JEE Advanced 2018 Physics

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT

VGZ\ > @@ VBPT@DT TOD\@HI — 7 > (Mgx`mum Mgras > :<)  \b`s sodt`hi dhitgìs T@R (65) quost`his. (65) quost`his.  Ogdb quost`hi bgs EH_Z hpt`his hpt`his ehr dhrrodt giswor(s). HIO HZ MHZO \BGI HIO HIO he tboso ehur hpt`hi(s) `s (gro) dhrrodt hpt`hi(s). ogdb quost`hi, dbhhso tbo dhrrodt hpt`hi(s) th giswor tbo quost`hi. quost`hi.  Ehr ogdb  Giswor th ogdb quost`hi w`cc jo ovgcugtol gddhrlìk th tbo ehcchwìk mgraìk dbhsoi. Eucc Mgras

>

+< @e hicy (gcc) tbo dhrrodt hpt`hi(s) `s (gro) (gro) dbhsoi.

Vgrt`gc Mgras >

+4 @e +4 @e gcc tbo ehur hpt`his gro dhrrodt jut HICP tbroo hpt`his gro dbhsoi.

Vgrt`gc Mgras >

+: +: @e tbroo hr mhro hpt`his gro dhrrodt jut jut HICP twh hpt`his gro dbhsoi, jhtb he wb`db gro dhrrodt hpt`his.

Vgrt`gc Mgras >

+7 @e +7 @e twh hr m hro hpt`his gro dhrrodt jut HICP hio hpt`hi `s dbhsoi gil `t `s g dhrrodt hpt`hi.

ôrh Mgras >

6 @e ihio he tbo hpt`his `s dbhsoi (`.o. tbo quost`hi `s uigisworol).

Iokgt`vo Mgras > —: @i —: @i gcc htbor dgsos. Ehr Oxgmpco > > @e e`rst, tb`rl gil ehurtb gro tbo HICP tbroo dhrrodt hpt`his ehr g quost`hi w`tb sodhil hpt`hi joìk gi ìdhrrodt hpt`hi1 socodtìk hicy twh he tbo tbroo dhrrodt hpt`his (o.k. tbo e`rst gil ehurtb hpt`his), w`tbhut socodtìk giy ìdhrrodt hpt`hi (sodhil hpt`hi ì tb`s dgso), w`cc rosuct ì +: mgras. Tocodtìk hicy hio he tbo tbroo dhrrodt hpt`his (o`tbor e`rst hr tb`rl hr ehurtb hpt`hi), w`tbhut socodtìk giy ìdhrrodt hpt`hi (sodhil hpt`hi ì tb`s dgso), w`cc rosuct ì +7 mgras. Tocodtìk giy ìdhrrodt hpt`hi(s) (sodhil hpt`hi ì tb`s dgso), w`tb hr w`tbhut socodt`hi he giy dhrrodt hpt`hi(s) w`cc rosuct ì —: mgras.

7

:<

 jc QagM osg Ik (65) `z'u kTG e y, pan ehlP` ei, x, kTgG ju pan ehlPàsg osg cs ,l 1a ,l , l cs ve/al  `zZ1sl `z'u ls ckb mÐan ³mÐanasg½ ls ey, ehlP` ckb kT³kTg½G  `zZ1sl `z'u ls ey,] `z'u la la ³ls½ mÐan isus ksrq ehlP` ³ehlPàsg ½ las pqu gsG 1aglu euOu vg lu 1astua ls vuqcan kasxa %  `zZ1sl `z'u ls mÐan la owP1ag `w.a^ vgl % +< 1ei lshy ³cans½ ckb ehlP` ³ehlPàsg½ las pqua x1a kTG vage'al vgl % +4 1ei panasg ehlP` ckb kTg `n_rq lshy rbu ehlPàsg las pqua x1a kTG vage'al vgl % +: 1ei rbu 1a rbu cs ve/al ehlP` ckb kT `n_rq lshy ias ehlPàsg las pqua x1a kT vaTn p us q kq, iasuasg ehlP` ckb ehlP` kT gG vag e'al vgl % +7 1ei ias 1a ias cs ve/al ve/al ehlP` ckb kTg `n_rq `n_rq lshy ,l ehlP` las pqua x1a kT vaTn pqua kqva ehlP` ckb ehlP` kTG 'aw_1 vgl % 6 1ei elcb Bab ehlP` las ukbg pqua x1a kT ³vEaa^r~ `z'u vuqÐaenr kT G½ X.a vgl % —: v_c cBab èneCEaer1asg osgG  1ei elcb `z'u ls ey, lshy `kya ] rbcna ,gh paTEaa ckb ehlP` kTg vaTn iwcna ehlP` xyr kT] ras lshy cBab rbu ckb ehlPàsg la la p1u lnus `n kb +< vgl eoysgxsG edua lasj^ xyr ehlP` pqus ³jc miakn.a osg iwcna ehlP`½] rbu ckb ehlPàsg os cs ecW^ ias pquus `n `n ³miakn.ar% `kya rEaa paTEaa ehlP`½ +: vgl eoysgxsG edua lasj^ xyr xyr ehlP` pqusG ³jc miakn.a osg iwcna ehlP`½] rbu ckb ehlPàsg osg cs ecW^ ,l las pquus `n ³`kya 1a rbcna 1a paTEaa ehlP`½ +7 vgl eoys xs g G lasj^ Bab Bab xyr ehlP` pquus `n ³jc miakn.a osg iwcna ehlP`½] —: vgl eoys xs g ] paks ckb ehlP` ³ehlPàsg½ las pqua x1a x1a kas 1a u pqua x1a kasG 7.

Ehrdo hi g pgrt`dco mhvìk ì strg`kbt cìo cìo sudb tbgt rgto he dbgiko ì `ts aìot`d oiorky w`tb t`mo vgròs la gs = t, wboro  `s g dhistgit. Dbhhso tbo dhrrodt hpt`hi(s). lt (G*) Ehrdo ` s dhisorvgt`vo. (J*) Ehrdo `s dhistgit. (D*) Tpool he tbo pgrt`dco vgròs w`tb t`mo gs zv  t. (L) L`spcgdomoit he tbo pgrt`dco vgròs w`tb t`mo gs x  t.

Zoshigido O Oluvoitur os C Ctl. ZOK. & DHZVHZG\O HEE@DO > DK \hwor, G-<5 & ?:, @V@G, Iogr D`ty Mgcc, Mgcc, Nbgcgwgr Zhgl, Ahtg (Zgn.) - 4:<66? Vb.Ih. > +07-;<<-467::::, 554???? | \h Aihw mhro > sms ZOTH gt ZOTH gt ?55;; [ojs`to > www.roshigido.gd.ì | O-mg`c > dhitgdtFroshigido.gd.ì | D@I > _2646:ZN:66;VCD6:<6:0 \b` s sshcut`hi w wgs l lhwic hgl e e rhm Z Zoshigido NNOO G GLUGIDOL : :672 T Thc ut`hi p phrtgc

VGKO # 70


cny nsQaa osg xer'aby l.a l.a `n vanase`r dy jc `zlan kT el jclb xert xert Ïta^ osg ènh^ru

la = t ls lt

vuq can

ènherr kasrb kT 1ka[g  ,l eu1ragl kTG ckb ehlPàsg la p1u elet,G (G*) dy cng{ab kTG (J*) dy eu1r kTG can ènher^^r kasrb kTG (D*) l.a lb pay v  t ls vuq ènher^r kasrb kTG (L) l.a la ehCEaaù x  t ls vuqcan ènher^ Thc.

mv

lv la = = t lt lt

v lv =

 m

t lt

 t: v: = : m : lv = dhistgit eu1r lt lx  t lt :.

 v  t  e = dhistgit eu1r  x  t:

@i roshigido dhcumi tujo oxpor`moit, twh dhisodut`vo roshigido gro hjtgìol gt ?6.; dm gil 24.0 dm w`tb g tuiìk ehra he eroquoidy ?66 Bz. (G*) vochd`ty he shuil `s 44: m/s (J) oil dhrrodt`hi `s 6.0 dm (D*) wgvocoiktb `s 55.< dm (L) e`rst roshigido hddurs gt ?6.; dm vuquai uyb `z1 x as osg ?66 Bz. vahfeÐa hays Chen=a ls caEa ias Òoaxr vuquai Òo'a% ?6.; dm rEaa 24.0 dm `n

`za@r kasrs kTG (G*) /heu

la hsx

44: m/s kT

(D*) rngxiT/1^ 55.< dm kT Thc.

(:i + 7) (:i + 4)

 <

cg'aas/au

6.0 dm kT

(L) `zEao

vuq uai

?6.; dm `n

`za@r kasra kT

= ?6.; dm +o



= 24.0 dm +o < usìk i = 7 o = — 6.0 dm ls  = 55.< dm v = e  = 44: m/s

4.

(J) ecna

`z1asx }ana

G dgp`ccgry `s l`ppol ìth g shcut`hi he suregdo tois`hi tois`hi  . Gikco he dhitgdt `s  tboi (G) bo`kbt th wb`db c`qu`l r`sos ì t bo tujo `s ìlopoiloit he . (J*) ehr g k`voi pg`r he c`qu`l gil dgp`ccgry tujo b `s ìvorsocy prhphrt`higc th r. (D*) ehr g k`voi dgp`ccgry tujo b `s prhphrt`higc th r (L*) è `t `s aopt ì g cèt gddocorgtol upwgrls tboi b lodrogsos lodrogsos

,l ls'a uyb las  `f"J ruah hays ehy1u osg iqdas1a tara tara kTG C`'a^ las las.a  kas ras (G) uyb

osg pM+s kq,s izh lb Ïpaj^  `n euBa^n ukbg lnrb

(J*) ei1s

x,s ls'a uyb rEaa rEaa izh 1qRo ls ey,

(D*) ei Thc.

xj^ ls'a uyb ls ls ey,

(L*) 1ei (J,D,L)

b, r ls

b, r ls

H1qrÒoauqàrb kT

coauqàrb kTG

jclas Ï`n lb rnW Zhnbr Zhnbr eyµU osg nQa ei1a ta, ras b la oau 8aUsxaG


VGKO # :6


b= <.

: dhs 

kr

G pcgto `s mhvol w `tb vochd`ty v6 hi g tbì cgyor he h`c hi g suregdo wboro h`c he tb`daioss b(mudb coss tbgi w`ltb he pcgto) gil dhoee`dòit dhoee`dòit he v`sdhs`ty v`sdhs`ty  `s gvg`cgjco (G) ehrdo gppcòl `s ìlopoiloit he grog he pcgto (J*) sbogr stross `s prhphrt`higc th  . (D*) sbogr stross hi jgso ìdrogsos w`tb ìdrogso ì v6 (L*) sbogr stross hi jgso `s l`rodt cy prhphrt`higc th

7 b

,l @ysU v6 hsx cs rsy lb `ryb `nr `n xer'aby kTG rsy lb `nr lb oasUaj^ b( @ysU lb oasUaj^ cs dkqr lo ) rEaa rsy '1aura xq.aal  kTG (G) vanase`r

dy @ysU ls {as=aWy `n veuBa^n kT G

(J*) v`>`.a

`zerdy  ls coauqàrb kTkTG

(D*) va/aan

`n v`>`.a `zerdy v6 d3+ us ls caEa d3ra kTG

(L*) va/aan

`n v`>`.a `zerdy]

7 ls b

cb/as coauqàrb kTG

v6 E

Thc. b

e =  G

=  G

lv ly

v6 b


VGKO # :7


?.

Dhis`lor Dhis`lor g ihi dhiludtìk sbocc he rglùs Z. Gi ìeì`to chik w`ro, bgvìk dbgrko lois`ty  `s aopt gchik g dbhrl he spboro gs sbhwi ì e`kuro. Dbhhso tbo dhrrodt hpt`his Z e=a\1a ls vpayl las'a lb lPùa lbet,G ,l v_ur yOda ran etcla vahs'a 8auZh  kT] ep=aauqcan las'a lb

,l tbha ls vuq vuqei'a eCEar kTG ckb ehlPàs g la p1u lbet, ^



R

7:6¶

4 Z

(G*) Ocodtr`d ecux erhm spboro `s (J) Ocodtr`d ecux erhm spboro `s

6 Z 6

(D*) Ocodtr`d eòcl gchik z-gx`s gt giy phìt he spboro spboro gchik z-gx`s `s zorh (L) Ocodtr`d eòcl gt ogdb phìt he spboro `s  th spbor`dgc suregdo.

Thc.

cs xqtnus haya eh|q eh|qr WyLc

(J) xasys

cs xqtnus haya eh|q eh|qr WyLc

(D) xasys

ls elcb Bab ed_iq `n `n

(L) xasys

ls `zZ1sl ed_iq `n eh|qr {as=a xasyb1 crk ls yOdhr~ kTG

Woid = 

 = 5.

4 Z

(G) xasys

Woid

6

z- v{a

6

kTG

Z kTG 6

ls vuqei'a eh|qr {as=a 'aw_1 kTG

4 Z



4 Z

6

Dhis`lor tbo k`voi iudcogr rogdt`hi :4:

:7:

R  2:P  x  y Dbhhso tbo dhrrodt hpt`his (G) iumjor he - pgrt`dcos I = 5 (J) iumjor he -pgrt`dcos I = < (D*) iumjor he - pgrt`dcos I = ? (L*) iumjor he -pgrt`dcos I = : 06


VGKO # ::


ei xj^ uaeBael1 veBaeÒ1a lb lb lPùa lbet,gs 06

R

:4:

 2:P

:7:

 x  y

ckb ehlPàs la la p1u lbet, (G) - l.aasg

lb cgQ1a

(J) - l.aasg

lb cgQ1a I = <

(D*) - l.aasg Gis. Thc.

;.

I = 5

lb cgQ1a

I = ?

(L*) - l.aasg lb cgQ1a I = : (DL)  G = :4: — :7: = :6 =




rìk he rglùs Z bgvìk doitro gt 6,6, 6,6, 4Z bgs `ts gx`s gchik gchik z-l`rod z-l`rodt`hi. t`hi. @t @t dgrròs dgrròs durroit durroit @ gs sbhwi. sbhwi. Durroits @7 gil @: gro tgaoi phs`t`vo è tboy gro gchik +y l`rodt`hi. @e J6 `s mgkiot`d eòcl gt hr`kì tboi, wb`db he tbo e hcchwìk `s/gro `s/gro truo 8 ias ran w7 rEaa w : ep=aauq can xy ry osg y- v{a ls coa_rn eCEar kTG juosg `zhaekr `z haekr /aana Òo'a% @7 rEaa @: kTG Z e=a\1a

lb ,l hy1 etcla e tcla ls_iz

 6,6,

4Z

`n kT] lb v{a  `n kT

/aana @7 rEaa @ : las /auaZol eyet,sg] 1ei julb ei'aa euOu osg cs laTucaFlaTucs cs ehlP` ckb kTG

z- ei'aa

+y ls

ls vuqei'a kTG jc osg @ /aana ep=aauqcan `zhaekr kTG

vuqei'a kTG 1ei owy ed_iq `n pq p qOdel1 {as=a

J6 kas

ras

^ @

6, 6,6,

D

4Z

 P

w:

w7 H

x = —Z

x=Z

—P

(G*) @e @7 = @: tboi, J6  6 (J*) @e @7 9 6, @: 3 6 tboi J6 dgi jo zorh (D) @e @7 3 6, @: 9 6 tboi, J6 dgi jo zorh (L) @e @7 = @: tboi z dhmphioit he mgkiot`d e`col gt D `s (G*) 1ei @7 = @: kas

6  :Z

ras, J6  6 kTG

(J*) 1ei @7 9 6, @ : 3 6 kas (D) 1ei @7 3 6, @ : 9 6 kas

ras

J6 'aw_1

kas clra kTG

ras, J6 'aw_1 kas clra clra kTG


VGKO # :4


(L) 1ei @7 = @: kas Thc.

ras D `n pqOdlb1 {aT=a la z 8aUl

6  :Z

kTG

(GJ) Mgkiot`d eòcl luo th rìk gt hr`kì

hy1 ls lan.a owy ed_iq `n pqOdlb1 dlb1 {as=a :  @Z @  6 A˅   6  A˅  4  :  2Z 75Z Mgkiot`d eòcl gt hr`kì luo th w`ros

ranas ls ls lan.a owy ed_iq `n pqOdlb1 {as=a =

 6@7 6@:  ˅  :Z  :Z  A  

Boro @ 7 gil @: w`cc jo sujst`tutol w`tb s`ki nQaus `n @7 rEaa @: las ep_k cekr nQaus  @ @e @7 = @: tboi J6  6 A˅ 75Z  @ 1ei @7 = @: kas ras J6  6 A˅ 75Z @t dgi jo zorh

 

 

1k 'aw_1 kas clra kT @e 1ei @7 3 6, @: 9 6   6 @7  @:  .@  ˅ tboi kas ras J6     A 75Z   :Z @t dgi iht jo zorh

1k 'aw_1 kas clra kT 

2.

@e ehrdo hi g pgrt`dco he mgss = 7 ak `s E  t ˅`  ˅n (  = 7,  = 7) tboi (G) l`spcgdomoit he pgrt`dco gt t = 7 sod. `s

a˅ l`rodt`hi

(J) thrquo gjhut hr`kì gt t = 7 sod. `s ì (D*) gikucgr mhmoitum gt t = 7 sod. `s (L*) mgki`tulo he thrquo `s

1ei

Thc.

7 ak izH1oau

7 4

7˅ ` 5

7  a˅ 4

gt t = 7 sod.

ls l.a `n vanase`r dy



ras E  t ˅`  ˅n ( = 7,  = 7) kas ras

7˅ ` kTG 5

(G) t = 7 sod `n

l.a la ehCEaaù ehCEaaù dy

(J) t = 7 sod `n

owy ed_iq ls ènr% ènr% dya8aw.a^ a˅ ei'aa os kT g kTG

(D) t = 7 sod `n

las.ab1 cghsx 

(L) t = 7 sod `n

dya8aw.a^ la

7˅ a kTG 4 7 ènoa.a kTG 4

m = 7ak 

 m g  E  t ˅`  ˅n

 (7) g  t ˅`  ˅n


VGKO # :<

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT 

lv lt

 t ˅`  ˅n

t: ˅ ˅ 7 ˅ ˅ `  tn  `  n : : 4 :  t t s  ˅`  ˅n 5 :  7 7 (G) s( t  7)  ˅`  ˅n 5 : 

v



 



  r E 7 7  =  ˅`  n    ˅`  ˅n   5 :  

(J)

7 ˅ ˅ 7 ˅ ˅ ( `  n)  ( n  ` ) 5 : : ˅ 7 7 = a˅  a˅  a 5 : 5 =





7 4

 a˅



(D) C  m( r  v ) =



7 ˅ a 7:

7 gt t = 7 sod 4 Gis. (D gil L) (L) || =

0.



G pgrt`dco w`tb phtoit`gc oiorky _ = ar : `s mhvìk grhuil hr`kì ì g d`rdco he rglùs Z. {Boro r `s phs`t`hi vodthr he pgrt`dco} wb`db he tbo e hcchwìk hpt`his hpt`his `s/gro dhrrodt 8 :a r m

(G*) vochd`ty vgròs w`tb r gs (J) vochd`ty vgròs w`tb r gs

a m

r

(D*) mhmoitum vgròs w`tb r gs

:amr :

(L) mhmoitum vgròs w`tb w`tb r gs

amr :

,l l.a etclb eCEaert Ïta^ _ = ar : kT] owy ed_iq ls ènr% eCEaer cei'a kTG} euOu osg cs laTucaFlaTucs ehlP` ckb ckb kT 8 (G*) r ls (J) r ls

:a r ls m

caEa hshsx] caEa hshsx]

a m

(D*) r ls

Thc.

caEa cghsx] (L) r ls caEa cghsx]   _ = ar :  E   :a r mv r

:

 :ar  v =

r ls

Z e=a\1a

ls hfÐa osg xer'aby kTG 1ka[ {



r l.a

la

vuqcan ènher^r kas kasra kTG

vuqcan ènher^r kas kasra kTG

:amr : ls

vuqcan ènher^r kasra kTG vuqcan ènher^r kasra kTG amr : ls vuq :a m

r


VGKO # :?


76.

@i tbo d`rdu`t sbhwi jhtb sw`tdbos T7 & T: gro hpoi ì`t`gccy gil durroit ì jhtb tbo ìludthr `s zorh. @e sw`tdbos gro dchsol s`muctgiohuscy tboi Tocodt dhrrodt stgtomoit gjhut durroit ì m` llco w`ro `zie'a^r ènÈa osg eChp eChp T7 h T: `zanOBa osg Qaqys kq, kT rEaa iasuasg `z snlZhasg osg /aana 'aw_1 kTG 1ei iasuasg eChp eC hp las ,l ,l

caEa d_i el1a ta1s ras hk co1 L1a kasxa] td dbp hays ran ososg /aana ve/alro kas rEaa jc ve/alro /aana /aana la oau Bab dravasgG Z

C

Z

:C

T7

T: U

U

U

(G*) mgx`mum durroit `s

(L) ve/alro~ Gis. Thc.

U

/aana /aana /aana

Z C Z

 i:

i:

U kTG
/aana

(D*) ve/alro~

:C

Z

kTG

:C  i: `n kTG Z C t= i: `n kTG Z t=

(GD) Z

C

Z

`7 U

:C

`: U

` (durroit ì m`llco w`ro) = ` 7 — `: hays ran ososg /aana ) = `7 — `: ` dbp ( Zt Zt     U U C :C =    7 o 7 o     Z  Z  Zt Zt   U   :C = o  o C  Z  Ehr `mgx >

ls `mgx ls 

l lt

ey, >

(  `)  6 l lt

(`) `)  6

U Z

 o Z C



Zt C



Z :C

o



Zt :C

 6 



o



Zt C

7 :

 o



Zt :C


VGKO # :5


 

o



Zt :C

7



gil rEaa ` mgx =

&

:

t=

:C  i: Z

U
77. \ G

J

L

D

U

Dhis`lor tbo gjhvo \omporgturo v/s Uhcumo krgpb, dbhhso tbo dhrrodt hpt`hi(s)

m`nasLr raòau-va1ru xzaW ls ey, ckb ehlPàsg la p1u lbet,G

Gis. Thc.

(G*) ì prhdoss DL bogt `s rocogsol (D) prhdoss GL gil JD gro iht `shjgr`d kasxbG (G*) DL `zÒo osg Ï"oa mZcet^r kas (D) GL rEaa JD `zÒo coiadb1 ukbg kTG (GJL) GJ `s `shtbormgc LG `s `shdbhr`d DL `s `shtbormgc GJ cora`b1 kTG LG cova1rub1 kTG DL cora`b1

7:.

(J*) ì prhdoss GJ bogt `s gjshrjol (L*) prhdoss GL `s `shdbhr`d (J*) GJ `zÒo osg Ï"oa vh'aas e"ar kasxbG (L*) GL `zÒo cova1rub1 kTG

kTG

Ehr gi hjnodt gs sbhwi ì e`kuro pcgdol ì erhit he g dhidgvo m`rrhr wb`db he tbo hpt`his dhrrodtcy roprosoits tbo `mgko ehrmol

`zie'a^r ep=a osg ,l hCrq vhry i`^ i `^.a ls caous ep=aauqcan eCEar kT laTuca ehlP` ckb >@a cs duus hays `ze redOd las `zie'a^r lnsxaG

(G)

(J*)



6

  3

VGKO # :;


(L)



(D)

Thc.

\bo gikco he tbo hjnodt `s
whucl jo 'D' jut ehr
hCrq la las.a

,hg
cBab ed_iqvasg ls ey, Waslc `zie'a^r ukb kTG IasUs las.a ls ey, mÐan

kT 'D' kT

`n_rq

ey, mepr ehlP` J kTG

TOD\@HI — : > (Mgx`mum Mgras > :<) TOD\@HI-: (Mgx`mum Mgras > :<)

 \b`s sodt`hi dhitgìs O@KB\ (62) quost`his. (62) quost`his. \bo giswor th ogdb quost`hi `s I_MOZ@DGC UGC_O. UGC_O .  Ehr ogdb quost`hi, oitor tbo dhrrodt iumor`dgc vgcuo (ì lod`mgc ihtgt`hi, truidgtol/rhuilol-hee th tbo sodhil lod`mgc pcgdo1 o.k. 5.:?, ;.66, —6.44, —6.46,,46.:;, —7:;.46) usìk tbo mhuso gil tbo hi-sdrooi v`rtugc iumor`d aoypgl ì tbo pcgdo los`kigtol th oitor tbo giswor. ogdb quost`hi w`cc jo ovgcugtol gddhrlìk th tbo ehcchwìk mgraìk mgraìk sdbomo >  Giswor th ogdb Eucc Mgras

>

ôrh Mgras >

+4 @e HICP tbo dhrrodt dhrrodt iumor`dgc vgcuo `s oitorol gs gs giswor. 6 @i gcc htbor dgsos.

:

:<)

 jc QagM osg vaJ (62) `z'u kTG `zZ1sl `z'u la mÐan ,l cgQ1aZol oau (I_MOZ@DGC UGC_O) kTgG  `zZ1sl `z'u ls mÐan ls ckb ckb cgQ1aZol oau ³i'aoyh vglu osg] i'aoyh l lss e}rb1 CEaau rl >e.MrFeuleUr% miakn.ar% 5.:?, ;.66,—6.44, —46.:;, —7:;.46 ½ las oamt (MH_TO) vaT n va[u CÒbu (HI-TDZOOI) hpq^vy _1wosenl lb`TM (U@Z\_GC I_MOZ@D AOPVGL) la `z1asx cs mÐan ls ey, euei^"U CEaau `n it^ lnsgG  `zZ1sl `z'u ls mÐan la owowP1aglu euOu vglnu 1astua ls vuqcan kasxa %& `w.a^ vgl % +4 1ei ecW^ ckb cgQ1aZol oau (Iumor`dgc vgcuo) kb mÐan Ch>` it^ el1a x1a kTG 'aw _1 vgl % 6 v_1 cBab èneCEaer1asg osgG


VGKO # :2

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT 

74.

\wh vodthrs gro k`voi gs G 







 g ˅` gil J  g dhs t ˅`  g sì t˅n , wboro  



 5

. Eìl tbo t`mo wboi tbo

roc gt`hi | G  J | 4 | G  J | w`cc bhcl.

ias cei'a euOu `zlan ei1s tars tars kT] 



   g ˅` rEaa J  g dhs t ˅`  g sì t˅n 1ka[   kTG hk co1 Aar lbet,G

5



| G  J | 4 | G  J | kTG

td 

Thc.





G



 g ˅` gil rEaa J  g dhs t ˅`  g sì t˅n     | G  J | 4 | G  J |

G

(g  g dhs t ):

 (g sì t ): = 4 t t  : dhs   4  : sì :

tgi

t :



t :

t

 (g sì t ):

:

7



 i 

(g  g dhs t ):

4

 5

 i 



7: 5 t = (7 (7:i  :)s = :s, 76s, 7
7<.

Jchda he mgss 7 ak dhcc`los ocgst`dgccy w`tb jchda he mgss : ak gttgdbol th hio oil he sprìk he sprìk dhistgit a = : I/m. Gcc suregdos gro smhhtb. Eìl tbo sopgrgt`hi jotwooi tbo jchdas wboi : ak jchda rogdbos th `ts mogi phs`t`hi ehr tbo e`rst t`mo. zx cs tqM+s kq, : ak izH1oau ls Dya[l cs `zZ1aCEa >` cs Ulnara kTG eC`gzx la dy 7 ak izH1oau la Dya[l] eC`g

eu1ragl a = : I/m kTG cBab crk eplub kTG td iasuasg Dya[las ls o/1 iwnb L1a L1a kasxbG 7 ak

Gis. Thc.

: ak izH1oau

la Dya[l `kyb dan oa/1 eCEaer `n `kq[pra kT rd

A = : I/m

: m/s

: ak

:.60 Nust Joehro Dhcc`s`hi

7 ak

: m/s

: ak

Nust Getor Dhcc`s`hi U:

U7

7 ak

: ak

U7 + U: = : :U7 — U: = < 4U7 = <  U7 

.....(7) .....(:) < 4

U: = : —

< 4



: 4

m/s


VGKO # :0

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT : 7 \ = =  sod. : 7 :

t =

nb = U: = L`stgido iw 7?.

<<  :   ::   4   ;  m = :7 m = :.60    

E`kuro sbhws tbroo dgpgd`thrs he g`r dgpgd`tgido D ogdb. Gt t = 6, T7 `s dchsol gil romgìs dchso ehr g chik t`mo. Ihw sw`tdb T 7 `s hpoiol gil T : `s dchsol. @e phtoit`gc lèeoroido gdrhss dgpgd`thr D7 `s ? vhct getor g chik t`mo tboi vgcuo he r `s `s > ep=a osg rbu cg/aaen=a a aen=a `zZ1s l /aaenra D hays `z ie'a^ z r kTG t = 6 `n, T 7 las dgi el1a tara kT rEaa yOds co1 co1 rl dgi

nQaa tara kTG vd eChp T7 las Qaasyln ? hasPU kas ras r la oau kasxaG T7

T: las

dgi el1a tara kTG 1ei cg/aaen=a

D7 `n

ehBaah_rn yOds co1 `'par~

T: r

D7

2U

Gis. Thc.

7.?6 T: r

U6

U6 = 2U

q

q —q

DU6 — q

q —q

DU6

q

q





q

r D D q 7 ?= 7   r  D D



  r 



4

= 7 +

7

r

r = =

DU6

q

D

?

2D — q = ?D

7

= 4 7 ?

= 6

 q = 4D  4 :

7

r

=

: 4

= 7.?


VGKO # 46


75.

Mhihdbrhmgt`d c`kbt he oiorky sc`kbtcy mhro tbgi whra euidt`hi 5.:? oU `s ìd`loit hi dgtbhlo. @e ìtois`ty he c`kbt `s :66 [ gil om`ss`hi oee`dòidy `s 766 % tbgi dgcducgto ehrdo hi gihlo, @e gihlo `s poreodtcy gjshrjìk. (K`voi Mo = 0 Û 76 —47 ak gil o = 7.5 Û 76 —70 D) ,l h.ab^1 `zla'a lb Ïta^ la1^ Wyu 5.:? oU cs EaasM+b cb ve/al kT] 1k lTEaasM `n vaèrr kasra kTG 1ei `zla'a

lb rbhzra :66 [ rEaa mZctû {aora 766 % kas ras ,uasM `n dy Aar Aa r lnas] 1ei ,uasM `w.a^ >` cs vh'aas"al kTG kT G —47 —70 ei1a kT Mo = 0 Û 76 ak rEaa o = 7.5 Û 76 D) ( Gis. Thc.

:<.66 :66[ I 5.:?oU E = I :ma :66 E= Û 7.5  5.:?  7670

:0  76 47  7.5  7670

 ?66

= :<.66 7;.

C`kbt he ìtois`ty 7.45 A[/m: egccs hi dhivox cois gs sbhwi ì e`kuro. \bo ìtois`ty hi tbo sdrooi aopt porpoil`ducgr th prìd`pgc gx`s gt g l`stgido he :: dm `s. 7.45 A[/m: rbhzra la `zla'a ,l m Ðay yTgc `n ep=aauqcan vaèrr kTG oqQ1 v{a `n yTgc cs :: dm iwnb `n

yOdhr~ eCEar ìs^ `n rbhzra Aar Aar lbet,G E = :6 dm

:: dm

Gis. Thc.

:

7456 [/m

6 G6

6 G6 :dm

:6 dm :

G6 

G 7  :      G6   6 G6  :6  766 766  G 6   6 6  766 6  745 A[ / m: G 6 766


VGKO # 47


72.



J7 v6 x-gx`s 

J7 



_ièhrm mgkiot`d eòcl J7 ox`sts gjhvo x-gx`s gil jochw x-gx`s J: ox`ts. Jhtb gro l`rodtol hutwgrl porpoil`ducgr th tbo pgpor. G phìt dbgrko bgvìk dbgrko q gil mgss m `s prhnodtol erhm hr`kì w`tb g vochd`ty  n˅ m/s. Eìl gvorgko vochd`ty he tbo pgrt`dco wboi `t drhssos x-gx`s ehr tbo sodhil t`mo. K`voi tbgt J: =


co>` pqOdlb1 {as=a

J7 , x-v{a

ls Ï`n rEaa pqOdlb1 {as=a



J: , x-v{a

ls ubps eh|oau kTG iasuasg laxt ls ry ls

yOdhr~ dakn lb vasn euisê'ar kTG vahs 'a q rEaa izH1oau m la ,l ed_iqhr~ l.a owy ed_iq cs hsx  n˅ m/s }ana `z{ase`r el1a tara kTG td ,l l.a iwcnb dan x-v{a cs xqtnra kT rd jc v_rnay ls iaTnau vaTcr hsx Aar lbet,G ei1a kT J: =
Gvorgko vochd`ty = 7.:6 m/s, Gvorgko spool = : m/s Dgso-@ > @e gvorgko vochd`ty `s dhis`lorol gchik x-gx`s -@ > 1ei vaTcr hshsx x-v{a ls vuqei'a ey1a ta1s Z7



mv 6

qJ7 Z7 9 Z:

, Z: 

mv 6

mv 6



qJ:

< qJ7

L`spcgdomoit gchik x-gx`s x = :(Z7 — Z:) = x-v{a

ls vuqei'a ehCEaaù x = :(Z7 — Z:) =

\htgc t`mo =

lq y co1

=

m qJ7

m qJ7

m







qJ:

m qJ :



m qJ7

m qJ7





m
m
 

5mv6
5mv 6
? m
? m
5mv 6

Mgki`tulo he gvorgko vochd`ty =



5v 6 ?

5

 m/s ?

5mv 6 5v @e > @e gvorgko spool `s dhis`lorol gchik x-gx`s -@@ > 1ei vaTcr pay pay x-v{a ls vuqei'a yb ta1s ta 1s

vaTcr hsx la ènoa.a

Z7



mv 6 qJ7

, Z: 

=

mv 6 q J:



mv 6 < qJ7

Z7 9 Z:


VGKO # 4:

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT ?mv 6

l`stgido gchik x-gx`s  x = :(Z7 + Z:) = x-v{a

?mv6

ls vuqei'a iwnb x = :(Z7 + Z:) =

\htgc t`mo =

lq y co1 =

m qJ7

m qJ7





m qJ :

m qJ:





m qJ7

m qJ7





m
m
:qJ7

:qJ7





?mv 6 :qJ7 Mgki`tulo he gvorgko vochd`ty = ? m
? m
? m
 :m/s

?mv 6

vaTcr hsx la ènoa.a = 70.

Thc.

:6.

:qJ7 ? m
 :m/s

Ehr g sìkco ocodtrhi `hi w`tb gthm`d iumjor z. Oiorky rocogsol lurìk trgis`t`hi erhm 7 st oxd`tol stgto th krhuil stgto `s ;<.2 oU mhro tbgi tbo oiorky rocogsol lurìk trgis`t`hi erhm : il oxd`tol stgto he 7st oxd`tol stgto. Eìl ^ 8 ,ly jysLUª u a[ va1u la `noa.aq `noa .aq Òoal z kTG `zEao mZrs mZ rsetr vhCEaa cs owy vhCEaa v hCEaa osg cÒo.a ls iaTnau ;<.2 oU il st Ïta^ mZcet^ mZcet^r kasrb kT] tas lb : mZrsetr vhCEaa cs 7 mZrsetr vhCEaa osg cÒo.a ls iaTnau mZcet^r Ïta^ cs \1aia kTG. ^ la oau Aar lnas lnas g 8 8

 

 7 7 = ;<.2 oU + 74.5 z:     < < 0  77   74.5 Û ^:   = ;<.2  72  :  ^ = 0  ^ = 4 74.5 ^:  7 

7

\wh shuil shurdos he eroquoidy 7<46 Bz gro mhvìk gs sbhwi ì e`kuro. Eìl tbo jogt eroquoidy hjsorvol jy tbo hjsorvor gt hi y-gx`s gt (6, 7:). (spool he shuil = 446 m/s) 7<46 Bz vahfeÐa ls ias /heu C=aasr ep=aauqcan xer'aby kTG y-v{a `n eCEaer (6, 7:) `n eCEar `zs{al }ana `zse{ar

ehC`_i vahfeÐa L1a kasxbG (/heu lb pay = 446 m/s) y

7:m T7

T: 7m/s

:m/s

x

76m

Thc.


VGKO # 44

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT H

7:m

 T7



:m/s

?m

7m/s T:



x

v v     e:  e   e     v  : dhs    v  dhs    : dhs    dhs   e7  e:  e  7    e 7 v  v      4dhs    e    v  ?    7< 46  4  ?  74  446  e7

:7.

G w`ro he coiktb 7m gil l`gmotor 6.?mm `s suspoilol gs sbhwi yhuik's mhlucus he w`ro `s ` s : x 7677 : I/m . G voriòr sdgco `s usol th mogsuro oxtois`hi. Mgì sdgco he voriòr dgc`por bgs cogst dhuit he 7mm gil 0 mgì sdgco l`v`s`hi oxgdtcy dhìd`los w`tb 76 l`v`s`hi he voriòr sdgco. @i`t`gccy zorh he voriòr sdgco dhìd`los w`tb zorh he mgì sdgco. \boi t bo voriòr sdgco roglìk dhìd`lìk w`tb tbo mgì sdgco, è oxtrg mgss he 7.: ak `s bgikol bgikol erhm w`ro, `s- (\gao k = 76m/s:,  = 4.::) 7m yOdaj^ rEaa 6.?mm H1ac la ran ep=aauq can yUla kqva kT] ran la 1gx xq .aagl : Û 7677 I/m : kTG ,l heu^1n

`Toau la m`1asx ran osg `zcan Aar lnus ls ey, el1a tara kTG heu^1n lTey`n ls oqQ1 `Toaus la vP`roagl 7mm rEaa oq Q1 `T oaus oaus ls 0 Baax] heu^1n `Toaus ls 76 Baax ls caEa ckb >` cs cqoseyr kasrs kTG `zanOBa osg heu^1n `Toaus la 'aq_1] oqQ1 `Toaus ls 'aw_1 ls caEa cOàrb kT] ras heu^1n `Toaus la laT uca ep_k] oqQ1 `Toaus ls caEa cOàrb kasxa] 1ei ran cs 7.: ak la verenLr izH1oau yUla yUla ei1a ta1s (k = 76m/s:,  = 4.:: ysg)

M

Gis.

4

Thc.

 =

E = Gy

7.:x76x7 :

 ?x76 —<  77   x:x76 :  

Thcvìk tb`s wo kot

ky lnus `n ko `za@r lnrs lnrs kT  = 6.4 mm Tìdo cogst dhuit he voriòr dgc`pors `s 6.7mm. Th, tb`rl mgraìk he voriòr sdgco w`cc dhìd`lo w`tb mgì sdgco.


VGKO # 4<


pqgel heu^1n lTey`n la vP`roagl kasxaG ::.

6.7mm kTG

jcey, heu^1n `Toaus la rbcna ep_k oqQ1 `Toaus ls aus ls caEa cOàrb

Dgcducgto dbgiko ì ìtorigc oiorky è vhcumo `s ìdrogsol th o`kbt t`mos gil ì`t`gc tomporgturo \ = 766A. Gssumo prhdoss `s gl`gjgt`d gil tboro `s hio mhco `logc mhihgthm`d kgs.

xTc lb va_renl Ïta^ osg ènhr^ u Aar lbet, 1ei xTc la va1ru vaJ xqua ln ei1a ta1s rEaa `zaneOBal raòau raòau Òo >)as"o oaeu, rEaa xTc ,l ooasasy ,l `noa.aql xTc kTG \ = 766A kTG `z Thc.

 —7 —7 = \ (2U) \ U —7 e (2U) \ \ =  \e = ? —7 < (2) 4

_ = iDv \ =

e e  —4\  iZ\ = 7.Z.   : :  < 

4 4 x 2 x x 766 : < = —066 N = —

:4.

Dhis`lor Dhis`lor tbo k`voi grrgikomoit grrgikomoit ì stogly stgto. K`voi tbgt rglùs he drhss sodt`hi he hio rhl `s bgce he A gihtbor rhl g sbhwi. Eìl 7 A:

CEaa1b vhCEaa osg ib xj^ H1hCEaa `n ehpan lbet,G ei1a x1a kT el ,l IM+ la vuq`zCEa laU iwcnb IM+ IM+ ls vuq`zCEa laU cs ep=aauqcan va/aa kTG kT G

A7 Aar A:

lbet,G

C 466A

C A:

A7

766A

:66

Thc.

 :<.



Z7 = Z:

C7 C: = A7G 7 A:G:

A7 G = : = < A: G7

G pgrt`dco `s prhnodtol erhm krhuil gt
ls `'par~ `'par~ 1k tobu cs Ulnara Ulnara kT rEaa ha`c {aTert cs 46¾ las.a duars kq, xert Ïta^ osg ha`c mIyra kTG ha`c mIyus ls ls `'par~ ve/alro Ï¡paj^ L1a kasxbG

?6% kaeu

ls caEa

Thc. uy

u

v

7:6m = B 46¾ ux

A: =

7 :

mu:

_ _x

= tgi46¾ =

7 4


VGKO # 4?

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT u: sì :
B= =

u:

= 7:6m

Ae = =

7 :

Ae = =

7 7 mu: = m (u:x  uy: ) : :

A`



7 m (u:x :



u:x



usìk ux =



 uy: ) =

 u:y =

: y

4 u

7 7 x mu: : :

u: : 4 uy

 u =

:

u: :

:



u: =

b=

:?.

4 uy = u x.

:k

u 2

u: :k

=

u: 75k

=

 u:  B 7:6 = 46 m   = = < 
G jchda he mgss m = 6.
h`c

Gis. Gis. Thc.

5.46m N 7 ? v6 = = = m/s m 6.< : s = v6



o

—t / 

lt

6

= v6  (7 — o —7) ? =   (<) (6.54) = 5.46 m : :5.

G dh`c he ?6 t uris gil turi grog : Û 76 —< m: gil ros`stgido ?6  `s usol ì kgcvgihmotor w`tb rgl`gc mgkiot`d eòcl 6.6: \. \. @e sueeors mgx`mum loecodt`hi he 6.7 rgl gkgìst gkgìst thrs`hi he thrs`higc dhistgit D = 76 —< Im/rgl. @t iools th jo dhivortol ìth gi gmmotor mogsurìk upth 7G. Eìl sbuit ros`stgido roqu`rol. ?6 8asns rEaa : Û 76 —< m : {aT=aWy hayb lq.Myb ,hg ?6  `zernas/a la m`1asx lnls 6.6: \ e=a\1b1 pqOdel1 {aT =a ls caEa caEa /aanaoa`b la euoa^.a el 1a tara kTG 1k onasMb eu1ragl D = 76 —< Im/rgl ls caEa 6.7 nseM1u la ve/alro

eh{as`.a isra kTG 1ei jc /aanaoa`b las `zernas/a Aar lnasG Thc.

7G `nac

ls vobUn osg ènher^r lnua kas ras jcls ey, vah'1l 'a_U

I = ?6 G = : Û 76 —< m: D = 76 —<, Z = ?6  , J = 6.6: \,  = 6.: rgl I` GJ = D `k =

D I GJ



76 <  6.: ? 6  :  7 6 <  6 . 6 :


VGKO # 45


= 6. 7 G `k Û K = (` — ` k) T 6.7 Û ?6 = (7 — 6.7) Û T ? = 6.0ÛT ?6  T= 0 :;.

G uièhrm uièhrm rìk rìk gro rocogsol s`muctgiohuscy s`muctgiohuscy erhm thp he ìdcìo pcgio. Turegdo he ìdcìo pcgio `s rhukb oihukb th provoit giy sc`ppìk. @e t7 gil t : gro tbo t`mo tgaoi th rogdb jhtthm he ìdcìo jy rìk gil l`sd rospodt`vocy gil t: — t7 =

: 4 76

, tboi tbo vgcuo he b `s >

,l co>` hy1 rEaa ,l plrb las urry ls 'ab"a^ cs ,l caEa Ias M+a tara kTG urry lb crk jc `zlan Qaqninb kT el 1k eWcyu xer las naslus ls ey, `1a^@r kTG 1ei hy1 rEaa plrb las urry ls ubps rl `k¡qpus osg yxa : 4 co1 Òo'a% t7 rEaa t: ,hg t: — t7 = kas, ras b la oau L1a kasxa > 76

b 56¶

Thc.

gdm =

ksì  A: 7 : Z

grìk



gl`sd





:b 4 4k <





<

4

4k 4k



4





75b 4k

:b

:. t l`sd



4k :  4k 7 7 < 4k :  k 7 4 7 : :.

trìk

4k : A: 7 : Z

4 k

4 k



4

t  

75b 4k



b  75  k  4

  <  

 <   :  k 4 

b


VGKO # 4;


: :



b : 4  k  4 b 4

b 4

  

7



7 :



b



4 <

 6.;?m

TOD\@HI — 4 > (Mgx`mum Mgras > 7:)  \b`s sodt`hi dhitgìs \[H (6:) pgrgkrgpbs. (6:) pgrgkrgpbs. Jgsol hi ogdb pgrgkrgpb, tboro gro \[H (6:) quost`his. (6:) quost`his.  Ogdb quost`hi bgs EH_Z hpt`his. EH_Z hpt`his. HICP HIO he HIO he tboso ehur hpt`his dhrrosphils th tbo dhrrodt giswor.  Ehr ogdb quost`hi, dbhhso tbo hpt`hi dhrrosphilìk th tbo dhrrodt giswor.  Giswor th ogdb ogdb quost`hi w`cc jo ovgcugtol gddhrlìk th tbo ehcchwìk mgraìk mgraìk sdbomo > Eucc Mgras

>

+4 @e HICP tbo dhrrodt dhrrodt hpt`hi `s dbhsoi.

ôrh Mgras >


Iokgt`vo Mgras >

—7 @i —7 @i gcc htbor dgsos.

4

   

7:)

jc QagM osg ias (6:) vuqVIsi kTG `zZ1sl vuqVIsi `n va/aaenr ias (6:) `z'u ei, x, kTgG `zZ1sl `z'u ls ey, pan ehlP` ei, ei, x, kTG ju pan ehlPàsg osg ecW^ ,l ehlP` kb ckb mÐan las euei^"U lnra kTkTG `zZ1sl `z'u ls ey, mc ehlP` las pqusg tas ckb mÐan las euei^"U lnra lnra kTG `zZ1sl `z'u ls mÐan la owP1ag 1aglu euOu vglu 1astua ls ls vuq can kasxa%& `w.a^ vgl % +4 1ei ecW^ ckb ehlP` kb pqua x1a kTgG 'aw_1 vgl % 6 1ei lasj^ Bab ehlP` ukbg pqua x1a kT ³vEaa^r~ `z'u vuqÐaenr kT½G X.a vgl % —7 v_1 cBab èneCEaer1asg osg Vgrgkrgpb ehr Wuost`hi Ihs. :2 th :0 :2 :0 [o aihw tbgt g dbgrkol pgrt`dco oxporòido oxporòido ehrdo ì ocodtr`d gil mgkiot`d eòcl gs wocc gs spool he c`kbt `s giy bhw rocgtol th pormogj`c`ty pormogj`c`ty gil porm`tt`v`ty he molùm. O = ocodtr`d eòcl, J = mgkiot`d eòcl, 6 = pormogj`c`ty he vgddum O6 = pormogj`c`ty he vgddum. (uso l`mois`hi he coiktb gil l`mois`hi he t)

ko taurs kT el el ,l vahse'ar l.a eh|qr dy rEaa pqOdlb1 dy vuqBah lnra kTG jcb `zlan `zla'a lb pay oa/1o lb eh|qr 'abyra rEaa pqOdlb1 ànxO1ra `n euBa^ n lnrb kTG O = eh|qr {aT{aT=a , J = pqOdlb1 {aT=a, 6 = oa/1o lb pqOdlb1 ànxO1ra O6 = euha^r lb eh|qr 'abyra ( yOdaj^ lb ehoa rEaa co1 t lb ehoa m`1asx elet,) :2.

L`mois`hi he ocodtr`d gil mgkiot`d eòcl gro rocgtol

eh|qr {aT=a rEaa pqOdlb1 {aT{aT=a lb ehoa elc `zlan cOde_/ar kTG

Thc.

(G*) QO] = QJ] QC\ —7] (J) QO] = QJ] QC —7\ —7] (D) QO] = QJ] QC —7\] (L) QO] = QJ] Q C\] @i torms he l`mois`hi

ehoa ls ìasg osg qO = qvJ O = vJ


VGKO # 42


6 gil 6 gro rocgtol O6 rEaa 6 lb ehoa elc `zlan cOde_/ar k kTTG : —: (G*) Q6] = Q 6 ] C \ (J) Q6] = Q 6 ] C —: \: (D) Q6] = Q 6 ] C: \: (L) Q6] = Q 6 ] C \ —:

:0.

L`mois`hi he

Thc.

D=

7

6 6 7

D: =

6 6 6 = 6 . D: Vgrgkrgpb ehr Wuost`hi Ihs. 46 th 47 46 47 @e r =

1ei

x y

r=

tboi x y

kas ras ras

x  x r = y  y è

y y

1ei 46.

Thc.

47.



x   y  x 7   7  y  y x  

 7 tboi

y y

r r

 7 kas ras

=

r r

x x =

+

x x

7

y y

+

y y

Gt t = 6 Iumjor he gdt`vo iudcò gro I6 oqugc th 4666. Gt t = 7.6 sod iumjor he gdt`vo iudcò gro I(t) = 7666  <6. Eìl mgx`mum porm`ss`jco orrhr lodgy dhistgit he rgl`h gdt`vo iudcò. m = 6.
7 g 7 g : g

`zEao  sod osg r1 iwnb Aar lnasG (D*) 6.6<

(L) 6.6?

tboi vgcuo he lr `s prhphrt`higc th

(7  g )

:

(J)

:gg (7  g )

:

(D)

: g (7  g ) :

(L)

:gg (7  g: )


VGKO # 40


TOD\@HI — 7 > (Mgx`mum Mgras > 7:)  \b`s sodt`hi dhitgìs EH_Z (6<) quost`his. (6<) quost`his.  Ogdb quost`hi bgs \[H (6:) mgtdbìk (6:) mgtdbìk c`sts 1 C@T\-@ gil C@T\-@ gil C@T\-@@. C@T\-@@.  EH_Z hpt`his hpt`his gro k`voi roprosoitìk mgtdbìk he ocomoits erhm C@T\-@ gil C@T\-@@. HICP HIO he tboso ehur ogdb quost`hi, dbhhso tbo hpt`hi, dbhhso tbo hpt`hi dhrrosphilìk th tbo dhrrodt mgtdbìk.

 Ehr ogdb quost`hi, mgra w`cc jo gwgrlol gddhrlìk th tbo ehcchwìk mgraìk sdbomo > Eucc Mgras

>

+4 @e HICP tbo hpt`hi dhrrosphilìk dhrrosphilìk th tbo dhrrodt mgtdbìk `s dbhsoi.

ôrh Mgras >


Iokgt`vo Mgras >

—7 @i —7 @i gcc htbor dgsos.

7

7:)

@@  jc QagM osg pan (6<) ë'u kTkTG `zZ1sl ë'u osg ias (6:) cqosyu cwep1a¡ (mgtdbìk c`sts) kT % cwpb&@ vaTn cw pb& b —@ vaTn cwpb —@@ cqosyuasg las i'aa^rs kq, pan ehlP` ei, x, kTG ju pan ehlPàsg osg ecW^ ,l ehlP`  cwp —@ —@@ ls rZhasg ls cq kb ckb cqosyu ëie'a^r lnra kTkTG las pqusgG  `zZ1sl `z'u ls ey, ckb cqosyu ëie'a^r lnus hays ehlP` las  `zZ1sl `z'u ls mÐan la owP1ag 1aglu euOu vglu 1astua ls ls vuq can kasxa%& `w.a^ vgl % +4 1ei ecW^ ckb ehlP` kb pqua x1a kTgG 'aw_1 vgl % 6 1ei lasj^ Bab ehlP` ukbg pqua x1a kT ³vEaa^r~ `z'u vuqÐaenr kT½G X.a vgl % —7 v_1 cBab èneCEaer1asg osgG 4:.

V-U ìl`dgthr ìl`dgthr l`gkrgm ehr <-prhdossos <-prhdossos (7), (:), (4) & (<) `s sbhwi. sbhwi. \gjco \gjco 7 sbhws tbo prhdoss prhdoss gil gil tgjco tgjco (:) sbhws g rosuct rokgrlìk tbgt prhdoss. prhdoss. Mgtdb tbo prhpor oitròs ehrm dhcumi-: th dhcumi-7 V (7) (:) `s `shtbormgc 4V6 (4) `s gl`gjgt`d (<) V6

(4)

(:)

U6

\gjco-7 (G) Vrhdoss (7) (J) Vrhdoss (:) (D) Vrhdoss (4) (L) Vrhdoss (<) v ansQa pan V-U cwpl vans can.ab-: `zÒo ls cgxr

4U6

U

\gjco-: () whra lhio 6 () whra lhio 5V6U6 () Bogt oxdbgiko 6 (U) Dbgiko ìtorigc oiorky 6 `zÒoasg (7), (:), (4) h (<) ls ey, ep=a osg `zie'a^r kTG can.ab -7 `zÒo -: la la[yo -7 -7 ls caEa mepr >` cs eoyau èn.aao las i'aa^rb kTkTG la[ yo -: V (7) (:) cora`b1 4V6

las i'aa^rb kT rEaa lbet,G

(4) >)as "o

(<) V6 U6

-7

(4)

(:)

4U6

U

-:

(G) `zÒo (7) (J) `zÒo (:)

'aw_1 kTG () el1a x1a la1^ 'aw () el1a x1a la1^ 5V 5V6U6 kTG


VGKO # <6


Gis. Thc.

(D) `zÒo (4) (L) `zÒo (<) (G) — : 1 (J) — < 1 (D) — 4 1 (L) — 7 (7) Vrhdoss `zÒo -7 -7

w = 5V6U6, U 

:

'aw_1 kTG 'aw_1 kTG

(0V6U6 — 4V6U6) = 0V6U6, W = 7?V6U6

Vrhdoss `zÒo -: -:

(:)

w = 4V6U6 i 4, U = 6, W = 4V6U6 i 4 Vrhdoss `zÒo -4 -4 ?/4  4V6U6 = V6 U6?/4 U = 44/?U6 VU  V U 4 42/ ? w = ` ` e e  V6 U6 (4  44 / ? )  V6 U6 (4: / ?  7)  7 : : U = — [, W = 6

(4)

(<)

44.

4

() vaiau `ziau lb xj^ Ï"oa osg ènhrû (U) va_renl Ïta^ os

Vrhdoss-< [ = 6

U = —4V6U6

W = —4V6U6

Dhcumi -: sbhws g systom he dbgrkos gil dhcumi-7 roprosoit roprosoit lopoiloido he ocodtr`d eòcl gt phìt V cyìk gt l`stgido l erhm hr`kì. hr`kì. Mgtdb tbo prhpor oitròs oitròs erhm dhcumi-: th dhcumi-7. dhcumi-7. Dhcumi-7 y

Dhcumi-:

(G)

(7) @ilopoiloit he l x

W

Vhìt dbgrko W, aopt gt hr`kì y (J) +W

—W

(:)



(4)



(<)



x

7 l

\wh phìt dbgrkos gro aopt hi x-gx`s vory dchso th ogdb htbor. y

+ :

x

(D)

—

7 l:

\wh ìeì`to w`ros dgrryìk uièhrm cìo dbgrko lois`ty aopt ì x — y pcgio hi sbhwi. V `s g phìt hi z-gx`s. (l 999 ) (L) @ieì`to pcgio sboot aopt ì y-z pcgio.

7 l4

V `s phìt hi x — y pcgio la[yo -: -: vahs'aas g ls eula1 las

`zie'a^r lnra kT rEaa rEaa la[yo -7 nb `n eCEar ed_iq V `n eh|qr {as=a -7 owy ed_iq cs l iw lb euBa^nra las `zie'a^ e'a^r lnra kTG la[ yo -: -: las la[yo -7 -7 cs eoyau lbet,G


VGKO # <7


-7

-: y

(7) l cs

(G)

veuBa^n kTG

x

W

ed_iqhr~ vahs'a W ow y ed_iq `n eCEar kTG y

(:) 

(J) +W

x

—W

ias ed_iqhr~ vahs'a

x-v{a y

7 l

`n ,l&iwcns ls dkqr utibl eCEar kTG

+ :

x

(D)

—

(4)



7 l:

ias vu_r ran etula nsQab1 vahs'a 8auZh co>` kT] x-y ry osg ep=aauqcan eCEar kTG V, z-v{a `n eCEar kTG (l 999 ) ed_iq V, (L) cory

vu_r èU~Ula

y-z ry

osg eCEar kT G

(<) 

7 l4

ed_iq V, V, x-y ry os g eCEar kTG Gis.

(G) - < (J) - 4 (D) - 7 (L) — :

Thc.

(7) ì dgso he phìt dbgrko O =

ed_iqhr~ vahs'a lb eCEaer osg

O=

(:) @i dgso he l`phco O =

AV l4

e}/azqh lb eCEaer osg

O=

AW l: AW l:

AV l4

(4)


VGKO # <:


:a r 

:a r

r l 

+

O=

A dhs   r

a l:

 :

=



l:

 :

=

 :6

(<) O = 4<.

—



\wh sgtocc`tos he mgssos M7 gil M: gro rovhcvìk grhuil g pcgiot ì d`rducgr pgtbs rgl`` Z 7 gil Z:. @e m7 Z 7 = : gil 7 = . \boi Tocodt dhrrodt gctorigt`vos. gctorigt`vos. m: Z: <

rEaa M: izH1oau M7 rEaa Z7

= : rEaa

Z: Dhcumi - @ -@ (G) (J) (D) (L)

v7 v:

=

7 <

ls ias m`xzk ,l xzk ls panasg vaTn

(W)

C7 C: \7 \:

Gis.

(G) — V 1 (J) — W 1 (D) — Z 1 (L) — T

Thc.

(7) v6 =

v:

=

m:

: 7 2 7

(Z)

7

(T)

7 2

(\)

v7

m7

Dhcumi — @@ -@@ (V)

A:

ls hfralan Èaasg osg xer'aby kT G 1ei

kas ras la[yoasg la ckb ckb >` cs eoyau lbet,G

A7

Z7 rEaa Z: e=a\1a

7 <

KM Z

Z: Z7

(:) AO =

=

: 7

KMm Z


VGKO # <4

| NOO GLUGIDOL-:672 | LG\O > :6-6?-:672 | MOMHZP JGTOL | VBPT@DT A7 A:

m7

=

m:

x

Z7 Z:

:

=

7

<

x

7

= 2

(4) C = mvZ C7 m v Z : : 7 = 7 = 7 = 7 = x x = 7 C: m: v: Z: 7 7 < 4/:

Z  (<) =  7  \:  Z:  \7

4<.

7

=

2

Dhcumi - @

Dhcumi - @@

 (G) r  t   t ˅`   t ˅n

(V) V  dhis tg tgi t



(J) r  t    dhs t ˅` 

(D) r  





   sì t ˅n

( W) C  dhis tg t gi t

t: ˅ t `   ˅n : :

( Z) Z) AO  dhis t gi gi t

 (L) r   dhs t ˅`   sì t ˅n

(Z) _  dhis tg tgi t (\) \  dhis tg tgi t

-@

-@@ 

 (G) r  t   t ˅`  t ˅n

(V) V  eu1r

 (J) r  t    dhs t ˅`    sì t ˅n

(W) C  eu1r





(D) r



t: ˅ t `   ˅n : :

(Z) AO  eu1r

 (L) r   dhs t ˅`   sì t ˅n

(Z) _  eu1r (\) \  eu1r

Gis. Thc.

(G) VWZT\ 

(J) W\

(D) \ 

(G) U = dhistgit eu1r g 

(L) WZT\

6



(J) g  : r 

eu1r (D) g = dhistgit eu1r 

(L) g = —7 r 

U = dhistgit eu1r


VGKO # <<

JEE Advanced 2018 Physics

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