖeYZv ev ag©‡K w¯’wZ RoZv e‡j|

w¯’wZ RoZvi D`vniY

(i) evm w¯’i Ae¯’v n‡Z nVvr Pj‡Z ïiæ Ki‡j, hvÎxiv wcQ‡bi w`‡K †n‡j c‡ob| evm hLb w¯’i Ae¯’vq _v‡K

ZLb hvÎxi kixiI w¯’i Ae¯’vq _v‡K| evm Pj‡Z ïiæ Ki‡j hvÎxi kix‡ii †h Ask ev‡mi mv‡_ †j‡M _v‡K A_©vr

kix‡ii wb¤œfvM ev‡mi MwZcÖvß nq| wKš‘ kix‡ii Dc‡ii Ask w¯’wZ RoZvi Rb¨ w¯’i Ae¯’vq _vK‡Z Pvq| ZvB

kix‡ii bx‡Pi Ask kix‡ii Dc‡ii As‡ki Zzjbvq GwM‡q hvq| d‡j kix‡ii Dc‡ii Ask wcQ‡b †n‡j c‡o Ges

hvÎx‡`i kixi wcQ‡b n‡j co‡Q e‡j g‡b nq (wPÎ 3.1)|

wPÎ-3.1 : w¯’wZ RoZv

(ii) K¨vivg †Ljvi mgq w¯’wZ RoZvi Av‡iv GKwU ev¯Íe AwfÁZv cvIqv hvq

(wPÎ- 3.2: w¯’wZ RoZv)| jÿ¨ Ki‡j †`Lv hvq GKwU ¸wUi Dci hLb Ab¨ GKwU

¸wU _v‡K ZLb Lye †Rv‡o óªvBKvi w`‡q AvNvZ Ki‡j wb‡Pi ¸wUUv m‡i hvq,

Dc‡ii ¸wUUv w¯’i RoZvi Kvi‡Y wb‡Ri Ae¯’v‡b w¯’i _v‡K Ges wb‡Pi ¸wUi ¯’vb

`Lj K‡i|

MwZ RoZvi D`vniY:

(i) evm MwZkxj Ae¯’v n‡Z nVvr †_‡g †M‡j hvÎxiv mvg‡bi w`‡K Szu‡K

c‡ob (wPÎ- 3.3: MwZ RoZv)| evm hLb MwZkxj Ae¯’vq _v‡K ZLb

hvÎxi kixiI MwZkxj Ae¯’vq _v‡K| evm nVvr †eªK Kl‡j, hvÎxi kix‡ii

†h Ask ev‡mi mv‡_ _v‡K A_©vr kix‡ii wb¤œfvM ev‡mi mv‡_ w¯’i Ae¯’v

cÖvß nq| wKš‘ kix‡ii Dc‡ii Ask MwZ RoZvi Rb¨ MwZkxj Ae¯’vq

_vK‡Z Pvq| ZvB kix‡ii bx‡Pi Ask kix‡ii Dc‡ii As‡ki Zzjbvq wcwQ‡q c‡o| d‡j kix‡ii Dc‡ii Ask

mvg‡b Sz‡K c‡o Ges kixi mvg‡bi w`‡K Szu‡K co‡Q e‡j g‡b nq|

(ii) wiKkvq Povi ci jÿ¨ Ki‡j †`Lv hvq wiKkvIqvjv gv‡S gv‡SB c¨v‡Wj

K‡i GKUz wekÖvg †bb| (wPÎ-3.4 : MwZ RoZv) c¨v‡Wj bv Ki‡jI G mgq

wiKkv GwM‡q hvq MwZ RoZvi Rb¨ Ges wiKkvi MwZkxjZv cieZ©x c¨v‡Wj

Kivi AvM ch©šÍ Ae¨nZ iv‡L|

c`v_©weÁvb


wPÎ-3.5 : w ’wZ RoZv

(wPÎ- 3.6 (K)) (wPÎ- 3.6 (L))

wPÎ-3.6 : w ’wZ RoZv

wPÎ-3.7: wbDU‡bi cÖ_g m~Î

G‡mv wb‡R Kwi

GKwU cvwb fwZ© Møvm wbb| Møv‡mi Dci GKwU k³ KvMR †hgb KvW©

RvZxq KvMR ivLyb| Gevi KvW©wUi Dci me‡P‡q fvix †h K‡qb,

cuvP UvKvi GKwU K‡qb ivLyb (wPÎ-3.5 : w¯’wZ RoZv) KvW©wU‡K

†Rv‡o Av½yj w`‡q †UvKv w`b| wK †`Lv hv‡e? †`Lv hv‡e K‡qbwU

Møv‡mi g‡a¨ c‡o †M‡Q| KvW©wU‡K nVvr †Rv‡o †UvKv †`qvi Kvi‡Y

KvW©wU MwZkxj n‡q m‡i †M‡Q, wKš‘ w¯’wZ RoZvi Kvi‡Y K‡qbwU

wbR Ae¯’v‡b w¯’i _vK‡Z PvIqvq Møv‡mi g‡a¨ c‡o †Mj|

e¯‘i RoZvi cwigvc wbf©i K‡i e¯‘i f‡ii Dci| †h e¯‘i fi

†ewk, †m e¯‘i RoZv †ewk| Avi RoZv †h e¯‘i †ewk †m e¯‘‡K

MwZkxj Kiv ev †Vjv w`‡q ’vb cwieZ©b Kiv ZZ KwVb|

G‡mv wb‡R Kwi

†Uwe‡ji Dci GKwU ievi Ges GKwU eB ivLyb| Gevi ieviwUi

GK cv‡k nv‡Zi AvOzj w`‡q †UvKv w`b| wK †`L‡Z cv‡eb? ieviwU

nv‡Zi AvOz‡ji †UvKvq Zvi wb‡Ri Ae¯’vb †_‡K A‡bK`~i m‡i

†M‡Q| GLb eBwU‡K GKB fv‡e AvOz‡ji †UvKv w`b (wPÎ- 3.6

(K))| G‡ÿ‡Î wK †`L‡Z cv‡eb? †`L‡Z cv‡eb eBwU GKUzI `~‡i

mi‡Q bv ev Zvi Ae¯’vb cwieZ©b Ki‡Q bv| GLb nvZ w`‡q

eBwU‡K av°v w`b| †`Lv hv‡e eBwU ~‡i m‡i hv‡e (wPÎ- 3.6

(L))|

G NUbv †_‡K Avgiv eyS‡Z cvwi †h, †h e¯‘i fi †ewk †m e¯‘‡K

Kg f‡ii e¯‘i †P‡q A‡cÿvK…Z †ewk †Rv‡i av°v w`‡Z nq| Ab¨fv‡e ejv hvq †h e¯‘i fi †ewk †m e¯‘i RoZv

Kg f‡ii e¯‘i Zzjbvq †ewk _vKvq †ewk †Rv‡i av°v w`‡Z nq|

3.1.2 e‡ji ¸YMZ aviYvÑ wbDU‡bi cÖ_g m~Î

Qualitative concept of Force-Newton’s first law. wbDU‡bi MwZ welqK cÖ_g m~Î

Newton’s first law of Motion

cÖ_g m~Î: evwn¨K ej cÖ‡qvM bv Ki‡j w¯’i e¯‘ w¯’iB _vK‡e Ges

MwZkxj e¯‘ mylg `ªæwZ‡Z mijc‡_ Pj‡Z _vK‡e|

c~‡e©B Avgiv RoZv m¤ú‡K© Av‡jvPbv Ki‡Z wM‡q N‡ii g‡a¨

wewfbœ w¯’i e¯‘ †hgb †Uwej, LvU, †Uwjwfkb, †mvdv‡m‡Ui K_v

e‡jwQ| G mKj e¯‘ wbR †_‡K Zvi Ae¯’vb cwieZ©b K‡i bv|

Zvn‡j G mKj e¯‘ wKfv‡e ¯’vb cwieZ©b K‡i? w¯’i e¯‘ ‡jv‡K

†U‡b ev †V‡j Zvi Ae¯’v‡bi cwieZ©b Kiv nq| G Uvbv ev †Vjv‡K

ej e‡j| G ej w¯’i e¯‘i Dci cÖ‡qvM Ki‡j Zv w¯’i e¯‘‡K

MwZkxj K‡i ev MwZkxj Kivi †Póv K‡i| Avevi MwZkxj e¯‘i

GmGmwm †cÖvMÖvg


Dci ej cÖ‡qvM Ki‡j Zv e¯‘wU‡K _vgv‡Z A_©vr e¯‘i †eM n«vm Ki‡Z cv‡i ev e¯‘i †eM e„w×I Ki‡Z cv‡i| †eM

e„w×i d‡j Z¡i‡Yi m„wó nq| Avevi ej †Kvb e¯‘i AvKvi cwieZ©b Ki‡Z cv‡i| Bjvwó‡Ki ev w¯úªs‡mi `ycÖvšÍ

A‡bKÿb a‡i Uvb‡j ev evi evi Uvb‡j, Gi AvKvi cwieZ©b nq (wPÎ-3.7: wbDU‡bi cÖ_g m~Î)|

wbDU‡bi MwZi cÖ_g m~Î Ges Dc‡ii ch©v‡jvPbvi Av‡jv‡K Avgiv wb¤œwjwLZfv‡e RoZv Ges e‡ji ¸bMZ aviYv

cvB|

†Kvb e¯‘B Zvi Ae¯’vi cwieZ©b NUv‡Z Pvq bv| w¯’i e¯‘ wPiKvj w¯’i _vK‡Z Pvq| Avi MwZkxj e¯‘ wPiKvj mylg

`ªæwZ‡Z mijc‡_ Pj‡Z Pvq| e ‘i wb‡Ri Ae¯’v‡b _vKvi G ag©B n‡jv RoZv| wbDU‡bi cÖ_g m~Î †_‡K RoZvi

aviYv Gfv‡eB cÖwZcv`b Kiv hvq|

c~‡e©B †R‡bwQ, †Kvb e¯‘B Zvi wb‡Ri Ae¯’vb n‡Z w¯’wZ ev MwZ m¤úK©xq Ae¯’vi cwieZ©b Ki‡Z Pvq bv hZÿb bv

evB‡i †_‡K Gi Dci Uvbv ev †Vjv †`qv nq| A_©vr hv e¯‘i Dci wµqv K‡i e¯‘i Ae¯’vi cwieZ©b K‡i ev Ki‡Z

Pvq, ZvB n‡”Q ej| Gfv‡e wbDU‡bi cÖ_g m~Î †_‡K e‡ji msÁv cvIqv hvq|

e‡ji msÁv t hv †Kvb w¯’i e¯‘i Dci wµqv K‡i Zv‡K MwZkxj K‡i ev Ki‡Z Pvq ev †Kvb MwZkxi e¯‘i Dci

wµqv K‡i Gi MwZi cwieZ©b K‡i ev Ki‡Z Pvq, Zv‡K ej ejv hvq|

e‡ji msÁv DcwiD³fv‡e †jLvB †kÖq| GLb ej Avi RoZvi m¤úK©‡K Av‡iv cwi®‹vifv‡e †jLvi Rb¨ e‡ji

wb‡¤œv³ msÁv †`qv nj:

Òhv †Kvb e¯‘i Dci wµqv K‡i Gi RoZvi cwieZ©b K‡i ev Ki‡Z Pvq, ZvB n‡”Q ej|Ó

3.1.3 e‡ji cÖK…wZ

Nature of Force

ˆ`bw›`b Rxe‡bi wewfbœ ev¯Íe NUbvi mv‡_ mswkøóZvi cwi‡cÖwÿ‡Z ej‡K mvaviYfv‡e `yÕfv‡M fvM Kiv hvq|

(i) ¯úk© ej

(ii) A¯úk© ej

(i) ¯úk© ej t †h mKj ej cÖ‡qv‡Mi Rb¨ e¯‘i ms¯úk© cÖ‡qvRb nq Zv‡K ¯úk© ej e‡j| A_©vr †h ej m„wói Rb¨

`yBwU e¯‘‡K cÖZ¨ÿ ms¯ú‡k© Avm‡Z nq Zv‡K ¯úk© ej e‡j| ¯úk© ej Avevi wewfbœ cÖKv‡ii n‡Z cv‡i, †hgb-

Uvb ej, Nl©Y ej, msNl© ej| 3.7 wP‡Î (K) GKwU BjvwóK‡K Uvbv

n‡”Q| GwU n‡”Q Uvb ej| 3.8 wP‡Î GKwU ev·‡K †g‡Si Dci w`‡q

Uvbv n‡”Q, d‡j †g‡S Ges ev‡·i †h Zj †g‡Si ms¯ú‡k© jvMv‡bv

Zv‡ì g‡a¨ Nl©Y e‡ji m„wó n‡”Q hv ev·wUi MwZi weiæ‡× KvR Ki‡Q|

msNl© ej m¤ú‡K© Avgiv we¯ÍvwiZfv‡e cieZ©x‡Z Rvbe|

(ii) A¯úk© ej t †h ej m„wói Rb¨ `yBwU e¯‘‡K cÖZ¨ÿ ms¯ú‡k©

Avm‡Z nq bv Zv‡K A¯úk© ej e‡j| `yÕwU KYvi gaëZ©x ej gnvKl© ej| `yÕwU AvwnZ e¯‘i gaëZ©x ej Zwor ej,

GKwU Pz¤K GK GKwU †PŠ¤K c`v‡_©i g‡a¨ wµqvkxj ej †PŠ¤K ej|

G‡mv wb‡R Kwi

GKwU KvMR wbb| KvMRwU‡K wQ‡o †QvU †QvU UzK‡iv Kiæb| GLb UzK‡iv¸‡jv †Uwe‡ji Dci ivLyb| GKwU wPiæbx

w`‡q †Zjnxb ïK‡bv Pzj AvPovb| GLb wPiæbxwU‡K UzK‡iv¸wj‡K KvQvKvwQ Avbyb| wK †`L‡Qb? †`Lv hv‡”Q,

KvM‡Ri UzK‡iv¸‡jv wPiæbxi ùv‡Zi mv‡_ †j‡M wPiæbx‡Z D‡V Avm‡Q| wPiæbx KvM‡Ri UzKivi cÖZ¨ÿ ms¯ú‡k©

Avmvi cÖ‡qvRb nqwb| Zwor e‡ji Kvi‡YB N‡U‡Q| G ej‡K A¯úk© ej e‡j|

c`v_©weÁvb


(K) mvg¨ ej; (L) Amvg¨ ej

wPÎ-3.9

(K) mvg¨ ej; (L): Amvg¨ ej

wPÎ-3.11

wPÎ-3.10 : mvg¨ ej

3.3 mvg¨ I Amvg¨ ej

Balanced and Unbalanced Forces

mvg¨ ej

GKvwaK ej †Kvb e¯‘i Dci wµqv Ki‡j hw` e‡ji jwä k~b¨ nq

A_©vr e¯‘wUi †Kvb Z¡ib bv nq, ZLb Avgiv ewj e¯‘wU mvg¨ve¯’vq

Av‡Q| Avi †h ej¸‡jv G mvgë¯’vi ˆZwi K‡i Zv‡ì‡K mvg¨ ej

e‡j [wPÎ-3.9 (K): mvg¨ ej ]|

Avcbvi c`v_©weÁvb eBwU GKwU †Uwe‡ji Dci ivLyb| wK NU‡e? c`v_©weÁvb eBwU †Uwe‡ji DciB mvg¨ve¯’vq

_vK‡e (wPÎ-3.10 : mvg¨ ej)| Pjyb Avgiv GLb Gi KviY e¨vL¨v Kwi| eBwUi Dci c„w_exi gnvKl©xq ej Z_v

e¯‘i IRb W j¤fv‡e wb‡Pi w`‡K wµqv K‡i| Ab¨w`‡K †UwejwU eBwUi Dci F ej

Lvov Dc‡ii w`‡K wµqv K‡i|

†h‡nZz ej `yBwU mgvb Ges wecixZgyLx, myZivs G‡K Aci‡K wbw®Œq K‡i †`‡e|

eBwU mvg¨ve¯’vq _vK‡e|

GKvwaK ej †Kvb e¯‘i Dci wµqv Ki‡j hw` e‡ji jwä k~b¨ bv nq Z‡e e¯‘wUi

Ae¯’vi cwieZ©b N‡U (wPÎ-3.9 (L) : Amvg¨ ej)| †h ej¸‡jv G Ae¯’vi cwieZ©b

NUvq Zv‡K Amvg¨ ej e‡j|

ej

GKwU †MvjK‡K M GKwU ó¨v‡Ûi mv‡_ myZv w`‡q Szwj‡q w`B| GLb e¯‘wUi

Dci AwfKl©xq ej Z_v †MvjKwUi IRb W j¤fv‡e wb‡Pi w`‡K wµqv

Ki‡e| Aciw`‡K myZvi Uvb T j¤fv‡e Dc‡ii w`‡K wµqv Ki‡e| ej yBU

mgvb Ges wecixZgyLx nIqvq G‡K Aci‡K wbw®Œq K‡i †`‡e d‡j e ‘wU

mvgë¯’vq _vK‡e [wPÎ-3.11 (K): mvg¨ ej]|

GLb hw` myZvwU †K‡U †`qv nq Z‡e myZvi Uvb T ej Avi j¤fv‡e Dc‡ii

w`‡K wµqv Ki‡e bv| †MvjKwUi Dci GKgvÎ AwfKl©xq ej wµqv Ki‡e| d‡j †Mvj‡Ki g‡a¨ Z¡i‡Yi m„wó n‡e

Ges †MvjKwU Z¡iY mnKv‡i wb‡Pi w`‡K co‡e [wPÎ-3.11 (L) : Amvg¨ ej]| GLv‡b AwfKl© ej ev e¯‘i IRb

n‡”Q Amvg¨ ej|

mvi-ms‡ÿc:

RoZv (Inertia): RoZv e¯‘i GKwU ag©, †h a‡g©i Kvi‡Y w¯’i e¯‘ w¯’i _vK‡Z Pvq Ges MwZkxj e¯‘ mylg

`ªæwZ‡Z MwZkxj _vK‡Z Pvq|

RoZv `yÕcÖKvi-

(i) w¯’wZ RoZv (Inertia of rest) Ges

(ii) MwZ RoZv (Inertia of motion)

(i) w¯’wZ RoZv (Inertia of rest): w¯’i e¯‘ wPiKvj w¯’i _vK‡Z Pvq, e¯‘i G cÖeYZv ev ag©‡K w¯’wZ RoZv

e‡j|

GmGmwm †cÖvMÖvg


(ii) MwZ RoZv (Inertia of motion): mylg MwZkxj e¯‘ wPiKvj mylg MwZkxj _vK‡Z Pvq, e¯‘i G cÖeYZv

ev ag©‡K MwZ RoZv e‡j|

wbDU‡bi cÖ_g m~Î: evwn¨K ej cÖ‡qvM bv Ki‡j w¯’i e¯‘ w¯’iB _vK‡e Ges MwZkxj e¯‘ mylg `ªæwZ‡Z mijc‡_

Pj‡Z _vK‡e|

wbDU‡bi cÖ_g m~ÎwU e¯‘i RoZv I e‡ji ¸YMZ aviYv †`q|

ej: hv †Kvb w¯’i e¯‘i Dci wµqv K‡i Zv‡K MwZkxj K‡i ev Ki‡Z Pvq ev †Kvb MwZkxj e¯‘i Dci wµqv

K‡i Gi MwZi cwieZ©b K‡i ev Ki‡Z Pvq, Zv‡K ej e‡j|

cv‡VvËi g~j¨vqb-3.1

mwVK DË‡ii cv‡k wUK () wPý w`b

1| wbDU‡bi MwZi cÖ_g m~Î †Kvb ivwki aviYv †`q-

K) fi‡eM L) KvR M) RoZv N) kw³ 2| †Kvb a‡g©i Kvi‡Y w¯’i e¯‘ w¯’i _vK‡Z Pvq Ges MwZkxj e¯‘ MwZkxj _vK‡Z Pvq?

K) ej L) ÿgZv M) kw³ N) RoZv

cvV-3.2 fi‡eM I wbDU‡bi MwZ wØZxq m~Î

Momentum and Newton's second law of motion

D‡Ïk¨


fi‡eM e¨vL¨v Ki‡Z cvi‡eb|

wbDU‡bi MwZi wØZxq m~Î eY©bv Ki‡Z cvi‡eb|

wbDU‡bi MwZi wØZxq m~Î eënvi K‡i ej Ges Z¡i‡bi m¤úK©, F=ma wbY©q Ki‡Z cvi‡eb|

3.2.1. fi‡eM (Momentum)

aiv hvK, GKwU MwZkxj mvB‡Kj Ges GKwU MwZkxj cÖvB‡fU Mvwo mg`ªæwZ‡Z GKwU wbw`©ó w`‡K

Pj‡Q| †Kvb e¯‘wU‡K _vgv‡bv mnR A_ev †Kvb e¯‘‡K _vgv‡bv KwVb n‡e? Avgiv Avgv‡ì ev¯Íe AwfÁZv †_‡K

ej‡Z cvwi| GKwU MwZkxj mvB‡Kj‡K _vgv‡bvi †P‡q GKwU MwZkxj cÖvB‡fU Mvwo _vgv‡bv A‡bK KwVb| †Kvb

MwZkxj e¯‘‡K Avgiv hw` _vgv‡Z PvB, Zvn‡j Avgiv †h evavi gy‡LvgywL nB Zvi GKwU cwigvb n‡”Q fi‡eM|

fi‡eM n‡”Q, MwZkxj e¯‘i fi I †e‡Mi mgš‡q MwVZ GKwU †fŠZ ivwk| GwU MwZkxj e¯‘i fi I †e‡Mi Dci

wbf©ikxj|

GLb cÖkœ n‡”Q, †Uwej †Uwbm ej‡K _vgv‡bvi †P‡q GKwU MwZkxj UªvK _vgv‡bv A‡bK KwVb †Kb, hwÌ e¯‘ `ywU

mg`ªæwZ‡Z Pj‡Q| KviY †Uwej †Uwbm ej Ges cÖvB‡fU Mvwo GKB `ªæwZ‡Z MwZkxj _vKv m‡Ë¡I cÖvB‡fU Mvwoi

fi‡eM †ewk|

c`v_©weÁvb


myZivs Dc‡ii Av‡jvPbv †_‡K eySv hvq †h, †Kvb MwZkxj e¯‘‡K _vgv‡bv KZ KwVb Zv wbf©i K‡i MwZkxj e ‘wUi

fi‡e‡Mi cwigv‡ci Dci|

†Kvb e¯‘i fi I †e‡Mi ¸Ydj‡K Gi fi‡eM e‡j|

g‡b Kwi, GKwU e¯‘i fi = m Ges †eM= v

fi‡eM, p = mv

fi‡eM GKwU †f±i ivwk| Gi w`K †e‡Mi w`‡K|

fi‡e‡Mi GKK kgms-1Ges gvÎv MLT-1

|

3.2.2. e ‘i MwZi Dci e‡ji cÖfve

Effect of force on motion of a body

ej cÖ‡qv‡Mi d‡j w ’wZkxi e¯‘ MwZkxj n‡Z cv‡i

dzUej †Ljvi gv‡V †Ljv ïiæ nq wK fv‡e? cÖ_‡g, GKRb †L‡jvqvi dzUejwU‡K wKK K‡i| wKK Kivi mv‡_ mv‡_

wK N‡U? dzUejwU‡K †h w`K eivei wKK Kiv nq, dzUejwU †m w`‡K Mov‡Z ïiæ K‡i| A_©vr dzUejwU w¯’i Ae¯’v

n‡Z Z¡iY jvf K‡i MwZkxj nq|

ej cÖ‡qv‡Mi d‡j MwZkxj e ‘i †eM e„w× n‡Z cv‡i

GKwU Mov‡bv dzUej †hw`‡K Mov‡”Q †mw`K eivei wKK Ki‡j wK N‡U? GwU Av‡iv †Rv‡o Mov‡Z ïiæ K‡i|

G‡ÿ‡Î dzUejwUi MwZ e„w× †c‡q‡Q|

ej cÖ‡qv‡M MwZkxj e¯‘i †eM n«vm cvq

Pjgvb mvB‡Kj‡K †U‡b ai‡j wK nq? Gi MwZ K‡g hvq A_©vr ej cÖ‡qv‡M e¯‘i †eM n«vm cvq|

ej cÖ‡qv‡M MwZkxj e¯‘i †e‡Mi w`K cwieZ©b n‡Z cv‡i

wµ‡KU †Ljvi mgq GKRb e¨vUmgvb ej †h w`‡K MwZcÖvß n‡q avegvb nq, Zvi wecixZ w`‡K e¨vU Øviv ej‡K

AvNvZ K‡i| e¨vU Øviv AvNvZ Kivi ci ejwUi †e‡Mi gvb I w`K Df‡qB cwieZ©b nq| ejwU †hw`‡K avegvb

wQj e¨vU Øviv AvNv‡Zi ci GwU Ab¨ w`‡K avweZ nq|

3.2.3. e ‘i AvKv‡ii Dci e‡ji cÖfve

Effect of force on the shape of a body

ej cÖ‡qvM Ki‡j wKQz wKQz e¯‘i AvKv‡ii cwieZ©b nq| G e¯‘ ‡jvi g‡a¨ i‡q‡Q, wewfbœ cvbx‡qi wU‡bi K¨vb, wUb

RvZxq e¯‘, cøvwó‡Ki †evZj, cøvwóK RvZxq

e¯‘, ivevi e¨vÛ BZ¨vw`|

wUb ev cøvwó‡Ki cvbxq enbKvix †evZj‡K

nvZ w`‡q †Rv‡o †P‡c ai‡j GwU AvKvi

cwieZ©b K‡i (wPÎ- 3.12: e¯‘i AvKv‡ii

Dci e‡ji cÖfve)| Avevi ivevi e¨v‡Ûi

`yÕcÖvšÍ a‡i †U‡b GwU j¤v Kiv hvq| hLb

GwU j¤v nq ZLb Gi ˆ`N© e„w× cvq Avi

GwU miæ n‡q hvq| A_©vr Gi AvKv‡ii cwieZ©b nq|

KL‡bv KL‡bv G AvKv‡ii cwieZ©b ÿY¯’vqx, Avevi KL‡bv KL‡bv G cwieZ©b ¯’vqx nq| †hgb: cvbxq enbKvix

wUb ev cøvwó‡Ki K¨vb nvZ w`‡q †Rv‡i †P‡c a‡i `yg‡o-gyP‡o †dj‡j, †`Lv hvq, GwU ¯’vqxfv‡e AvKvi cwieZ©b

wPÎ-3.12 : e ‘i AvKv‡ii Dci e‡ji cÖfve

GmGmwm †cÖvMÖvg


K‡i‡Q| Avevi cøvwó‡Ki †evZj‡K nvZ w`‡q nvjKv Pvc w`‡j GwU AvKv‡ii mvgvb¨ cwieZ©b K‡i, Avevi †Q‡o

w`‡j GwU Av‡Mi AvKvi aviY K‡i|

3.2.4. wbDU‡bi wØZxq m~Î : ej Ges Z¡i‡Yi g‡a¨ m¤úK©, F=ma wbY©q

Newton's second law : Relation between force and acceleration, determination of F=ma. c~‡e©i cvV †_‡K Avgiv †R‡bwQ, wbDU‡bi cÖ_g m~Î e‡ji ¸YMZ aviYv †`q| wbDU‡bi wØZxq m~Î e‡ji cwigv‡ci

mgxKiY cÖwZcv`b K‡i|

wbDU‡bi wØZxq m~Î:

Òe¯‘i fi‡e‡Mi cwieZ©‡bi nvi Gi Dci cÖhy³ e‡ji mgvbycvwZK Ges ej †hw`‡K wµqv K‡i e¯‘i fi‡e‡Mi

cwieZ©bI †mw`‡K N‡UÓ|

awi, GKwU e¯‘i fi m Ges Avw`‡eM u| GLb, m fiwewk÷ e¯‘wUi Dci F aªæe ej e¯‘wUi †e‡Mi Awfgy‡L t mgq a‡i cÖ‡qvM Ki‡j e¯‘wU †e‡Mi cwieZ©b K‡i| awi, ej cÖ‡qvM Kivi d‡j e¯‘i †e‡Mi cwieZ©b nq| d‡j

e¯‘wUi †eM u n‡Z cwiewZ©Z n‡q v nq|

e ‘wUi Avw` fi‡eM = mu

e ‘wUi †kl fi‡eM = mv

t mg‡q e¯‘i fi‡e‡Mi cwieZ©b = mvmu

myZivs, e¯‘i fi‡e‡Mi cwieZ©‡bi nvi =

tmumv

=

tuvm

= ma Z¡iY,

tuva

wbDU‡bi MwZi wØZxq m~Îvbymv‡i, e¯‘i fi‡e‡Mi cwieZ©‡bi nvi cÖhy³ e‡ji mgvbycvwZK

A_©vr Fma

ev, ma = kF

GLv‡b, k GKwU mgvbycvwZK aªæeK, Gi gvb e‡ji GK‡Ki Dci wbf©i K‡i| G mgxKiY †_‡K e‡ji GK‡Ki

msÁv cvIqv hvq| Avgiv Rvwb, e‡ji GKK wbDUb N |

hw`, 1k nq hLb

2ms1,kg1 am

ZLb NF 1 aiv nq d‡j, kFma †_‡K cvIqv hvq-

111 k ev 1k nq|

myZivs fi m †K kg , Z¡iY a †K

2ms Ges ej F †K N Øviv cÖKvk Ki‡j mgxKiY, kFma †_‡K

cvIqv hvq-

Fma 1

ev, maF ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (3.1)

ev, ej = fiZ¡iY

e‡ji gvÎv : F =

2MLT

c`v_©weÁvb


MvwbwZK D`vniY: 3.1| GKwU N588 IR‡bi e¯‘‡K

2ms70.0 Z¡iY w`‡Z Gi Dci KZ ej cÖ‡qvM Ki‡Z

n‡e?

mgvavb:

Avgiv Rvwb, maF =

20.70ms60kg GLv‡b

= N42 e¯‘i Z¡iY, a =

2ms70.0

D: N42 e¯‘i IRb, mgW

e¯‘i fi, 2ms8.9N588

g

Wm

= kg60

ej, F=?

MvwbwZK D`vniY: 3.2: GKwU evjK N60 ej Øviv kg30 f‡ii GKwU e ‘‡K av°v †`q| e ‘wUi Z¡iY KZ n‡e?

mgvavb:

Avgiv Rvwb, GLv‡b,

maF e¯‘i fi, kg30m

mF

a cÖhy³ ej, N60F

=

kg30N60

e¯‘i Z¡iY, a =?

=

2ms2 DËi:

2ms2

mvi-ms‡ÿc:

fi‡eM (Momentum): †Kvb e¯‘i fi I †e‡Mi ¸Ydj‡K Gi fi‡eM e‡j|

fi‡eM, mvp

GLv‡b, m =e¯‘i fi, v =e¯‘i †eM|

fi‡eM GKwU †f±i ivwk, Gi w`K †e‡Mi w`‡K|

wbDU‡bi wØZxq m~Î: e¯‘i fi‡e‡Mi cwieZ©‡bi nvi Gi Dci cÖhy³ e‡ji mgvbycvwZK Ges ej †hw`‡K wµqv

K‡i e¯‘i fi‡e‡Mi cwieZ©bI †mw`‡K N‡U|

wbDU‡bi wØZxq m~ÎwU e‡ji cwigv‡ci mgxKiY cÖwZcv`b K‡i|

cv‡VvËi g~j¨vqb-3.2 mwVK DË‡ii cv‡k wUK () wPý w`b

1| wbDU‡bi wØZxq m~Î cÖwZcv`b K‡i-

K) e‡ji cwigv‡ci mgxKiY L) fi‡e‡Mi cwigv‡ci mgxKiY M) †e‡Mi cwigv‡ci mgxKiY N) f‡ii cwigv‡ci mgxKiY 2| wbDU‡bi wØZxq m~Î cÖwZcv`b K‡i-

K) fi‡eM=fi†eM L) Z¡iY =

†eM

mgq

M) ej=fiZ¡iY N) ej=mgqZ¡iY

GmGmwm †cÖvMÖvg


wPÎ- 3.14: wbDU‡bi Z…Zxq m~Î

wPÎ-3.15: gvwUi Dci nuvUv

wPÎ- 3.13: wbDU‡bi Z…Zxq m~Î

cvV-3.3 wµqv I cÖwZwµqv ej t wbDU‡bi MwZi Z…Zxq m~Î

Action and reaction force : Newton's third law of motion D‡Ïk¨


wbDU‡bi MwZi Z…Zxq m~Î eY©bv Ki‡Z cvi‡eb|

wbDU‡bi MwZi Z…Zxq m~Î eënvi K‡i wµqv I cÖwZwµqv ej e¨vL¨v Ki‡Z cvi‡eb|

wbDU‡bi MwZi Z…Zxq m~‡Îi D`vniY wn‡m‡e f‚wgi Dci `vov‡bv, gvwUi Dci w`‡q nuvUv Ges jwM w`‡q †bŠKv

Pvjv‡bv e¨vL¨v Ki‡Z cvi‡eb|

fi‡e‡Mi msiÿY m~Î e¨vL¨v Ki‡Z cvi‡eb|

msNl© e¨vL¨v Ki‡Z cvi‡eb|

`ywU e ‘i msN‡l©i †ÿ‡Î fi‡e‡Mi msiÿb m~Î cÖwZcv`b Ki‡Z cvi‡eb|

3.3.1. wbDU‡bi Z…Zxq m~Î - wµqv I cÖwZwµqv ej

wbDU‡bi cÖ_g I wØZxq m~Î GKwU e¯‘i MwZ m¤ú‡K© e¨vL¨v cÖ vb K‡i‡Q wKš‘ wbDU‡bi Z…Zxq m~Î `ywU

e¯‘i cvi¯úwiK msNl© wb‡q Av‡jvPbv cÖ vb K‡i|

wbDU‡bi Z…Zxq m~Îvbymv‡i-

ÒcÖ‡Z¨K wµqviB GKwU mgvb I wecixZgyLx cÖwZwµqv Av‡QÓ|

myZivs wbDU‡bi Z…Zxq m~Îvbymv‡i, hw` GKwU e¯‘ Ab¨ GKwU e¯‘i Dci ej

cÖ‡qvM K‡i, ZLb wØZxq e¯‘wUI cÖ_g e¯‘i Dci GKwU mgvb I wecixZ gyLx ej

cÖ‡qvM K‡i| 3.13 wP‡Î, hw` GKwU e ‘ P Ab¨ GKwU e¯‘ Q Gi Dci 1F ej

cÖ‡qvM K‡i ZLb Q e¯‘wUI wbDU‡bi Z…Zxq m~Îvbymv‡i P e¯‘i Dci mgvb wKš‘

wecixZgyLx ej 2F cÖ‡qvM Ki‡e (wPÎ- 3.13: wbDU‡bi Z…Zxq m~Î)| GLv‡b P

e¯‘ KZ©„K Q e¯‘i Dci cÖhy³ ej‡K wµqv ej (Action frec) Ges Q e¯‘

KZ©„K P e¯‘i Dci cÖhy³ ej‡K cÖwZwµqv ej (Reaction force) e‡j|

myZivs wbDU‡bi Z…Zxq m~Îvbymv‡i,

21 FF

D`vnviY:

gvwUi Dci ùvov‡bv

gvwUi Dci ùvwo‡q _vK‡j gvbylwU w¯’i _v‡K| KviY, gvbylwUi IR‡bi mgvb

GKwU ej bx‡Pi w`‡K gvwUi Dci wµqv K‡i| wbDU‡bi Z…Zxq m~Îvbymv‡i,

gvwUI bxP n‡Z gvbylwUi Dci ej cÖ‡qvM K‡i| GLv‡b, gvbylwUi IRb I gvwU

Øviv cÖhy³ cÖwZwµqv ej ci¯úi mgvb I wecixZ nIqvq mv‡gï m„wó K‡i|

gvbyl Øviv gvwUi Dci cÖhy³ ej wµqv ej Ges gvwU gvbylwUi Dci †h ej

cÖ‡qvM K‡i Zv cÖwZwµqv ej (wPÎ- 3.14: wbDU‡bi Z…Zxq m~Î)|

gvwUi Dci nuvUv

gvwUi Dci nuvUvi mgq †cQ‡bi cv Øviv gvwUi Dci GKwU wZh©Kfv‡e ej cÖ‡qvM

Kiv nq| G n‡jv wµqv ej| wbDU‡bi Z…Zxq m~Îvbymv‡i, gvwUi GB e‡ji

wecix‡Z GKwU mgvb cÖwZwµqv ej m„wó K‡i cv‡qi Dci wµqv K‡i| d‡j

c`v_©weÁvb


wPÎ-3.16: wbDU‡bi Z…Zxq m~Î

wPÎ-3.17: msNl©

wPÎ-3.18 (K) wPÎ-3.18 (L) wPÎ-3.18 (M)

gvbylwU iv¯Ívi Dci w`‡q fvimvg¨ †i‡L nuvU‡Z mÿg nq (wPÎ-3.15: gvwUi Dci nuvUv)|

Av‡ivnx †bŠKv n‡Z jvwd‡q Zx‡i bvg‡j

Av‡ivnx †bŠKv n‡Z jvwd‡q Zx‡i bvg‡j, †bŠKvwU †cQ‡b P‡j hvq| KviY

Av‡ivnx jvd †`evi mgq †bŠKvi Dci ej cÖ‡qvM K‡i d‡j †bŠKvwU wcQ‡b m‡i

hvq| †bŠKvwU wbDU‡bi Z…Zxq m~Îvbymv‡i, Av‡ivnxi Dci GKwU mgvb I

wecixZgyLx ej cÖ‡qvM K‡i hv Av‡ivnx‡K mvg‡bi Zx‡ii w`‡K jvwd‡q co‡Z

mvnvh¨ K‡i (wPÎ-3.16: wbDU‡bi Z…Zxq m~Î)|

3.3.2 fi‡e‡Mi msiÿb m~Î I msNl©

Conservation law of momentum and collision: GKvwaK e¯‘i g‡a¨ wµqv I cÖwZwµqv wfbœ Ab¨ †Kvb ej bv _vK‡j †h †Kv‡bv

w`‡K Zv‡`i †gvU fi‡e‡Mi †Kv‡bv cwieZ©b nq bv| GwU fi‡e‡Mi wbZ¨Zv ev

msiÿY m~Î|

moK `yN©Ubvi mKj NUbvB msNl© (wPÎ-3.17: msNl©)| gv‡e©j †Ljvi mgq

GKwU gv‡e©j‡K jÿ¨ K‡i Av‡iKwU gv‡e©j gviv nq| wØZxq gv‡e©jwU hw` cÖ_g

gv‡e©jwU‡K AvNvZ K‡i, Z‡e G‡K ywU gv‡e©‡ji g‡a¨ msNl© N‡U‡Q ejv hvq|

fi‡e‡Mi msiÿY m~‡Îi e¨vL¨v: g‡b Kwi, 1m I 2m fiwewkó `yÕwU e¯‘ h_vµ‡g 1u I 2u †e‡M GKB mij‡iLv

eivei Pj‡Q (wPÎ-3.18 (K)| AZGe e¯‘ `yÕwUi fi‡eM h_vµ‡g 11um I 22um | Kv‡RB e¯‘ `yÕwUi Avw`

fi‡e‡Mi mgwó 2211 umum |

GLv‡b 1m Gi †eM 2m Gi †e‡Mi †P‡q †ewk n‡j †Kvb GKmgq 1m e¯‘wU 2m e¯‘wU‡K av°v w`‡e (wPÎ-3.18

(L)|

1m e¯‘wU hw` 2m e¯‘wU‡K av°v †`q, Z‡e wbDU‡bi Z…Zxq m~Îvbymv‡i 2m e¯‘wUI 1m e¯‘wU‡K mgvb I wecixZ

av°v cÖ‡qvM Ki‡e| GLv‡b 1m e¯‘ 2m e¯‘i

Dci wµqv ej Ges 2m e¯‘ 1m e¯‘i Dci

cÖwZwµqv ej cÖ‡qvM Ki‡e| awi, wµqv I

cÖwZwµqvi mgq t | msN‡l©i ci e¯‘ `yBwU

cwiewZ©Z †e‡M GKB mij‡iLvq Pj‡Z _vK‡e

(wPÎ-3.18 (M)| awi, wµqv I cÖwZwµqvi ci e¯‘

`yBwUi †eM 1v I 2v | AZGe, wµqv I

cÖwZwµqvi ci 1m Ges 2m e ‘ `yÕwUi fi‡eM

h_vµ‡g 11vm I 22vm n‡e| Kv‡RB wµqv I

cÖwZwµqvi ci e¯‘ ywUi †gvU fi‡eM= 2211 vmvm |

wKš‘ fi‡e‡Mi wbZ¨Zv m~Îvbymv‡i,

wµqv I cÖwZwµqvi c~‡e© †gvU fi‡eM=wµqv I cÖwZwµqvi c‡i †gvU fi‡eM,

22112211 vmvmumum ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... (3.2)

fi‡e‡Mi wbZ¨Zv m~‡Îi MvwYwZK cÖgvY : g‡b Kwi, GKB mij‡iLvq Ges GKB w`‡K 1m Ges 2m fiwewkó `yÕwU

e¯‘ h_vµ‡g 1u Ges 2u Avw`‡e‡M Pj‡Q (wPÎ 3.18) GLv‡b 1m e¯‘wUi †eM 21, mu e¯‘wUi †eM 2u Gi †P‡q

†ewk|

1m Gi †eM †ewk nIqvq GwU hvÎvKv‡ji †h †Kv‡bv gyn~‡Z© 1m e¯‘wU wcQb n‡Z 2m e ‘wU av°v w`‡e| d‡j e ‘

`ywU GKB w`‡K mij c‡_ P‡j wµqv ev cÖwZwµqv Kvj t †Z h_vµ‡g 1v I 2v †eM cÖvß n‡e|

GmGmwm †cÖvMÖvg


1m e ‘wUi Avw` †eM = 1u

1m e ‘wUi msN‡l©i c‡i †eM = 1v

1m e ‘wUi †e‡Mi cwieZ©b = 11 uv

1m e ‘wUi †e‡Mi cwieZ©‡bi nvi =

tuv 11

Avevi 2m e¯‘wUi Avw` †eM = 2u

2m e ‘wUi msN‡l©i c‡i †eM = 2v

2m e ‘wUi †e‡Mi cwieZ©b = 22 uv

2m e ‘wUi †e‡Mi cwieZ©‡bi nvi =

tuv 22

wµqv I cÖwZwµqv e‡ji d‡j e ‘ yÕwUi Z¡iY hw` h_vµ‡g 1a I 2a n‡j, wbDU‡bi Z…Zxq m~Î Abyhvqx-

21 FF

ev, 2211 amam ev,

tuvm

tuvm 22

211

1

ev, 22221111 umvmumvm

ev, 22112211 vmvmumum

wµqvi c~‡e© fi‡e‡Mi mgwó = wµqvi c‡i fi‡e‡Mi mgwó|

myZivs Dc‡ii mgxKiY †_‡K ejv hvq †h, GKvwaK e¯‘i wµqv I cÖwZwµqv wfbœ Ab¨ †Kvb ej KvR bv Ki‡j

wµqvi c~‡e©i fi‡e‡Mi mgwó Ges wµqvi c‡ii fi‡e‡Mi mgwó AcwiewZ©Z _v‡K| BnvB fi‡e‡Mi msiÿY m~Î|

MvwYwZK D`vniY 3.3| GKwU g10 f‡ii ¸wj kg2 f‡ii GKwU e›`y‡Ki bj n‡Z

1ms300 †e‡M †ei n‡q

†Mj| e›`y‡Ki cðvr †eM wbY©q Ki|

mgvavb: awi, ¸wji †e‡Mi w`K A_©vr m¤§yL w`K abvZ¥K|

fi‡e‡Mi msiÿY m~Î n‡Z Avgiv cvB-

‡gvU Avw` fi‡eM = †gvU †kl fi‡eM,

GLv‡b,

22112211 vmvmumum ¸wji fi,

31 101010 gm

= kg10 2

ev, 11221122 vmumumvm e›`y‡Ki fi, kg22 m

ev,

2

1122112 m

vmumumv ¸wji Avw`‡eM, 01 u

e›`y‡Ki Avw`‡eM, 02 u

¸wji †kl †eM,

11 ms300 v

e›`y‡Ki, †kl‡eM, ?2 v

=

2kg300mskg1002kg0kg10 122

=

11

1.5ms2kg

3kgms

GLv‡b, e›`y‡Ki †eM FYvZ¥K A_©vr e› yKwU wcQb w`‡K MwZkxj n‡e|

DËi: cðvr †eM =

11.5ms

c`v_©weÁvb


MwYwZK D`vniY 3.4: kg4 f‡ii GKwU e¯‘

113ms †e‡M mij‡iLvq PjšÍ Ae¯’vq

110ms †e‡M GKB w`‡K

MwZkxj 2kg f‡ii GKwU e¯‘i mv‡_ GKmv‡_ wg‡j GKwU e¯‘‡Z cwiYZ n‡q, GKmv‡_ Pj‡Z _v‡K| wgwjZ

nIqvi ci Gi †eM KZ n‡e wbY©q Ki|

mgvavb:

fi‡e‡Mi msiÿY m~Î n‡Z Avgiv cvB-

‡gvU Avw` fi‡eM=‡gvU †kl fi‡eM

22112211 vmvmumum GLv‡b,

ev, vmvmumum 212211 cÖ_g e¯‘i fi, 1m = kg 4

ev,

21

2211

mmumumv

wØZxq e¯‘i fi, 2m = kg 2

= kg24ms10kg2ms13kg4 11

cÖ_g e¯‘i Avw`‡eM,

11 ms13 u

=

kg6kgms20kgms 52 11

wØZxq e¯‘i Avw`‡eM,

12 ms10 u

=

11

ms12kg6

kgms 72

cÖ_g e¯‘i †kl‡eM, vv 1

wØZxq e¯‘i †kl‡eM, vv 2

wgwjZ e¯‘i †kl‡eM, ?v

D: wgwjZ nIqvi ci †eM n‡e

1ms12

mvi-ms‡ÿc:

wbDU‡bi Z…Zxq m~Î (Newton's third law) : cÖ‡Z¨K wµqviB GKwU mgvb Ges wecixZ gyLx cÖwZwµqv

Av‡Q|

fi‡e‡Mi msiÿY m~Î (Conservation law of motion) : GKvwaK e¯‘i g‡a¨ wµqv I cÖwZwµqv wfbœ Ab¨

†Kv‡bv ej bv _vK‡j, †h †Kv‡bv w`‡K Zv‡`i †gvU fi‡e‡Mi †Kv‡bv cwieZ©b nq bv| GwU fi‡e‡Mi wbZ¨Zv

ev msiÿY m~Î|

msNl© (Collision) : †Kv‡bv GKwU MwZkxi e¯‘ hLb Ab¨ †Kv‡bv GKwU MwZkxj e¯‘‡K av°v †`q, ZLb e¯‘

`yÕwUi g‡a¨ msNl© n‡q‡Q ejv nq|



1| wb‡Pi †Kvb welqwU wbDU‡bi Z…Zxq m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq?

K) RoZv L) ej M) fi‡e‡Mi msiÿY m~Î N) kw³

GmGmwm †cÖvMÖvg


cvV-3.4 Nl©Y

Friction D‡Ïk¨


wewfbœ cÖKvi Nl©Y I Nl©Y ej e¨vL¨v Ki‡Z cvi‡eb|

e¯‘i MwZi Dci Nl©‡Yi cÖfve e¨vL¨v Ki‡Z cvi‡eb|

Nl©Y n«vm-e„w× Kivi Dcvq eY©bv Ki‡Z cvi‡eb|

Nl©Y GKwU cÖ‡qvRbxh Dc`ªe-e¨vL¨v Ki‡Z cvi‡eb|

3.4.1. Nl©Y I Nl©Y ej

Friction and force of friction Rxe‡bi wewfbœ ch©v‡qB Avgiv Nl©Y ev Nl©Y e‡ji gy‡LvgywL nB| wKš‘ G AwfÁZv‡K nqZ Avgiv

A‡b‡KB c`v_©weÁv‡bi fvlvq Rvwb bv, AvR Avgiv cÖvZ¨wnK Rxe‡bi mv‡_ wgwj‡q Nl©Y I Nl©Y e‡ji mv‡_

cwiwPZ ne|

wbDU‡bi MwZi cÖ_g m~Î †_‡K Avgiv Rvwb †h, †Kv‡bv e¯‘i Dci evwn¨K †Kv‡bv ej wµqv bv Ki‡j, w¯’i e¯‘ w¯’i

_vK‡e| MwZkxj e¯‘ mg‡eM mijc‡_ Pj‡Z _vK‡e| wKš‘ ev¯Í‡e Avgiv wK †`L‡Z cvB? GKwU †Ljbv †gvUi‡K

†g‡Si Dci w`‡q Mwo‡q w`b| †LjbvwU‡K hLb †g‡Si Dci w`‡q Mwo‡q †`qv nq, ZLb Gi Dci ej cÖ‡qvM Kiv

nq| d‡j †LjbvwU †g‡Si Dci MwZkxj nq| wbDU‡bi cÖ_g m~Îvbymv‡i, †LjbvwU †g‡Si Dci mg‡e‡M MwZkxj

_vKvi K_v| wKš‘ ev¯Íe †ÿ‡Î †`Lv hvq †h, †LjbvwU wKQz`~i hvIqvi ci †_‡g †M‡Q| †g‡Si mv‡_ †LjbvwUi

cvi¯úwiK Nl©‡Yi d‡j †LjbvwU wKQz `~i hvIqvi ci †_‡g hvq| †LjbvwU hLb †g‡Si Dci MwZkxj _v‡K, ZLb

†Ljbv I †g‡Si cvi¯úwiK Nl©‡bi d‡j GKwU Nl©Y e‡ji DrcwË nq| G Nl©Y ej MwZi wecixZ w`‡K wµqv K‡i

Ges †Ljbvi MwZ‡K evavMÖ Í K‡i| hw` †Ljbv Ges gv‡e©‡ji g‡a¨ Nl©Y ej wµqv bv KiZ Z‡e †LjbvwU mg‡e‡M

Aweivg Pj‡Z _vKZ|

`ywU e¯‘ ci¯ú‡ii ms¯ú‡k© †_‡K hw` GKwU Dci w`‡q AciwU Pj‡Z †Póv K‡i, Z‡e e¯‘ `yÕwUi ¯úk©Z‡j GKwU

evavi DrcwË m„wó nh, G evav‡K Nl©Y e‡j| Avi †h ej MwZkxj e¯‘wUi MwZi c‡_ evav m„wó K‡i, Zv‡K Nl©Y ej

e‡j|

3.4.4 Nl©‡Yi DrcwË

Production of friction

Avgiv Rvwb †h, hLb GKwU e¯‘i Zj Aci e¯‘i Z‡ji Dci w`‡q MwZkxj nq| ZLb cÖ‡Z¨K e¯‘ G‡K Ac‡ii

Dci Nl©Y ej cÖ‡qvM K‡i| GLb G Nl©Y e‡ji DrcwË nq wKfv‡e? cÖ‡Z¨K e¯‘iB Zj i‡q‡Q| Lvwj †Pv‡L G

Zj¸‡jv‡K hZB gm„Y †`LvK bv †Kb, †Kvb e¯‘B m¤ú~b© gm„Y n‡Z cv‡i bv| AbyexÿY h‡š¿i mvnv‡h¨ †`L‡j Gi

DuPz wbPz LuvR¸wj †`Lv hvq| d‡j hLb GKwU e ‘ Aci e¯‘i Dci w`‡q Pjvi †Póv K‡i ZLb e ‘ ywUi LuvR¸‡jv

G‡K Ac‡ii mv‡_ AvU‡K hvq| d‡j GKwU Z‡ji Dci w`‡q Aci Z‡ji MwZ evavcÖvß nq| e¯‘ wji Zj hZ

Agm„Y n‡e A_©vr Z‡ji DPz wbPz LuvR hZ †ewk Ges Mfxi n‡e, GK Z‡ji Dci w`‡q Aci Zj Pjvi mgq ZZ

†ewk evavMÖ Í n‡e| d‡j Nl©Y e‡ji gvbI †e‡o hv‡e| ¯úk©Z‡ji ga¨Kvi G evav‡K AwZµg Ki‡Z cvi‡j Z‡eB

e¯‘wU MwZkxj n‡e| Nl©‡bi d‡j Z‡ji Dci w`‡q Pjgvb e¯‘wUi MwZ evavcÖvß nq Ges Ae‡k‡l †_‡g hvq|

c`v_©weÁvb


wPÎ- 3.19: w ’wZ Nl©Y

wPÎ- 3.20: Pj ev wcQjv‡bv Nl©Y

3.4.3 Nl©‡Yi cÖKvi‡f`

Types of friction

Nl©Y mvaviYZ Pvi cÖKvi nq-

1. w¯’wZ Nl©Y (Static friction)

2. Pj ev wcQjv‡bv Nl©Y (Sliding friction)

3. AveZ© Nl©Y (Rolling friction) Ges

4. cÖevnx Nl©Y (Fluid friction)

w¯’wZ Nl©Y

`ywU e¯‘i Zj ci¯ú‡ii ms¯ú‡k© †_‡K GKwUi mv‡c‡ÿ AciwU MwZkxj bv n‡j, G‡`i wgjb Z‡j †h Nl©‡Yi m„wó

nq, Zv‡K w ’wZ Nl©Y e‡j|

†Kv‡bv e¯‘i Dci ej cÖ‡qvM Kivi c‡iI hw` e¯‘wU MwZkxj bv nq ZLb w¯’wZ

Nl©Y KvR K‡i| †hgb GKwU fvix ev·‡K ej cÖ‡qvM Kivi ciI hw` GwU ¯’vb

cwieZ©b bv K‡i A_©vr MwZkxj bv n‡j †h Nl©Y e‡ji DrcwË nq, Zv‡K w¯’wZ

Nl©Y ej e‡j, Avi G evav‡K w¯’wZ Nl©Y e‡j (wPÎ- 3.19: w¯’wZ Nl©Y)| AZGe

`yÕwU e¯‘ ci¯ú‡ii ms¯ú‡k© _vKv Ae¯’vq ej cÖ‡qv‡M GKwU‡K AciwUi Dci

MwZkxj Kivi †Póv Kiv n‡j, GKwU e¯‘ Aci GKwU e¯‘i Dci w`‡q MwZkxj

nIqvi c~e© gyn~Z© ch©šÍ †h Nl©Y ej wµqv K‡i Zv‡K w ’wZ Nl©Y e‡j|

Pj ev wcQjv‡bv Nl©Y:

hLb GKwU e¯‘ Ab¨ GKwU e¯‘i Z‡ji Dci w`‡q wcQwj‡q ev †N‡l P‡j

ev Pj‡Z †Póv K‡i (wPÎ- 3.20: Pj ev wcQjv‡bv Nl©b), ZLb MwZi

weiæ‡× †h Nl©‡Yi m„wó nq Zv‡K Pj ev wcQjv‡bv Nl©Y e‡j| Mvwo iv¯Ívi

Dci w`‡q Pjvi mgq nvW© †eªK Ki‡j, nvW© †eªK Kivi ciI MvwowU

wKQz`~i GwM‡q hvIqvi ci ev wKQzUv `~iZ¡ AwZµg Kivi ci _v‡g| A_©vr

MvwoUv wcQwj‡q wKQz`~i AwZµg K‡i| wcw”Qj iv¯Ívi Dci w`‡q Pjvi

mgq A‡bK mgq Avgiv LvwbKUv `~iZ¡ AwZµg Kivi ci c‡o hvB Ges

ewj wcQ‡j c‡o †MwQ| Dc‡ii `yÕwU NUbvB Pj ev wcQjv‡bv Nl©‡Yi

D`vniY|

AveZ© Nl©Y:

hLb GKwU e¯‘ Ab¨ GKwU e¯‘i Z‡ji Dci w`‡q Mwo‡q P‡j ZLb MwZi weiæ‡× †h

Nl©‡Yi m„wó nq Zv‡K AveZ© Nl©Y e‡j| AvaywbK mKj myU‡K‡m ev jv‡M‡R PvKv

jvMv‡bv _v‡K| PvKv jvMv‡bvi d‡j myU‡Km ev jv‡MR‡K mn‡R Avgiv PvKvi mvnv‡h¨

†g‡Si Dci w`‡q GK¯’vb †_‡K Ab¨¯’v‡b wb‡Z cvwi (wPÎ- 3.21: AveZ© Nl©b)| PvKv

bv jvMv‡bv _vK‡j myU‡Km ev jv‡MR‡K GK¯’vb †_‡K Ab¨¯’v‡b †bqv Kómva¨ n‡q

†hZ| G NUbv †_‡K †evSv hvq, wcQjv‡bv Nl©‡bi Rb¨ †h ej MwZi weiæ‡× m„wó nq

Zvi gvb AveZ© Nl©‡Yi Rb¨ m„ó e‡ji gv‡bi †P‡q †ewk| mvB‡K‡ji PvKvi MwZ,

gv‡e©‡ji MwZ AveZ© Nl©‡Yi D`vniY|

wPÎ- 3.21: AveZ© Nl©Y

PvKv

GmGmwm †cÖvMÖvg


wPÎ- 3.22: cÖevnx Nl©Y

wPÎ-3.23: †eqvwis

cÖevnx Nl©Y

hLb †Kv‡bv e¯‘ †h‡Kv‡bv cÖevnx c`v_© †hgb- Zij ev evqexq c`v‡_©i g‡a¨ cÖevwnZ nq ev MwZkxj _v‡K ev hLb

†Kv‡bv Zij ev evqexq c`v‡_©i MwZc‡_ †Kv‡bv w¯’i e¯‘ ivLv nq, ZLb Df‡qi g‡a¨ †h Nl©‡Yi m„wó nq Zv‡K

cÖevnx Nl©Y e‡j|

RvnvR cvwb‡Z Pjvi mgq GKwU evav AwZµg K‡i mvg‡bi w`‡K GwM‡q

hvq, Avevi cyKz‡i muvZvi KvUvi mgq cyKz‡ii cvwbi ga¨ w`‡q GKwU

evav‡K AwZµg K‡i mvg‡bi w`‡K G¸‡Z nq (wPÎ- 3.22: cÖevnx

Nl©Y)| Avi G evavB cÖevnx Nl©Y|

e„wói cvwb evZv‡mi ga¨ w`‡q covi mgq cÖevnx Nl©‡Yi DrcwË nq|

3.4.4 Nl©‡Yi n«vm e„w×

Increase and decrease of friction

‰`bw›`b Rxe‡b Avgiv bvbv Kv‡Ri gva¨‡g Nl©‡Yi mv‡_ cwiwPZ nB| Nl©‡Yi Kvi‡Y Avgiv bvbv iKg myweav

Amyweavi m¤§yLxb nB| G mKj Amyweav‡K Nl©Y evwo‡q ev Kwg‡q `~i Kiv †h‡Z cv‡i| GLb Avgiv Nl©Y‡K

Kxfv‡e n«vm I e„w× Kiv hvq Zv wb‡q Av‡jvPbv Kie|

Nl©‡Yi n«vm

Decrease of friction

Zj‡K gm„Y Kiv

GKwU fvix e¯‘‡K †U‡b GK ¯’vb †_‡K Ab¨ ¯’v‡b †bqv Kómva¨| fvix e¯‘wUi ¯úk©Zj hw` Agm„Y nq Z‡e †g‡Si

Dci w`‡q Uvbvi mgq Nl©‡Yi cwigvY †ewk n‡e| Kv‡RB e¯‘wU‡K GK ¯’vb †_‡K Ab¨ ¯’v‡b wb‡Z cwikÖg †ewk

Ki‡Z n‡e| fvix e¯‘wUi Zj‡K gm„Y Ki‡j Nl©‡Yi cwigvY n«vm cv‡e Ges A‡c¶vK…Z Kg cwikÖ‡g e¯‘wU‡K

GK¯’vb †_‡K ’v‡b †bqv hv‡e|

PvKvi eënvi

wewfbœ e¯‘‡K GK ¯’vb †_‡K Ab¨ ¯’v‡b †bqv ev wewfbœ e¯‘i GK ¯’vb †_‡K Ab¨ ¯’v‡b hvIqvi †ÿ‡Î PvKvi e¨venvi

AZ¨vek¨Kxq| PvKv eënvi bv Ki‡j evm, UªvKmn wewfbœ hš¿cvwZi Pvjv‡bv m¤¢e wQj bv| PvKvi Zj iv¯Ívi Dci

w`‡q Mwo‡q Pjvi Kvi‡Y GwU wcQwj‡q iv¯Ívi Dci w`‡q Pjvi †P‡q A‡bK Nl©Y e‡ji cwigvY bvwg‡q Av‡b| PvKv

jvMv‡bvi d‡j AveZ© Nl©‡Yi gvb wcQjv‡bv Nl©‡Yi Zzjbvq A‡bK K‡g hvq| myU‡K‡m PvKv jvMv‡bvi Kvi‡Y GwU

Uvbv mnRZi nq|

wcw”QjKvix c`v‡_©i eënvi

wcw”QjKvix c`v_© †hgb †Zj, gwej, wMÖR RvZxq c`v_© `ywU e¯‘i Z‡ji gaëZ©x ¯’v‡b eënvi K‡i Nl©‡bi cwigvb

n«vm Kiv hvq| G mKj wcw”QjKvix c`v_© wewfbœ BwÄ‡bi hš¿vs‡ki g‡a¨ e¨venvi K‡i Nl©‡Yi cwigvY n«vm Kiv

nq| Kv‡RB BwÄbwU my›ìfv‡e P‡j| †mjvB †gwk‡b †Zj eënvi Kiv nq hv‡Z GwU A‡cÿvK…Z Kg cwikÖ‡g

Pvjbv Kiv hvq|

ej-‡eqvwis -Gi eënvi

ej-‡eqvwis-Gi Avwe®‹vi PvKvi Avwe®‹v‡ii gZB hš¿cvwZi mPjZvi †ÿ‡Î ¸iæZ¡c~Y©

f‚wgKv †i‡L‡Q| wewfbœ h‡š¿i hš¿vs‡ki ms¯ú‡k© _vKv MwZkxj `yÕwU Z‡ji g‡a¨ mivmwi

Nl©Y A_©vr wcQjv‡bv Nl©Y Gov‡bvi Rb¨ ej-‡eqvwis eënvi Kiv nq (wPÎ-3.23:

†eqvwis)| Kv‡RB ej †eqvwis Gi eënvi wcQjv‡bv Nl©‡Yi cwie‡Z© AveZ© Nl©‡Yi m„wó

K‡i| d‡j Nl©‡Yi cwigvY n«vm cvq| ej-‡eqvwis-Gi eënv‡ii D`vniY n‡jv Mvwoi

PvKv, mvB‡Kj Ges ê`y¨wZK cvLv|

c`v_©weÁvb


Nl©‡Yi e„w×:

iv¯Ívi gm„YZv n«vm

wcw”Qj ev K`©gv¯Í iv¯Ívq UªvK ev evm Pj‡Z Amyweav nq Ges A‡bK mgq GK ¯’v‡b AvU‡K hvq| wcw”Qj ev

K`©gv³ iv¯Ívq PvKvi mv‡_ iv¯Ívi Z‡ji Nl©‡Yi cwigvY Kg nq| K`©gv³ iv¯Ívq DuPz wbPz LuvR bv _vKvq PvKvwUi

iv¯ÍvwU‡K AuvK‡o a‡i mvg‡b G‡Mv‡Z Amyweav nq| G Kvi‡Y Mvwoi Uvqvi‡K Ggbfv‡e ˆZwi Kiv nq †hb GwU

Pjvi mgq iv¯Ív‡K fv‡jvfv‡e AvK‡o a‡i iv‡L Ges mvg‡b G‡Mv‡bvi Rb¨ cwigvYg‡Zv Nl©Y ej m„wó K‡i|

UvqviwUi Dc‡ii c„‡ô wewfbœ ai‡bi LuvR KvUv ev ùvZ _v‡K| Gfv‡e Uvqv‡ii Zj‡K Agm„Y Kivi gva¨‡g Nl©Y‡K

evov‡bv nq|

RyZvi wb‡P LuvR KvUv

wbivc‡` nuvUvi Rb¨ Nl©Y LyeB cÖ‡qvRb| RyZv Ggbfv‡e ˆZix Kiv nq †hb Gi Zj‡`k †XD †Ljv‡bv ev LuvR KvUv

_v‡K| Gi d‡j RyZvi LvR¸‡jv iv Ív‡K AvK‡o a‡i Ges cwigvY g‡Zv Nl©Y ej m„wó K‡i| RyZv I iv¯Ívi g‡a¨

Nl©Y ej evov‡bvi Rb¨ RyZvi Giƒc wWRvBb Kiv nq| RyZv cyi‡bv n‡j LuvR¸‡jv A‡bKvs‡k mgZj n‡q hvq| G

mgq wcw”Qj ev †fRv iv Ívq RyZv cv‡q PjvPj KóKi nq| Avgv‡ì cv‡qi ZjvI mgZj bq|

3.4.5. Nl©Y : GKwU cÖ‡qvRbxq Dc`ªe

Friction : a necessary disturbance

Nl©‡Yi d‡j Avgiv Avgv‡ì cÖvZ¨wnK Rxe‡bi wewfbœ Kg©Kv‡Û Amyweavi m¤§yLxb nB| wKš‘ Nl©Y Qvov Avgv‡ì

Rxe‡bi Kg©KvÛ ¯’wei n‡q co‡Zv|

Nl©‡Yi d‡j Avgv‡ì cÖvZ¨wnK Rxe‡bi A‡bK Kg©KvÛB Amyweavi m¤§yLxb n‡jI, GwU Qvov Avgv‡ì ˆ`bw›`b

Rxeb ¯’wei| Nl©Y Qvov †h †Kv‡bv e¯‘B nq Awiivg Pj‡Zv A_ev Pj‡Z cvi‡Zv bv| Nl©Y Qvov Av¸b R¡j‡Zv bv|

Av¸b Qvov ivbœvmn ˆ`bw›`b Rxe‡bi A‡bK KvRB Am¤¢e| Nl©‡Yi Kvi‡Y cvKv `vjvb I evwoNi wbg©vb Kiv m¤¢e

n‡q‡Q| RyZv I iv¯Ívi g‡a¨ Nl©‡bi d‡j Avgiv nuvUvPjv Ki‡Z cvwi| Nl©‡Yi Rb¨ Avgiv Mvwoi MwZ wbqš¿Y Ki‡Z

cvwi| Nl©‡Yi Rb¨ Avgiv KvM‡R wjL‡Z cvwi|

Nl©‡Yi Kvi‡Y Avgiv A‡bK Amyweavi m¤§yLwb nB| wewfbœ h‡š¿i, hš¿vs‡ki g‡a¨ µgvMZ Nl©‡bi d‡j h‡š¿i

Avqy®‹vj K‡g hvq| †h †Kvb ai‡bi R¡vjvwb PvwjZ hvbevnb‡K AwZwi³ Nl©Y AwZµg Ki‡Z n‡j R¡vjvwb kw³i

AcPq nq| Avgiv gvbyl PvwjZ hvbevn‡bi †ÿ‡Î AwZwi³ cwikÖ‡gi cÖ‡qvRb nq hvbevnbwU‡K PvwjZ Ki‡Z|

Nl©‡Yi d‡j wewfbœ wRwblcÎ ÿqcÖvß nq| d‡j †`Lv hvq †h, Rxeb hvc‡bi †ÿ‡Î ‡hgb Nl©‡Yi cÖ‡qvRb

AZ¨vek¨Kxq †Zgwb AwZwi³ Nl©‡Yi AwfÁZv d‡j Avgiv wKQz Amyweavi m¤§yLxb nB| G Kvi‡YB Nl©Y‡K ejv nq

GKwU cÖ‡qvRbxq Dc`ªe|

mvi-ms‡ÿc:

Nl©Y I Nl©Y ej: `yÕwU e¯‘ ci¯ú‡ii ms¯ú‡k© †_‡K hw` GKwUi Dci w`‡q AciwU Pj‡Z †Póv K‡i, Z‡e e ‘

`yÕwUi ¯úk© Z‡j GKwU evavi m„wó nq| G evav‡K Nl©Y e‡j| Avi †h ej MwZkxj e¯‘wUi MwZi c‡_ evav m„wó

K‡i, Zv‡K Nl©Y ej e‡j|

Nl©Y mvavibZ Pvi cÖKvi-

1. w ’wZ Nl©Y (Static friction)

2. Pj ev wcQjv‡bv Nl©Y (Sliding friction)

3. AveZ© Nl©Y (Rolling friction)

4. cÖevnx Nl©Y (Fluid friction)

GmGmwm †cÖvMÖvg




1| myU‡Km ev jv‡MR‡K †g‡Si Dci w`‡q GK ¯’vb †_‡K Ab¨ ¯’v‡b wb‡Z †h Nl©‡bi m„wó nq Zv‡K e‡jÑ

K) cÖevnx Nl©Y L) AveZ© Nl©Y M) w¯’wZ Nl©Y N) wcQjv‡bv Nl©Y

2| Avgiv hLb evqy, cvwbi ga¨ w`‡q PjvPj Kwi, ZLb †Kvb Nl©‡bi m„wó nq?

K) w¯’wZ Nl©Y L) Pj Nl©Y

M) cÖevnx Nl©Y N) AveZ© Nl©Y

cvV-3.5 wbivc` ågY (Safe Journey)

D‡Ïk¨


wbivc` åg‡Yi †ÿ‡Î MwZ I e‡ji cÖfve e¨vL¨v Ki‡Z cvi‡eb|

wbivc` åg‡Yi †ÿ‡Î Nl©‡bi cÖfve eY©bv Ki‡Z cvi‡eb|

wbivc` åg‡Yi †ÿ‡Î UªvwdK AvBb †g‡b Pjvi cÖ‡qvRbxqZv e¨vL¨v Ki‡Z cvi‡eb|

3.5.1. wbivc` ågb t MwZ I ej

Safe journey : force and motion ˆ`bw›`b wewfbœ cÖ‡qvR‡b Avgiv GK ¯’vb †_‡K Ab¨ ¯’v‡b ågY Kwi| G ågY Avgiv wewfbœ hvbevn‡bi

gva¨‡g Kwi| mvaviYZ: mvB‡Kj, †gvUi mvB‡Kj, wi·v, cÖvB‡fU Mvwo, evm, jwi, UªvK, †Uªb BZ¨vw` hvbevn‡b

Avgv‡`i †`‡k hvÎxiv hvZvqvZ K‡ib, gvjvgvj cwienb K‡i| Gme hvbevnb Pjvi mgq Gi MwZ g~L¨ f‚wgKv

cvjb K‡i| wbivc‡` åg‡Yi Rb¨ Mvwoi MwZ wbqš¿Y Riæix| Mvwoi MwZ Ggb nIqv DwPr †hb PvjK †h †Kv‡bv

cwiw¯’wZ‡Z Mvwo‡K wbqš¿‡Y ivL‡Z cv‡ib| KviY Mvwoi MwZ A_©vr †eM wØ¸Y n‡j Gi fi‡eM c~‡e©i Zzjbvq wØ¸Y

nq| †eM wZb¸Y, Pvi¸Y n‡j Gi fi‡eM h_vµ‡g wZb¸Y I Pvi¸Y nq| d‡j Mvwoi Pvj‡Ki c‡ÿ †eM Kgv‡bv

ev wbqš¿Y KwVb n‡q c‡o Ges fqven `yN©Ubv N‡U|

Mvwoi PvjK‡K ågY ïiæ Kivi c~‡e©B Mvwo fv‡jvfv‡e cixÿv K‡i wb‡Z n‡e| Mvwoi †eªK, Mvwoi Uvqvi, Mvwoi

BwÄb, Mvwoi nb©, Mvwoi mKj evwZ wVKg‡Zv KvR K‡i wKbv cixÿv K‡i wbwðZ n‡Z n‡e| Mvwoi `c©Y¸‡jv‡K

cÖ‡qvRb Abyhvqx euvwK‡q wb‡Z n‡e|

Mvwoi PvjK Ges Av‡ivnx Dfq‡KB wmU †eë Aek¨B †eu‡a †bIqv DwPr| wmU †eë bv euva‡j, Mvwo nvW© †eªK

Ki‡j yN©Ubv NUvi m¤¢vebv _v‡K|

Mvwo m¤ú‡K© c~e© AwfÁZv Qvov †Kvb PvjK ivLv wVK bv ev c~e© AwfÁZv Qvov Pvj‡KiI Mvwo Pvjv‡bv DwPr bv|

G‡Z Mvwoi, Mvwoi PvjK wb‡R Ges hvÎxiv gvivZ¥K `yN©Ubvi m¤§yLxb n‡Z cv‡i|

Mvwo Pvjv‡bvi mgq Aek¨B UªvwdK AvBb †g‡b Pj‡Z n‡e| †gvo †Nvivi mgq mZK©Zv Aej¤b Ki‡Z n‡e|

A‡bK mgq 90

0

†Kv‡Y euvK wb‡Z nq| G euvK †bqvi mgq Mvwo PvjK‡K h‡_ó mveavbZv Aej¤b Kiv DwPr|

`c©‡bi w`‡K ZvwK‡q euv‡Ki Av‡k cv‡ki `„k¨ †`Lv †bqv cÖ‡qvRb| Zvn‡j wbivc‡` euvK †Nviv m¤¢e| UªvwdK mvBb

c`v_©weÁvb


wPÎ-3.24: Uvqvi

Ges UªvwdK AvBb †g‡b Pjv Mvwo Pvj‡Ki `vwqZ¡| cÖvB‡fU Mvwoi †ÿ‡Î Mvwoi gvwj‡KiI UªvwdK AvBb m¤ú‡K©

AeMZ nIqv DwPr| Mvwo Pvjbvi mgq Mvwo PvjK‡K Mvwo Pvjbvi †ÿ‡Î m¤ú~Y©iæ‡c g‡bvwb‡ek Ki‡Z n‡e Ges G

e¨vcv‡i Mvwoi hvÎx‡ìI Mvwoi PvjK‡K mvnvh¨ Ki‡Z n‡e|

3.5.2. MwZi Dci Nl©‡bi cÖfve

Effect of friction on motion

e¯‘i MwZ Ges Nl©Y GKmv‡_ hy³ n‡h e¯‘i Pjvi cÖK…Z MwZ wba©viY K‡i| Nl©Y n‡jv

GK ai‡bi evav`vbKvix ej, hv e¯‘i MwZ Kwg‡q †`q| hvbevnb Pvjbv Ges Avgv‡ì

PjvP‡ji †ÿ‡Î Nl©‡Yi f‚wgKv ¸iæZ¡c~Y©| PjvPj Ges hvbevnb Pvjbvi †ÿ‡Î Nl©Y

wKfv‡e cÖfve †d‡j Zv wb‡P Av‡jvPbv Kiv nj|

Uvqv‡ii c„ô

e¯‘i MwZ wbf©i K‡i Uvqvi c„‡ôi gm„YZvi Dci| Mvwoi Uvqvi Ges iv¯Ívi g‡a¨ Nl©‡Yi

Kvi‡YB Mvwo iv¯Ívi Dci w`‡q PjvPj K‡i| Nl©Y bv _vK‡j Mvwo PjvPj Ki‡Z cviZ

bv| Nl©Y e‡ji gvb wbf©i K‡i Uvqvi-Gi c„ô Ges iv¯Ívi Z‡ji gm„YZvi Dci| Mvwoi

IR‡bi DciI Nl©‡Yi gvb wbf©i K‡i| Mvwoi Uvqv‡ii Dc‡ii c„‡ô wewfbœ ai‡bi bKkvi ùvZ ev LuvR KvUv _v‡K

(wPÎ-3.24: Uvqvi)| ùvZ ev LuvR _vKvi Kvi‡Y Uvqv‡ii Dc‡ii c„ô gm„Y bv n‡q DuPz wbPz nq| bZzb Ae¯’vq

Uvqv‡ii ùvZ ev LuvR¸‡jv cÖKU _v‡K Ab¨w`‡K Uvqvi hZ eënvi Kiv nq, iv¯Ív I Uvqv‡ii Nl©‡Yi d‡j ùvZ ev

LuvR¸‡jvi cÖKUZv K‡g hvq| d‡j bZzb Ae¯’vq Uvqvi I iv¯Ívi g‡a¨ Nl©Y ej m‡e©v”P nq Ges MwZ Pvj‡Ki

wbqš¿‡Y _v‡K| cyivZb Ae¯’vq Uvqvi Ges iv¯Ívi g‡a¨ Nl©Y ej K‡g hvq| d‡j PvjK †eªK Ki‡jI Nl©Y Kg

_vKvq cÖ‡qvRb Abyhvqx Mvwo wVK RvqMvq wVK mg‡q bvI _vg‡Z cv‡i| GKvi‡YB Mvwoi Uvqvi cyivZb nIqvi

Av‡M cwieZ©b Kiv cÖ‡qvRb|

iv¯Ívi gm„YZv

e¯‘i MwZ iv¯Ívi gm„YZvi DciI wbf©i K‡i| iv¯Ív gm„Y n‡j hvbevnb PjvPj A‡bK mnRZi nq Ges Ab¨w`‡K

hvÎx‡ì ågY A‡bK Avivg`vqK nq| Nl©Y e‡ji gvb Uvqvi Ges iv¯Ív Df‡qiB gm„YZvi Dci wbf©i K‡i|

Nl©Y e‡ji gvb A‡bK K‡g †M‡j bvbv ai‡bi Amyweavi m„wó n‡Z cv‡i| †hgb- iv¯Ív hw` AwaKZi gm„Y nq Z‡e

_vgvi cÖ‡qvR‡b †eªK cÖ‡qvM Ki‡jI A‡bK mgq Mvwo‡K wVK RvqMvq _vgv‡bv m¤¢e nq bv| d‡j wec‡ì AvksKv

_v‡K| ZvB iv¯Ív‡K Lye †ewk gm„Y Kiv wVK bq| iv¯Ívi gm„YZv Ggb nIqv DwPr hv cÖ‡qvRbxq cwigvY Nl©Y ej

m„wó Ki‡Z cv‡i|

MwZ wbqš¿Y Ges †eªwKs ej

†eªK Kivi gva¨‡g hvbevn‡bi MwZ wbqš¿Y Kiv nq| GwU Ggb GKwU eë¯’v hvi mvnv‡h¨ PvKvi N~Y©b‡K cÖ‡qvRb

Abyhvqx Kwg‡q Nl©‡Yi cwigvY e„w× K‡i Mvwoi MwZ wbqš¿Y Kiv hvq| Mvwo _vgv‡bvi Rb¨ †eªK eënvi Kiv nq|

Mvwoi mvg‡bi PvKvi avZe PvKwZ‡K †ivUvi Avi wcQ‡bi PvKvi avZe PvKwZ‡K Wªvg e‡j| †eªK †c‡W‡j hLb ej

cÖ‡qvM Kiv nq Zv wewfbœ e¨ve¯’vcbvi ga¨ w`‡q †eªK c¨vW‡K wùZ K‡i N~Y©vqgvb †ivUv‡ii ms¯ú‡k© Av‡b Ges

Zv‡ì g‡a¨ Nl©Y m„wó K‡i †ivUv‡ii MwZ Kwg‡q Av‡b Ges †ivUvi‡K m¤ú~Y©iæ‡c _vwg‡q †`q|

Acic‡ÿ wcQ‡bi PvKvi †ÿ‡Î †eªK my avZe PvKwZi mv‡_ Nl©Y ˆZix K‡i PvKvi MvwZ‡K Kwg‡q †`q|

Gfv‡e †eªK †c‡W‡j ej cÖ‡qvM K‡i Mvwoi †eM n«vm Kiv nq|

GmGmwm †cÖvMÖvg


cvV-3.6 eënvwiK-6 : †Kv‡bv e¯‘i IRb wbY©q

D‡Ïk¨


w¯úªs wbw³ ev mvavib cvjøv eënvi K‡i †Kv‡bv e ‘i IRb wbY©q Ki‡Z cvi‡eb|

m~Î: Avgiv Rvwb, †Kvb e¯‘i Dci F ej wµqv Ki‡j Ges F ej cÖ‡qv‡Mi d‡j a Z¡ib m„wó n‡j,

F=ma m~ÎwU cÖwZcv`b Kiv hvq| GLv‡b m e¯‘i fi| AwfKl© e‡ji †ÿ‡Î e¯‘i Z¡iY a †K g Øviv

cÖKvk Kiv hvq| myZivs e¯‘i IRb, W=mg wjLv hvq hv AwfKl© ej‡K cÖKvk K‡i| GLv‡b e‡ji

D`vniY wn‡m‡e e¯‘i IRb wbY©q Kie|

cÖ‡qvRbxq hš¿cvwZ: w¯úªs wbw³, e ‘|

wb¤œwjwLZ Kv‡Ri aviv AbymiY K‡i e¯‘i IRb Z_v AwfKl© ej cwigvc Kiv hvq|

1. wbDUb GK‡K `vMvw¼Z GKwU w¯úªs wbw³ †`qv‡j Szwj‡q wbb|

2. GLb w¯úªs Gi wb‡P †h ûK Av‡Q Zvi mv‡_ e¯‘wU‡K Szwj‡q w`b|

3. w¯úªs wbw³i mvnv‡h¨ hy³ †¯‹‡ji †_‡K e¯‘i IRb Z_v AwfK‡l©i cvV †iKW© Kiæb Ges LvZvq wb‡Pi Q‡Ki

gZ QK †K‡U gvb emvb|

4. 3bs cÖwµqv AbymiY K‡i GKBfv‡e K‡qKevi e¯‘i IRb wbY©q Kiæb Ges Q‡K emvb|

5. Gevi e¯‘i Dci cÖhy³ Mo ej ev IRb wbY©q Kiæb|

µwgK msL¨v e¯‘i IRb

(wbDUb)

Mo IRb (wbDUb)

1

2

3

4

5

GLb GB e¯‘i cwie‡Z© wewfbœ e¯‘ wb‡q GKB c×wZ‡Z cixÿY mgvß K‡i, IRb wbY©q Kiæb|

P~ovšÍ g~j¨vqb-3

K. mvavib wbe©vPbx cÖkœ:


1| Avgv‡ì Pvicv‡ki †h mKj e¯‘ †`L‡Z cvB, mK‡jB wbR Ae¯’v‡b _vK‡Z Pvq- wbDU‡bi †Kvb m~Î GwU

e¨vL¨v K‡i?

(K) wbDU‡bi MwZi cÖ_g m~Î (L) wbDU‡bi gnvKl© m~Î

(M) wbDU‡bi MwZi Z…Zxq m~Î (N) wbDU‡bi AwfKl© m~Î

2| wbDU‡bi †Kvb m~‡Îi mvnv‡h¨ Avgiv wewfbœ f‡ii e¯‘i Dci e‡ji cÖfve e¨vL¨v Ki‡Z cvwi?

(K) wbDU‡bi MwZi cÖ_g m~Î (L) wbDU‡bi MwZi wØZxh m~Î

c`v_©weÁvb


(M) wbDU‡bi MwZi Z…Zxq m~Î (N) wbDU‡bi gnvKl© m~Î

3| evBmvB‡K‡ji MwZ wbDU‡bi †Kvb m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq?

(K) wbDU‡bi MwZi cÖ_g m~Î (L) wbDU‡bi MwZi wØZxq m~Î

(M) wbDU‡bi MwZi Z…Zxq m~Î (N) wbDU‡bi gnvKl© m~Î

4| ej †Rvovq †Rvovq wµqv K‡i- wbDU‡bi †Kvb m~Î e¨vL¨v K‡i?


(M) wbDU‡bi MwZi Z…Zxq m~Î (N) †KvbwUB bq

5| evwni n‡Z ej cÖ‡qvM bv Ki‡j, MwZkxj e¯‘ wPiKvj mg‡eM mij‡iLvq Pj‡Z Pvq- wbDU‡bi †Kvb m~‡Îi

mvnv‡h¨ e¨vL¨v Kiv hvq?


(M) wbDU‡bi MwZi Z…Zxh m~Î (N) wbDU‡bi AwfKl© m~Î

6| †Kvb m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq †h, mgvb ~iZ¡ AwZµ‡gi Rb¨ †ewk f‡ii e¯‘i Dci Kg f‡ii e¯‘i

†P‡q †ewk ej cÖ‡qvM Ki‡Z nq|


(M) wbDU‡bi MwZi Z…Zxq m~Î (N) fi‡e‡Mi wbZ¨Zvi m~Î

L. eûc`x eû wbe©vPbx mgvwß m~PK cÖkœ:

1| wbDU‡bi MwZi cÖ_g m~Îvbymv‡i-

i. w¯’i e¯‘ wPiKvj w¯’i _vK‡Z Pvq|

ii. MwZkxj e¯‘ wPiKvj MwZkxj _vK‡Z Pvq|

iii. w¯’i e¯‘ MwZkxj n‡Z Pvq|

mwVK DËi †KvbwU?

(K) i I ii (L) ii I iii (M) i I iii (N) i, ii I iii

2| RoZvi Kvi‡Y-

i. w¯’i e¯‘ wPiKvj w¯’i _vK‡Z Pvq|

ii. MwZkxi e¯‘ wPiKvj MwZkxj _vK‡Z Pvq|

iii. MwZkxj e¯‘ w¯’i n‡Z Pvq|

mwVK DËi †KvbwU?


3| ej cÖ‡qv‡M wb‡Pi †Kvb NUbvwU NU‡Z cv‡i-

i. w¯’wZkxj e¯‘ MwZkxj n‡Z cv‡i

ii. MwZkxj e¯‘i †eM e„w× n‡Z cv‡i

iii. MwZkxj e¯‘i †eM n«vm n‡Z cv‡i

iv. MwZkxj e¯‘i †e‡Mi w`K cwieZ©b n‡Z cv‡i

mwVK DËi †KvbwU?

(K) i I ii (L) ii I iii (M) iii I iv (N) i, ii, iii I iv

4| wbDU‡bi Z…Zxq m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq-

i. gvwUi Dci nvUv

ii. c„w_ex m~‡h©i Pvwiw`‡K Nyi‡Q, Nyi‡Q †Zv Nyi‡QB

GmGmwm †cÖvMÖvg


iii. Av‡ivnx †bŠKv †_‡K jvwd‡q Zx‡i bvg‡j

mwVK DËi †KvbwU?


5| Nl©‡bi DrcwË nq-

i. Puv` c„w_exi Pviw`‡K †Nvivi d‡j

ii. PvKv jvMv‡bv jv‡MR GK¯’vb †_‡K Ab¨¯’v‡b †bqvi d‡j|

iii. cyKz‡ii cvwbi ga¨ w`‡q muvZvi †K‡U mvg‡bi w`‡K G‡Mv‡bvi d‡j

mwVK DËi †KvbwU?

(K) i I ii (L) i I iii (M) ii I iii (N) i, ii I iii

M. Awfbœ Z_¨ wfwËK cÖkœ

wb‡Pi Z_¨¸wj co–b Ges cÖkœ ‡jvi mwVK DËiwU‡Z wUK w`b|

Pqb Zvi cwiev‡ii mv‡_ wZbw`‡bi Rb¨ †eov‡Z wM‡qwQj| Pqb beg †kÖYx‡Z c‡o| MÖx‡®§i QzwU Pj‡Q| AvR †m

Zvi cwiev‡ii mv‡_ wZbw`b evwn‡i _vKvi ci evmvq wdij| evmvq †divi ci Avevi Zuv‡`i Kg©e¨¯Í Rxeb ïiæ|

evev h_vixwZ †fv‡i wd‡iB GKUz wekÖvg wb‡q mKv‡j Awd‡m P‡j wM‡q‡Q| Pq‡bi gv I †ckvq GKRb ¯‹zj

wkÿK| wKš‘ AvR Zuvi ¯‹zj eÜ| wZwb msmv‡ii Kv‡R e¨¯Í| Pqb gv‡K msmv‡ii Kv‡R mvnvh¨ Ki‡Q| Pq‡bi ¯‹zj

AvMvgxKvj Lyj‡e|

Pq‡bi gv mKj wRwblcÎ mwi‡q Zv‡`i Nievwo cwi®‹vi Ki‡Q| Pqb jÿ¨ Kij, mKj wRwblcÎ †eov‡Z hvevi

Av‡M †h ¯’v‡b Ae¯’vb K‡i‡Q †m Ae¯’v‡bB i‡q‡Q| Pq‡bi gv A‡cÿvK…Z Kg f‡ii wRwbmcÎ wb‡RB mwi‡q

cwi®‹vi Ki‡Qb| KviY G‡Z Kg ej cÖ‡qvM Ki‡Z n‡”Q| wKš‘ eyK †mjdwU wZwb †kl ch©šÍ GKv miv‡Z cvi‡jb

bv| KviY eyK †mjdwUi fi Ab¨vb¨ wRwblc‡Îi f‡ii †P‡q †ewk| Pqb Ges Zvi gv GKmv‡_ A‡cÿvK…Z †ewk

ej cÖ‡qvM K‡i eyK‡mjdwU miv‡jb| ej cÖ‡qvM Kivi Av‡M †Kvb wRwblcÎB wbR †_‡K Ae¯’vb cwieZ©b K‡iwb|

Phb AviI jÿ¨ Ki‡jv †h, Zvi gv‡qi N‡i †h, †Wªwms †Uwej Avi †Wªwms †Uwe‡ji mv‡gb emvi Uzj i‡q‡Q| G

`yÕwU‡K GKB `~i‡Z¡ miv‡Z †ewk f‡ii †Wªwms †Uwe‡j †ewk †Rv‡i av°v w`‡Z n‡”Q A_©vr Uzj miv‡Z †h ej cÖ‡qvM

Ki‡Z n‡”Q †Wªwms †Uwej miv‡Z Zvi †P‡q †ewk ej cÖ‡qvM Ki‡Z n‡”Q|

Pqb nVvr Zvi †QvU fvB Aq‡bi wLj wLj nvwmi kã ïb‡Z †cj| †`Lj Zvi †QvU fvB Aqb GKwU wcs cs ej

wb‡q †Lj‡Q| hZeviB ejwU gvwUi w`‡K Qzo‡Q ZZeviB ejwU wecixZgyLx n‡q Aq‡bi nv‡Z †cŠQv‡”Q|

1| mKj wRwblcÎ †h ¯’v‡b Ae¯’vb K‡i‡Q, †m Ae¯’v‡bB i‡q‡Q| Z_¨wU wbDU‡bi †Kvb m~‡Îi mvnv‡h¨ e¨vL¨v

Kiv hvq?

(K) cÖ_g m~Î (L) wØZxq myÎ

(M) Z…Zxq m~Î (N) Nl©‡Yi m~Î

2| eyK †mjdwU Pq‡bi gv †kl ch©šÍ GKv miv‡Z cvi‡jbv| G‡ÿ‡Î †Kvb ai‡bi Nl©‡bi DrcwË n‡qwQj?

(K) w¯’wZ Nl©Y (L) Pj ev wcQjv‡bv Nl©Y

(M) AveZ© Nl©Y (N) cÖevnx Nl©Y

3| Pqb jÿ¨ Ki‡jv †h, †Wªwms †Uwej Ges UzjwU‡K GKB `~iZ¡ miv‡Z †Wªwms †Uwej‡K †ewk †Rv‡i av°v w`‡Z

n‡”Q Uz‡ji Zzjbvq| NUbvwU wbDU‡bi †Kvb m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq?

(K) cÖ_g m~Î (L) wØZxq m~Î

(M) Z…Zxq m~Î (N) gnvKl© m~Î

c`v_©weÁvb


4| Aqb hZeviB ejwU gvwUi w`‡K Qzo‡Q ZZeviB ejwU wecixZgyLx n‡q Aq‡bi nv‡Z †cuŠQv‡”Q| wbDU‡bi †Kvb

m~‡Îi mvnv‡h¨ GwUi e¨vL¨v cÖ vb Kiv hv‡e?

(K) cÖ_g m~Î (L) wØZxq m~Î

(M) Z…Zxq m~Î (N) gnvKl© m~Î

N. m„Rbkxj cÖkœ

Pqb I Aqb `yÕfvB| Pqb beg †kÖYx‡Z c‡o Avi Aqb PZz_© †kÖYx‡Z c‡o| Zviv cÖwZw`b mKv‡j ¯‹z‡j hvq| ¯‹zj

†_‡K ycyi bvMv` evmvq wd‡i| evmvq wd‡i nvZ gyL ay‡q ycy‡ii Lvevi †L‡q wekÖvg †bq| we‡K‡j †Lj‡Z †ei

nq| mÜ¨vi Av‡M evmvq wd‡i nvZ gyL ay‡q we‡K‡ji bv¯Ív †L‡q co‡Z e‡m|

Pqb Avi Aqb mKvj mv‡o mvZUvq ¯‹z‡ji D‡Ï‡k¨ †ei nq| evmv †_‡K †ei n‡q LvwbKUv c_ †nu‡U evm ó¨v‡Û

†cuŠQ‡Z nq| ¯‹zj evm, evm ó¨v‡Û †cuŠQ‡bvi ci, Pqb Zvi †QvU fvB Aqb‡K wb‡q ev‡m D‡V| ev‡m D‡VB Pqb Zvi

†QvU fvB Aq‡bi Rb¨ emvi wmU †Luv‡R| KviY Pqb jÿ¨ K‡i‡Q †m `vwo‡q _vKv Ae¯’vq evm Pjv ïiæ Ki‡j,

Aqb wcQ‡bi w`‡K †n‡j c‡o Avi c‡o hvIqviI m¤¢vebv _v‡K| GKB Ae¯’v N‡U evmwU nVvr K‡i †eªK Ki‡jI,

Aqb mvg‡bi w`‡K †n‡j c‡o hvIqvi m¤¢vebv _v‡K| ev‡m †n‡j c‡o hvIqvi NUbvwU ïay Aq‡bi †ÿ‡Î bq, mKj

hvÎx‡`i †ÿ‡ÎB mZ¨| Pqb Avi Aqb wbqwgZ we‡K‡j †Ljvi gv‡V hvq| `yfvB wg‡j dzUej †L‡j| Aqb dzUej

†Ljv wb‡q †gv‡UI Lywk bv KviY Aqb jvw_ w`‡q dzUej †ewk `~‡i cvVv‡Z cv‡i bv| wKš‘ Pqb eo nIqvi GKB

dzUe‡ji Dci †ewk ej cÖ‡qvM K‡i `~‡i cvVv‡Z cv‡i|

mÜ¨vi mgq Pqb Avi Aqb cÖwZw`b covi †Uwe‡j co‡Z e‡m| `yÕfvB GK †Uwe‡j co‡Z e‡m| Pqb Avi Aqb

`yR‡bi ¯‹zj e¨vMB eyK-‡mj‡di Dci ivLv _v‡K| covi mgq Pqb `yÕwU e¨vMB covi †Uwe‡j wb‡q Av‡m| Aq‡bi

e¨vM Pq‡bi e¨v‡Mi †P‡q †QvU Avi nvjKv, Aq‡bi e¨vM AwZ mn‡R Pqb eyK †mjd †_‡K †Uwe‡j G‡b ivL‡Z

cvi‡Q wKš‘ wb‡Ri e¨vM †Uwe‡ji Dci ivL‡Z wKQzUv †ewk Kó nq| cov †k‡l Pqb Avi Aqb `yÕR‡bB eB LvZv

¸‡jv †Uwe‡ji Dci mvwR‡q iv‡L †hb c‡ii w`b eB¸‡jv wVK RvqMvg‡Zv cvIqv hvq Zv‡Z Zv‡`i mg‡qi AcPq

Kg nq|

AvR Aqb nv‡Z e¨_v †c‡q‡Q, †Uwe‡ji Dci †Rv‡i GKUv _vào †`qv‡Z| Pq‡bi ¯‹zj †_‡K wb‡Pi AsK¸‡jv

evoxi KvR w`‡q‡Q| Pjyb Pq‡bi mv‡_ Avgiv wb‡Pi AsK¸‡jv mgvavb Kwi|

(i) 40kg Ges 60kg f‡ii `ywU e¯‘ ci¯úi wecixZ w`‡K h_vµ‡g 10ms-1 Ges 5ms-1

†e‡M hvIqvi c‡_ G‡K

Aci‡K av°v w`j| av°vi ci e ‘ ywU GK‡Î hy³ †_‡K KZ †e‡M Pj‡e?

(i) 30kg f‡ii GKwU e¯‘i Dci KZ ej cÖ‡qvM Ki‡j 1 wgwb‡U Gi †eM 36kmh-1 e„w× cv‡e?

wbDU‡bi cÖ_g m~Î:

1. wbDU‡bi cÖ_g m~ÎwU wjLyb|

2. Pqb I Aq‡bi cÖvZ¨wnK Rxe‡bi NUbv †_‡K wbDU‡bi cÖ_g m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq Ggb NUbv¸‡jv

wPwýZ Kiæb|

3. Dc‡ii wPwýZ NUbv¸‡jv wbDU‡bi cÖ_g m~‡Îi mvnv‡h¨ e¨vL¨v Kiæb|

4. Avcbvi cÖvZ¨wnK Rxeb †_‡K wbDU‡bi cÖ_g m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq Ggb GKwU NUbv wkLyb I e¨vL¨v

Kiæb|

wbDU‡bi wØZxq m~Î:

1. wbDU‡bi wØZxq m~ÎwU wjLyb|

2. Pqb I Aq‡bi cÖvZ¨wnK Rxe‡bi NUbv †_‡K wbDU‡bi wØZxq m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq Ggb NUbv¸‡jv

wPwýZ Kiæb|

3. Dc‡ii wPwýZ NUbv¸‡jv wbDU‡bi wØZxq m~‡Îi mvnvh¨ e¨vL¨v Kiæb|

GmGmwm †cÖvMÖvg


4. Avcbvi cÖvZ¨wnK Rxeb †_‡K wbDU‡bi wØZxq m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq Ggb GKwU NUbv wjLyb I e¨vL¨v

Kiæb|

wbDU‡bi Z…Zxq m~Î:

1. wbDU‡bi Z…Zxq m~ÎwU wjLyb|

2. Pqb I Aq‡bi cÖvZ¨wnK Rwe‡bi NUbv †_‡K wbDU‡bi Z…Zxq m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq Ggb NUbv wPwýZ

Kiæb|

3. Dc‡ii wPwýZ NUbv¸‡jv wbDU‡bi Z…Zxq m~‡Îi mvn‡h¨ e¨vL¨v Kiæb|

4. Avcbvi cÖvZ¨wnK Rxeb †_‡K wbDU‡bi Z…Zxq m~‡Îi mvnv‡h¨ e¨vL¨v Kiv hvq Ggb GKwU NUbv wjL I e¨vL¨v

Kiæb|

cvV wfwËK g~j¨vqb

cvV-1 : 1. M 2. N

cvV-2 : 1. K 2. M

cvV-3 : 1. M

cvV-4 : 1. N 2. M

P‚ovšÍ g~j¨vqb

K. mvaviY wbe©vPbx cÖkœ

1. K 2. L 3. M 4. M 5. K 6. L

L. eûc`x eû wbe©vPbx mgvwß m~PK cÖkœ

1. K 2. K 3. N 4. M 5. M

M. Awfbœ Z_¨wfwËK cÖkœ

1. K 2. K 3. L 4. M

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