jee 2014 booklet6 hwt electrostatics

7/22/2019 Jee 2014 Booklet6 Hwt Electrostatics

1/18

Xdkyflfnkdr Jifss`s

XLJ/@i`jtrostftdjs ;7 AR[-8/Uaysdjs

KF[@ 3 [DL@ 3 ;5 Ldnut`s LFWMZ 3 ] ___ /60\ [@Z[ JOK@ 3 @IZ[ ]6\

Z[FW[ [DL@ 3 @NK [DL@ 3 [DL@ [FM@N3 UFW@N[Z ZDBNF[PW@ 3

[ads t`st jontfdns f totfi oh 60 Ogc`jtdv` [yp` Vu`stdons. @fja qu`stdon jfrrd s 6 lfrm. [a`r` ds NO N@BF[DX@ lfrmdnb.

Jaoos` ta` jorr`jt fit`rnftdv . Oniy on` jaodj` ds jorr`jt.

6. [wo dk`ntdjfi jafrb`k spa`r`s susp`nk`k hrol f jollon podnt gy two lfssi`ss strdnbs oh i`nbta i fr` dndtdfiiy f kdstfnj`

k k i fpfrt g`jfus` oh ta`dr lutufi r`puisdon. [a` jafrb` g`bdns to i`fm hrol gota ta` spa`r`s ft f jonstfnt rft`. Fs f r`suit

jafrb`s fpprofja `fja ota`r wdta f vìojdtyv. [a`n fs f hunjtdon oh kdstfnj`xg`tw``n ta`l.

(F)6

v x (G) 6 7/v x (J) v x (K) 6 7/v x

7. [wo posdtdv` jafrb`s oh lfbndtuk`q fr` pifj`k ft ta` `nks oh f sdk` 6 oh f squfr` oh sdk` 7 f. [wo n`bftdv` jafrb`s oh ta` sfl`lfbndtuk` fr` m`pt ft ta` ota`r jorn`rs. Ztfrtdnb hrol r`st, dh f jafrb` Vlov`s hrol ta` ldkki` oh sdk` 6 to ta` j`ntr` oh squfr`,dts mdn`tdj `n`rby ft ta` j`ntr` oh squfr` ds 3

(F)5

6 7 66

; 0

qV

f

(G) z`ro

(J)5

6 7 66

6 0

qV

f

(K)

5

6 7 76

; 0

qV

f

:. F jafrb`k pfrtdji`qds saot towfrks fnota`r jafrb`k pfrtdji`V wadja ds hdx`k, wdta f sp``k v. Dt fpprofja`sVupto f jios`stkdstfnj`rfnk ta`n r`turns. Dh q saot wdta sp``k 7v, ta` jios`st kdstfnj` oh fpprofja wouik g` 3

(F);r

(G)7r

(J) 7r (K) r

;. [wo jonkujtdnb spa`r`s oh rfkdd :jl fnk 6jlfr` s`pfrft`k gy f kdstfnj` oh 65jl dn hr`` spfj`. Dh ta` spa`r`s fr` jafrb`k tosfl` pot`ntdfi oh 65X. `fja, ta` horj` oh r`puisdon g`tw``n ta`l ds 3

(F)46 65

:

N (G) 4

765

4

N (J) 4

665

4

N (K) 4

;65

:

N

0. Jafrb s 0 J fnk 65 J fr` pifj`k 6lfpfrt. Rorm kon` to grdnb ta`s` jafrb`s ft f kdstfnj` 5.0lhrol `fja ota`r ds 3

(F);4 65 C (G) ;61 65 C (J) 7;0 65 (K) 64 65 C

8. Jafrb`q7oh lfssl r`voiv`s frounk f stftdonfry jafrb`q6dn f jdrjuifr orgdt oh rfkdusr.[a` orgdtfi p`rdokdj tdl` ohq7wdii g` 3

(F)

6 77

6 7

; /

lr

mq q

(G) 76 7

67 7;

/mq q

lr

(J)

6 77 7

6 7

; /

lr

mq q

(K)

6 77 7

6 7

; /

lr

mq q

2. [wo dk`ntdjfi jafrb k spa`r`s fr susp`nk k gy strdnbs oh `qufi i`nbta. [a` strdnbs lfm` fn fnbi` oh :5 wdta `fja ota`r.

Ra`n susp`nk`k dn f idqudk oh k`nsdty :5 1. bjl , ta` fnbi` r`lfdns ta` sfl`. Dh k`nsdty oh ta` lft`rdfi oh ta` spa`r` ds :68b jl ,

ta` kdì`jtrdj jonstfnt oh ta` idqudk ds3

(F) ; (G) : (J) 7 (K) 6

1. [wo slfii spa`r`s oh lfss`s 6 7fnkL L fr` susp`nk`k gy w`dbati`ss dnsuiftdnb tar`fks

oh i`nbta 6 7fnkI I . [a` spa`r`s jfrry jafrb`s 6 7fnkV V r`sp`jtdvìy. [a` spa`r`s fr`

susp`nk`k suja taft ta`y fr` dn i`vì wdta on` fnota`r fnk ta` tar`fks fr` dnjidn`k to ta`v`rtdjfi ft fnbi`s oh tar`fks fr` dnjidn`k to ta` v`rtdjfi ft fnbi`s oh 6 7fnk fs saown.

Radja on` oh ta` hoiiowdnb jonkdtdons ds `ss`ntdfi, dh 6 7 ?

(F) 6 7 6 7gutL L V V (G) 6 7L L

(J) 6 7V V (K) 6 7I I


2/18

Xdkyflfnkdr Jifss`s

XLJ/@i`jtrostftdjs ;: AR[-8/Uaysdjs

4. [a`r` ds f undhorl ì`jtrdj hdìk oh dnt`nsdty@wadja ds fs saown. Aow lfnyifgì`k podnts afv` ta` sfl` ì`jtrdj pot`ntdfi fs ta` huiiy safk`k podnt.?(F) 7 (G) :(J) 1 (K) 66

65. [wo dk`ntdjfi jonkujtdnb gfiisF fnkGafv` posdtdv` jafrb`s 6 7fnkq q r`sp`jtdvìy gut 6 7q q . [a` gfiis fr` groubat tob`ta`rso taft ta`y touja `fja ota`r fnk ta`n m`pt dn ta`dr ordbdnfi posdtdons. [a` horj` g`tw``n ta`l ds 3(F) i`ss tafn taft g`hor` ta` gfiis touja`k (G) br`ft`r tafn taft g`hor` ta` gfii touja`k(J) sfl` fs taft g`hor` ta` gfiis touja`k (K) z`ro

66. Pnk`r ta` fjtdon oh f bdv`n jouiolgdj horj` ta` fjjì`rftdon oh fn ì`jtron ds 77 77 0 65. l / s . [a`n ta` lfbndtuk` oh ta`

fjjì`rftdon oh f proton unk`r ta` fjtdon oh sfl` horj` ds n`friy.

(F)64 76 8 65. l / s (G) :6 74 6 65. l / s (J) 65 76 0 65. l / s (K) 72 76 8 65. l / s

67. F jonkujtor afs g``n bdv`n f jafrb` 2: 65 J gy trfnsh`rrdnb ì`jtrons. Lfss dnjr`fs (dn mb) oh ta` jonkujtor fnk ta` nulg`r

oh i`jtrons fkk`k to jonkujtor fr` r`sp`jtdvìy.

(F) 68 :67 65 fnk 7 65

(G) :6 640 65 fnk 0 65

(J)64 68: 65 fnk 4 65 (K) 61 677 65 fnk 7 65

6:. Raft ds ta` totfi jafrb` dn jouiolg oh 20.5mboh ì`jtrons ?

(F)6:5 :7 65. J (G) 68: 7 65. J (J) 6:6 :7 65. J (K) 6:6 :7 65. J

6;. Pnk`r ta` dnhiu`nj` oh ta` jouiolg hdìk oh jafrb` V f jafrb` q ds lovdnb frounk dt dn fn ìidptdjfi orgdt. Hdnk out ta` jorr`jt

stft`l`nt(s).(F) [a` fnbuifr lol`ntul oh ta` jafrb` q ds jonstfnt (G) [a` idn`fr lol`ntul oh jafrb` q ds jonstfnt

(J) [a` fnbuifr vìojdty oh ta` jafrb` q ds jonstfnt (K) [a` idn`fr sp``k oh ta` jafrb` q ds jonstfnt

60. F jafrb`Vds pifj`k ft `fja oh ta` opposdt` jorn`rs oh f squfr`. F jafrb` qds pifj`k ft `fja oh ta` ota`r two jorn`rs. Dh ta` n`t

ì`jtrdjfi horj` onVds z`ro, ta`n ta` V

q `qufis =

(F) 7 7 (G) 6 (J) 6 (K)6

7


3/18

Xdkyflfnkdr Jifss`s

XLJ/@i`jtrostftdjs ;; AR[-8/Uaysdjs

KF[@ 3 [DL@ 3 ;5 Ldnut`s LFWMZ 3 ] ___ /60\ [@Z[ JOK@ 3 @IJL ]7\


[ads t`st jontfdns f totfi oh 60 Ogc`jtdv` [yp` Vu`stdons. @fja qu`stdon jfrrd`s 6 lfrm. [a`r` ds NO N@BF[DX@ lfrmdnb.

Jaoos` ta` jorr`jt fit`rnftdv`. Oniy on` jaodj` ds jorr`jt.

6. [wo dk`ntdjfi posdtdv` jafrb`s fr` hdx`k on ta` y-fxds ft `qufi kdstfnj`s hrol ta` ordbdn O. F n`bftdvìy jafrb`k pfrtdji` stfrts onta` x-fxds, ft f ifrb` kdstfnj` hrolO, lov`s fionb ta` x-fxds, pfss`s taroubaO fnk lov`s hfr fwfy hrolO. Dts fjjì`rftdon f dstfm`n fs posdtdv` fionb dts kdr`jtdon oh lotdon. [a` g`st brfpa g`tw``n ta` pfrtdji`'s fjjì`rftdon fnk dts x-joorkdnft` dsr`pr`s`nt`k gy 3

(F) (G) (J) (K)

7. [wo dk`ntdjfi jonkujtdnb spa`r s jfrrydnb kdhh`r`nt jafrb`s fttrfjt `fja ota`r wdta f horj`Hwa`n pifj`k n fdr l`kdul ft fkdstfnj`kfpfrt. [a` spa`r`s fr` posdtdons. Now ta` two spa`r`s r`pì `fja ota`r wdta f horj` waos` lfbndtuk` ds `qufi to taft ohta` dndtdfi fttrfjtdv` horj . [a` rftdo g`tw``n dndtdfi jafrb`s on ta` spa`r`s ds =

(F) : 1 oniy (G) : 1 oniy

(J) : 1 or : 1 (K) :

:. Dn nftur`, ta` i`jtrdj jafrb` oh fny syst`l ds fiwfys `qufi to 3(F) afih dnt`brfi luitdpi` oh ta` i`fst flount oh jafrb` (G) z`ro(J) squfr` oh ta` i`fst flount oh jafrb` (K) dnt`brfi luitdpi` oh ta` i`fst flount oh jafrb`

;. F soidk spa`r` oh rfkdusW6fnk voiul` jafrb` k`nsdty 5r

ds `njios`k gy f aoiiow spa`r` oh rfkdusW7 wdta n`bftdv` surhfj`

jafrb` dn ta` syst`l ds z`ro, 5 ds f posdtdv` jonstfnt fnkrds ta` kdstfnj` hrol ta` j`ntr` oh ta` spa`r`. [a` rftdo7

6

W

Wds 3

(F)5

(G) 57 / (J) 5 7/ (K)

5

0. F soidk spa`rdjfi jonkujtor oh rfkdus Wafs f spa`rdjfi jfvdty oh rfkdus f f W ft dts j`ntr`. F jafrb` V ds m`pt ft ta` j`ntr`.

[a` jafrb` ft ta` dnn`r surhfj`, out`r surhfj` fnk ft f posdtdon r f r W fr` r`sp`jtdvìy.

(F) 5V V (G) 5V V (J) 5 5V (K) 5 5V

8. [a` jolg run tarouba on`'s kry afdr fttrfjts slfii gdts oh pfp`r. [ads ds ku` to 3(F) jolg ds f book jonkujtor(G) pfp`r ds f book jonkujtor(J) ta` ftols dn ta` pfp`r b`t poifrds`k gy ta` jafrb`k jolg(K) [a` jolg poss`ss`s lfbn`tdj prop`rtd`s

2. FfnkGfr` two dk`ntdjfi spa`rdjfi jafrb`k gokd`s wadja r`pì `fja ota`r wdta horj`H, m`pt ft f hdndt` kdstfnj`. F tadrk unjafrb`kspa`r` oh ta` sfl` sdz` ds groubat dn jontfjt wdta spa`r` G fnk r`lov`k. Dt ds ta`n m`pt ft ldk-podnt ohF fnk G. Hdnk ta`lfbndtuk` oh horj` onJ.(F) H/7 (G) H/1 (J) H (K) S`ro


4/18

Xdkyflfnkdr Jifss`s


1. Jafrb` fr` pifj`k ft jorn`rs oh f squfr` oh sdk` f fs saown dn ta`

hoiiowdnb hdbur`. [a` jafrb`Fds dn `qudidgrdul. [a`rrftdo 6

7

q

qds 3

(F) 6 (G) 7

(J)

6

7 (K) 7 7

4. Jonsdk`r f nùtrfi jonkujtdnb spa`r`. F posdtdv` podnt jafrb` ds pifj`k outsdk` ta` spa`r`. [a` n`t jafrb` on ta` spa`r` ds ta`n.(F) n`bftdv` fnk kdstrdgut`k undhorliy ov`r ta` surhfj` oh ta` spa`r`.(G) n`bftdv` fnk fpp`frs oniy ft ta` podnt on ta` spa`r` jios`st to ta` podnt jafrb`(J) n`bftdv` fnk kdstrdgut`k non-undhorliy ov`r ta` `ntdr` surhfj` oh ta` spa`r`(K) z`ro

65. [wo dk`ntdjfi jafrb`s r`p i `fja ota`r wdta f horj` `qufi to 65lb wtwa n ta`y fr 5 8. l fpfrt dn fdr 765b ls . [a` vfiuòh fja jafrb` ds3

(F) 7lJ (G) 27 65 J (J) 7nJ (K) 7 J

66. [wo spa`rdjfi jonkujtors G fnkJafvdnb `qufi rfkdd fnk jfrrydnb `qufi jafrb`s dn ta`l r`pì`fja ota`r wdta f horj`Hwa`n m`pt fpfrt ft sol` rfkdus fs taft ohGgut unjafrb`k, ds groubat dnjontfjt wdtaG, ta`n groubat dn jontfjt wdtaJfnk hdnfiiy r`lov`k fwfy hrol gota. [a` n`w horjòh r`puisdon g`tw``nGfnkJds 3

(F);

H(G)

:

;

H

(J)1

H(K)

:

1

H

67. [ar`` jafrb`s 6 6 fnk 7J J J fr` m`pt ft v`rtdj`s ohF,GfnkJ oh fn `qudift`rfi trdfnbi`FGJoh 65jlsdk` r`sp`jtdvìy.

[a` r`suitfnt horj` on ta` jafrb` ftJds 3(F) 5.54N (G) 6.1N (J) 7.27N (K) :.67N

6:. Horj` g`tw``n two dk`ntdjfi jafrb`s pifj`k ft f kdstfnj` ohrdn vfjuul dsH. Now f sifg oh kdì`jtrdj oh kdì`jtrdj jonstfnt ; dsdns`rt`k g`tw``n ta`s` two jafrb`s. Dh ta` tadjmn`ss oh ta` sifg ds r/7, ta`n ta` horj` g`tw``n ta` jafrb`s wdii g`jol`

(F) H (G):0H (J)

;4H (K)

;H

6;. [a` gog oh sdlpi` p`nkuiul ds afnbdnb v`rtdjfiiy kown hrol f hdx`k dk`ntdjfi gog gy l`fns oh f strdnb oh i`nbta i. Dh gota gogsfr` jafrb`k wdta f jafrb`q`fja, tdl` p`rdok oh ta` p`nkuiul ds (dbnor` ta` rfkdd oh ta` gogs)

(F)7

7

7 i

rq

bi l

(G)7

7

7 i

qb

i l

(J) 7 i

b (K)

77

i

qb

i

60. F p`nkuiul gog jfrrd`s f n`bftdv` jafrb` q. F posdtdv` jafrb` q ds aìk ft ta` podnt oh support. [a`n, ta` tdl` p`rdok oh ta`

gog ds3

(F) br`ft`r ta`n 7 I

b (G) i`ss tafn 7

I

b (J) `qufi to 7

I

b (K) `qufi to

77

I

b


5/18

Xdkyflfnkdr Jifss`s


KF[@ 3 [DL@ 3 ;5 Ldnut`s LFWMZ 3 ] ___ /60\ [@Z[ JOK@ 3 @IJL ]:\



Jaoos` ta` jorr`jt fit`rnftdv`. Oniy on` jaodj` ds jorr`jt. Aow`v`r, qu`stdons lfrm`k wdta * lfy afv` Lor` tafn

On` jorr`jt optdon.

6. [wo dk`ntdjfi spa`r`s wdta jafrb` ; 7q q m`pt sol` kdstfnj` fpfrt `x`rt f horj`Hon `fja ota`r. Dh ta`y fr` lfk` to touja `fja

ota`r fnk r`pifj`k ft ta`dr oik posdtdons, ta` horj` g`tw``n ta`l wdii g` 3

(F)64H (G)

61H (J)

41H (K)

14H

7. Dk`ntdhy ta` wronb stft`l`nt dn ta` hoiiowdnb. Jouiolg's ifw jorr`jtiy k`sjrdg`k ta` ì`jtrdj horj` taft(F) gdnks ta` ì`jtrons oh fn ftol to dts nujiùs(G) gdnks ta` protons fnk nùtrons dn ta` nujiùs oh fnk ftol

(J) gdnks ftols tob`ta`r to horl loi`jui`s(K) gdnks ftols fnk loi`jui`s to horl soidks

:. Hour l`tfi jonkujtors afvdnb kdhh`r`nt safp`s]6\ f spa`r` ]7\ jyidnk`r ]:\ p`fr ];\ idbatdnb jonkujtorfr` lount`k on dnsuiftdnb stfnk fnk jafrb`k. [a` on` wadja ds g`st sudt`k to r`tfdn ta` jafrb`s hor f ionb`r tdl` ds 3(F) 6 (G) 7 (J) : (K) ;

;. [a` hdbur` saows hour sdtuftdons dn wadja jafrb`s fs dnkdjft`k (q> 5) fr` hdx`k on fn fxds. Dn wadja sdtuftdon ds ta`r` f podnt to taì`ht oh ta` jafrb s wa`r` fn ì`jtron wouik g` dn `qudidgrdul?(F) 6 fnk 7 (G) 7 fnk ; (J) : fnk ; (K) 6 fnk :

0. [wo ionb jonkujtors, s`pfrft`k gy f kdstfnj`kjfrry jurr`nts 6 7fnkD D dn ta` sfl` kdr`jtdon. [a`y `x`rt f horj` H on `fja ota`r.

Now ta` jurr`nt dn on` oh ta`l ds dnjr`fs`k to two tdl`s fnk dts kdr`jtdon ds r`v`rs`k. [a` kdstfnj` ds fiso dnjr`fs`k to : k.[a` n`w vfiu` oh ta` horj` g`tw``n ta`l ds 3

(F) 7H (G) :H / (J) 7 :H / (K) :H /

8. Fn dnhdndt` nulg`r oh jafrb`s, `fja oh jafrb` i J , fr` pifj k on ta` x - fxds wdta jo-orkdnft s 6 7 ; 1x ..... . Dh f jafrb` oh

6Jds m`pt ft ta` ordbdn, ta`n waft ds ta` n`t horj` fjtdnb on 6Jjafrb` ?(F) 4555N (G) 67555N (J) 7;555N (K) :8555N

2. Ra`n f goky ds `frta jonn`jt`k, ì`jtrons hrol ta` `frta hiow dnto ta` goky. [ads l`fns ta` goky ds 3

(F) jafrb`k n`bftdvìy (G) fn dnsuiftor (J) unjafrb`k (K) jafrb`k posdtdvìy.

1. [wo slfii spa`r` gfii `fja jfrrydnb jafrb` 65q J fr` susp`nk`k gy two dnsuift`k tar`fks oh

`qufi i`nbta 6l`fja, hrol f podnt hdx`k dn ta` j`didnb. Dt ds hounk taft dn `qudidgrdul, tar`fks fr`

s`pfrft`k gy fn fnbi 85 g`tw``n ta`l fs saown dn hdbur`, ta` t`nsdon dn ta` tar`fk ds 3

(F) 5.61N (G) 61N(J) 6.1N (K) Non` oh ta` fgov`


6/18

Xdkyflfnkdr Jifss`s


4. Jonsdk`r fn ì`jtrdj hdìk 5@ @ x @, wa`r` 5@ ds f jonstfnt. [a` hiux tarouba ta`

safk`k fr` (fs saown dn ta` hdbur`) ku` to tads hdìk ds 3

(F)7

57@ f (G)7

57@ f

(J)7

5@ f (K)7

5

7

@ f

65. F wook`n giojm p`rhorlsZALon f hrdjtdoni`ss surhfj` wdta hr`qu`njy 5v . [a` giojm jfrrd`s f jafrb` V on dts surhfj`. Dh not f

undhorl ì`jtrdj hdìk @ds swdtja`k on fs saown, ta`n ta` ZAL oh ta` giojm wdii g` 3(F) oh ta` sfl` hr`qu`njy fnk wdta sadht`k l`fns posdtdon(G) oh ta` sfl` hr`qu`njy fnk wdtay ta` sfl` l`fn posdtdon(J) oh jafnb`k hr`qu`njy fnk wdta sadht`k l`fn posdtdon(K) oh jafnb`k hr`qu`njy fnk wdta ta` sfl` l`fn posdtdon

*66. F h`w ì`jtrdj hdìk idn`s hor f syst`l two jafnb`s 6 7fnkV V hdx`k ft two kdhh`r`nt podnts on ta`x-fxds fr` saown dn ta` hdbur`.

[a`s` idn`s subb`st taft

(F) 6 7|V | |V |

(G) 6 7|V | | V |

(J) ft f hdndt` kdstfnj` to ta` i`ht oh 6V ta` ì`jtrdj hdìk ds z`ro.

(K) ft f hdndt` kdstfnj` to ta` rdbat oh 7V ta` ì`jtrdj hdìk ds z`ro.

67. F undhorliy jafrb`k tadn spa`rdjfi saìi oh rfkdus W jfrrd`s undhorl surhfj`k`nsdty oh p`r undt fr`f. Dt ds lfk` oh two a`ldspa`rdjfi saìis, aìk

tob`ta`r gy pr`ssdnb ta`l wdta horj`H(s`` hdbur`).Hds proportdonfi to 3

(F)7 7

5W

(G)

7

5

6W

(J)

7

5

6W

(K)

7

75

6

W

6:. F tadn s`ld-jdrjuifr rdnb oh rfkdusrafs f posdtdv` jafrb qkdstrdgut`k undhorliy ov`r dt. [a` n`t hdìk @ft ta` j`ntrÒds3(F)

7 75;

qd

r

(G) 7 7

5;

qc

r

(J)7 7

57

qd

r (K)

7 757

qc

r

6;. I`t tar`` g` f spa`rdjfiiy syll`trdj jafrb` kdstrdgutdon wdta jafrb` k`nsdty vfrydnb fs 50;

rr

W

upto r < W, fnk

5r hor r W , wa`r`rds ta` kdstfnj` hrol ta` ordbdn. [a` ì`jtrdj hdìk ft f kdstfnj` r r W hrol ta` ordbdn ds bdv`n gy 3

(F) 5

5

; 0: :

r r

W

(G) 5

5

0; :

r r

W

(J) 5

5

; 0: ;

r r

W

(K) 5

5

0: ;

r r

W

60. Fn ì`jtron dndtdfiiy ft r`st hfiis f kdstfnj` oh 6.0 jldn f undhorl ì`jtrdj hdìk oh lfbndtuk` ;7 65 N / J . [a` tdl` tfm`n gy ta`

ì`jtron to hfii tads kdstfnj` ds 3

(F)76 : 65. s (G) 677 6 65. s (J) 656 8 65. s (K) 47 4 65. s


7/18

Xdkyflfnkdr Jifss`s


KF[@ 3 [DL@ 3 ;5 Ldnut`s LFWMZ 3 ] ___ /60\ [@Z[ JOK@ 3 @IJL ];\




6. [a` ì`jtrdj hdìk ft ta` j`ntrodk oh fn `qudift`rfi trdfnbi` jfrrydnb fn `qufi jafrb`qft `fja oh ta` v`rtdj`s ds 3

(F) z`ro (G)7

7mq

r(J)

77

mq

r(K)

7:mq

r

7. F soidk spa`r` oh rfkdusW afs f jafrb`Vkdstrdgut`k dn dts voiul` wdta f jafrb` k`nsdty fmr , wa`r`mfnk f fr` jonstfnts fnk

rds ta` kdstfnj` hrol dts j`ntr`. Dh ta` ì`jtrdj hdìk ft6

ds7 1

Wr tdl`s taft ft r W , hdnk ta` vfiu` ohf.

(F) 7 (G) : (J) 7.0 (K) 5.7

:. f spa`rdjfi saìi oh rfkdusWafs f jafrb` q undts. [a` ì`jtrdj hdìk ku` to ta` saìi ft podnt.

(F) dnsdk` ds z`ro fnk vfrd`s fs 6r outsdk` dt (G) dnsdk` ta` jonstfnt fnk vfrd`s fs 7r outsdk` dt

(J) dnsdk` ds z`ro fnk vfrd`s fs 7r outsdk` dt (K) dnsdk` ds jonstfnt fnk vfrd`s fs 6r outsdk` dt

;. F pfrtdji` oh lfssl jfrrydnb jafrb`qds m`pt ft r`st dn f undhorl ì`jtrdj hdìk @fnk ta`n rì`fs`k. [a` mdn`tdj `n`rby bfdn`k gyta` pfrtdji`, wa`n dt lov`s tarouba f kdstfnj`yds3

(F)76

7q@y (G) q@y (J)

7q@y (K)

7q@ y

0. F l`tfiidj spa`rdjfi saìi oh rfkdus Wafs f jafrb` V on dt. F podnt jafrb` + V ds pifj`k ft ta` j`ntr` oh ta` saìi. Radja oh ta`

brfpas saown gìow lfy jorr`jtiy r`pr`s`nt ta` vfrdftdon oh ta` ì`jtrdj hdìk @ wdta kdstfnj` r hrol ta` j`ntr` oh ta` saìi ?

(F) (G) (J) (K)

8. [a` jafrb` q ds proc`jt`k dnto f undhorl ì`jtrdj hdìk@, worm kon` wa`n dt lov`s f kdstfnj`Tds 3

(F) q@T (G) qT

@(J)

q@

T(K)

T

q@

2. Dh ta` idn`fr jafrb` k`nsdty oh f jyidnk`r ds 6; Jl ta`n ì`jtrdj hdìk dnt`nsdty ft podnt :.8 jl hrol fxds ds 3

(F)0 6; 65 NJ (G) 8 67 65 NJ (J) 2 61 65 NJ (K) 2 667 65 NJ

1. [a` hdbur` saows i`jtrdj hdìk@ft f kdstfnj`rdn fny kdr`jtdon hrol ta` ordbdnO. [a` ì`jtrdj hdìk @ ds ku` to 3(F) f jafrb`k aoiiow l`tfiidj spa`r` oh rfkdusOUwdta j`ntr` ftO(G) f jafrb`k soidk l`tfiidj spa`r` oh rfkdusOUwdta j`ntrÒ(J) f undhorliy jafrb`k non-jonkujtdnb spa`r` oh rfkdusOUwdta j`ntrÒ(K) f undhorliy jafrb`k non-jonkujtdnb aoiiow spa`r` oh rfkdusOUwdta j`ntr` ftO

4. F sdlpi` p`nkuiul afs i`nbtai fnk ta` lfss oh ta` gog ds l. [a` gog ds bdv`n f jafrb`qjouiolg. [a` p`nkuiul ds susp`nk kg`tw``n ta` v`rtdjfi pift`s oh f jafrb`k pfrfiiì pift` jfpfjdtor. Dh@ds ta` ì`jtrdj hdìk str`nbta g`tw``n ta` pift`s, ta` tdl` p`rdokoh ta` p nkuiul ds bdv`n gy 3

(F) 7 i

b (G)

67

q@b

l

(J) 7 i

q@b

l

(K)7

7

7 i

q@b

l


8/18

Xdkyflfnkdr Jifss`s


65. Raft ds fnbi` g`tw``n ì`jtrdj hdìk fnk `qdpot`ntdfi surhfj` ?

(F) 45 fiwfys (G) 5 fiwfys (J) 5 to 45 (K) 5 to 615

66. Radja oh ta` hoiiowdnb stft`l`nt ds jorr`jt?(F) @i`jtrdj hdìk ds z`ro on ta` surhfj` oh jurr`nt jfrrydnb wdr`.(G) @i`jtrdj hdìk ds non - z`ro on ta` fxds oh aoiiow jurr`nt jfrrydnb wdr`.

(J) Zurhfj` dnt`brfi oh lfbn`tdj hdìk hor fny jios`k surhfj` ds `qufi to 5 tdl`s oh totfi fibogrfdj sul oh jurr`nt wadja fr`

jrossdnb tarouba ta` jios`k surhfj`.(K) Non` oh ta` fgov`

67. [wo ifrb` l tfi pift`s fr` pifj k pfrfiiì to `fja ota`r. [a` dnn`r surhfj`s oh pift`s fr jafrb`k gy fnk 7Jl .[a` out`r surhfj`s fr` nùtrfi. [a` ì`jtrdj hdìk dn ta` r`bdon g`tw``n ta` pift`s fnk outsdk` ta` pift`s ds 3

(F)5 5

(G)

5z`ro

(J)

5

7z`ro

(K)

5

7z`ro

6:. Jonsdk`r f tadn spa`rdjfi saìi oh rfkdusWjonsdstdnb oh undhorl surhfj` jafrb` k`nsdty . [a` ì`jtrdj hdìk ft f podnt oh kdstfnj`

xhrol dts j`ntr` fnk outsdk` ta` saìi ds3

(F) dnv`rsìy proportdonfi to (G) kdr`jtiy proportdonfi to 7x

(J) kdr`jtiy proportdonfi to (K) dnv`rsìy proportdonfi to 7x

6;. F spa`rdjfi portdon afs g``n r`lov`k hrol f soidk spa`r` afvdnb fjafrb` kdstrdgut`k undhorliy dn dts voiul` fs saown dn ta` hdbur`.[a` ì`jtrdj hdìk dnsdk` ta` `lptd`k spfj` ds3(F) z`ro v`rywa`r`(G) non-z`ro fnk undhorl(J) non-undhorl(K) z`ro oniy ft dts j`ntr`

60. Uosdtdv` fnk n`bftdv` podnt jafrb`s oh `qufi lfbndtuk` fr` m`pt ft 5 5 fnk 5 57 7f f

, r`sp`jtdvìy. [a` worm kon` gy ta`

ì`jtrdj hdìk wa`n fnota`r posdtdv` podnt jafrb` ds lov`k hrol ( 5 5 to 5 5f f ds 3(F) posdtdv`(G) n`bftdv`(J) z`ro(K) k`p`nks on ta` pfta jonn`jtdnb ta` dndtdfi fnk hdnfi posdtdons


9/18

Xdkyflfnkdr Jifss`s

XLJ/@i`jtrostftdjs 05 AR[-8/Uaysdjs





6. Jafrb`s fr` pifj`k on ta` v`rtdj`s oh f squfr` fs saown. I`t @g` ta` ì`jtrdj hdìk fnkXta`pot`ntdfi ft ta` j`ntr`. Dh ta` jafrb`s onFfnkGfr` dnt`rjafnb`k wdta taos` onKfnkJr`sp`jtdvìy, ta`n

(F) @ r`lfdns unjafnb`k,Xjafnb`s

(G) gota @fnkXjafnb`

(J) @ fnkXr`lfdn unjafnb`k

(K) @ jafnb`s,Xr`lfdns unjafnb`k

7. [a` pot`ntdfi ft f podntx(l`fsur`k dn l ) ku` to sol` jafrb`s sdtuft`k on ta`x - fxds ds bdv`n gy

775 ; voitX x / x

[a` ì`jtrdj hdìk@ft ;x l ds bdv`n gy

(F)6 60

:X l

fnk dn ta` v` kdr`jtdon (G) 6 60:

X l fnk dn ta` +v`xkdr`jtdon

(J)6 665

4X l

fnk dn ta` vx kdr`jtdon (K) 6 665

4X l

fnk dn ta` +v`xkdr`jtdon

:. [a` pot`ntdfi oh ta` ì`jtrdj hdìk prokuj`k gy podnt jafrb` ft fny podnt (x,y,z) ds bdv`n gy 7: 0X x , wa`r`x,yfr` dn l`tr`s

fnkXds dn voits. [a` dnt`nsdty oh ta` ì`jtrdj hdìk ft 7 6 5 ds 3

(F)662Xl (G) 662Xl (J) 667 Xl (K) 667Xl

;. Jafrb` 7 fnkq q q fr` pifj`k ft ta` jorn`rs, F ,G fnkJ oh fn `qudift`rfi trdfnbi`FGJ. Dh@ ds ta` ì`jtrdj hdìk ft ta`

jdrjulj`ntr Ooh ta` trdfnbi`, ku` to ta` jafrb` +q, ta`n ta` lfbndtuk` fnk kdr`jtdon oh ta` r`suitfnt ì`jtrdj hdìk ftOds 3(F) @fionbFO (G) 7@fionbFO (J) @fionbGO (K) @fionbJO

0. Radja oh ta` hoiiowdnb jonhdburftdons oh ì`jtrdj idn`s oh horj` ds not possdgi`?

(F) (G) (J) (K) Gota (g) fnk (j)

8. Raft ds not tru` hor `qudpot`ntdfi surhfj` hor undhorl ì`jtrdj hdìk?

(F) @qudpot`ntdfi surhfj` ds hift (G) @qudpot`ntdfi surhfj` ds spa`rdjfi(J) @i`jtrdj idn`s fr` p`rp`nkdjuifr to `qudpot`ntdfi surhfj` (K) Rorm kon` ds z`ro

2. [a` spftdfi kdstrdgutdon oh ta` ì`jtrdj hdìk ku` to jafrb`s (F,G) ds saown dnta` hdbur`. Radja on` oh ta` hoiiowdnb stft`l`nts ds jorr`jt?

(F) F ds fnkv` G v`,| F| | G | (G) ds fnkF v` G v`, | F | |G |

(J) Gota fr` gutv` F G (K) Gota fr` gutv` F G


10/18

Xdkyflfnkdr Jifss`s


1. I`tXg` ta` ì`jtrdj pot`ntdfi ft f bdv`n podnt. [a`n ta` ì`jtrdj hdìk x@ fionb x-kdr`jtdon ft ta` podnt ds bdv`n gy 3

(F)5

Xkx

(G) kX

kx(J)

kX

kx (K)

kXX

kx

4. F aoiiow spa`r` oh jafrb` ko`s not prokuj` fn ì`jtrdj hdìk ft fny 3

(F) dnt`rdor podnt (G) out`r podnt (J) g`yonk 7l (K) g`yonk 65l

65. Uot`ntdfi fnk hdìk str`nbta ft f j`rtfdn kdstfnj` hrol f podnt jafrb` fr` 855 X fnk 6755NJ . Kdstfnj` oh ta` podnt hrol ta`

jafrb` ds 3(F) 7l (G) ;l (J) 1l (K) :l

66. [ar`` dnhdndtìy ionb jafrb` sa``ts fr` pifj`k fs saown dn hdbur`. [a` ì`jtrdj hdìk ft podntUds 3

(F)

5

7m

(G)

5

7m

(J)

5

;m

(K)

5

;m

67. F jafrb`k gfii Gafnbs hrol f sdim tar`fk Z, wadja lfm`sfn fnbi` wdta f ifrb` jafrb`k jonkujtdnb sa``t U, fssaown dn ta` hdbur`. [a` surhfj` jafrb` k`nsdty oh ta`sa``t ds proportdonfi to 3(F) jos

(G) jot

(J) sdn

(K) tfn

6:. [wo podnt jafrb`s 1 fnk 7q q fr` iojft`k ft 5x fnk x I r`sp`jtdvìy. [a` iojftdon oh f podnt on ta`x-fxds ft wadja ta`n`t ì`jtrdj hdìk ku` to ta`s` two podnt jafrb`s ds z`ro ds 3(F) 1I (G) I/; (J) 1I (K) ; I

6;. [a` rfkdus oh soidk l`tfiidj non-jonkujtdnb spa`r` ds 85jlfnk jafrb` on ta` spa`r ds 055 J . [a` ì`jtrdj hdìk ft f kdstfnj` 65

jl hrol j`ntr` oh spa`r` ds 3

(F)8 67 65 NJ (G) 1 67 65 NJ (J) 8 60 65 NJ (K) 1 60 65 NJ

60. Zdx jafrb`s, tar`` posdtdv` fnk tar`` n`bftdv` oh `qufi lfbndtuk` fr`to g` pifj`k ft ta` v`rtdj`s oh f r`buifr a`xfbon suja taft ta` ì`jtrdjhdìk ft ) ds kougi` ta` ì`jtrdj hdìk wa`n oniy on` posdtdv` jafrb` oh

sfl` lfbndtuk` ds pifj`k ftW. Radja oh ta` hoiiowdnb frrfnb`l`ntsoh jafrb`s ds possdgi` horU,V,W,Z,[fnkPr`sp`jtdvìy?(F) (G)

(J) (K)


11/18

Xdkyflfnkdr Jifss`s






6. F jonkujtor afvdnb f jfvdty ds bdv`n f posdtdv` jafrb`. [a`n hdìk str`nbta fnkF G J@ @ @ ft podntF(wdtadn jfvdty), ftG(wdtadn

jonkujtor gut outsdk` jfvdty) fnkJ(n`fr jonkujtor) r`sp`jtdvìy wdii g` 3

(F) 5 5 5F G J@ @ @ (G) 5 5 5F G J@ @ @

(J) 5 5 5F G J@ @ @ (K) Non` oh ta` fgov`

7. Fn dnhdndt` idn` jafrb` prokuj` f hdìk oh 62 617 65. NJ ft f kdstfnj` oh 7jl. [a` idn`fr jafrb` k`nsdty ds 3

(F); 62 72 65. Jl (G) ; 62 41 65. Jl (J) ; 62 66 65. Jl (K) ; 62 5; 65. Jl

:. F l`tfiidj saìi afs f podnt jafrb`q m`pt dnsdk` dts jfvdty. Radja on` oh ta` hoiiowdnb kdfbrfls jorr`jtiy r`pr`s`nts ta` ì`jtrdj

idn`s oh horj`s?

(F) (G) (J) (K)

;. [a` ì`jtrdj hdìk ft f podnt ku` to fn ì`jtrdj kdpoi`, on fn fxds dnjidn`k ft fn fnbi` 45 to ta` kdpoi` fxds, ds p`rp`nkdjuifr

to ta` kdpoi` fxds, dh ta` fnbi` ds 3

(F)6 6

7tfn

(G) 6 7tfn (J) 6 67

tfn

(K) 6 7tfn

0. [ar`` jonj`ntrdj l`tfiidj spa`rdjfi saìis oh rfkddW, 7W, :Wfr` bdv`n jafrb`sV6,V7,V: r`sp`jtdvìy. Dt ds hounk taft ta` surhfj`

jafrb` k`nsdtd`s on ta` out`r surhfj`s oh ta` saìis fr` `qufi. [a`n, ta` rftdo oh ta` jafrb`s bdv`n to ta` saìis,V63V73V:ds3(F) 6 3 7 3 : (G) 6 3 : 3 0 (J) 6 3 ; 3 4 (K) 6 3 1 3 61

8. Fn ì`jtrdj kdpoi` oh ta` kdpoi` lol`nt p ds pifj`k dn f undhorl ì`jtrdj hdìk @. [a` lfxdlul torqu` `xp`rd`nj`k gy ta`

kdpoi` ds 3

(F) p@ (G) p

@(J)

@

p(K) p . @

2. [orqu` fjtdnb on fn ì jtrdj kdpoi dn f undhorl i`jtrdj hd ik ds lfxdlul dh ta` fnbi` g`tw``n fnkp @ds 3

(F) 615 (G) 5 (J) 45 (K) ;0

1. Jonsdk`r f syst`l oh tar`` jafrb`s: :

q q fnk

7

:

q pifj`k ft podntsF,GfnkJ, r`sp`jtdvìy, fs saown dn ta` hdbur`. [fmÒto g`

ta` j`ntr` oh ta` jdrji` oh rfkdusWfnk fnbi` 85JFG .

(F) [a` ì`jtrdj hdìk ft podntOds7

51

q

Wkdr`jt`k fionb ta` n`bftdv`x - fxds.

(G) [a` pot`ntdfi `n`rby oh ta` syst`l ds z`ro.

(J) [a` lfbndtuk` oh ta` horj` g`tw``n ta` jafrb`s ftJfnkGds7

750;

q

W

(K) [a` pot`ntdfi ft podnt O ds567

q

W


12/18

Xdkyflfnkdr Jifss`s

XLJ/@i`jtrostftdjs 0: AR[-8/Uaysdjs

Ufrfbrfpa hor Vu stdons 4 - 65

Jonsdk`r f giojm oh jonkujtdnb lft`rdfi oh r`sdstdvdty saown dn ta` hdbur`. Jurr`nt D `nt`rs ft F fnk i`fv`s hrol K. R` fppiy

sup`rposdtdon prdnjdpi` to hdnk voitfb` X k`vìop`k g`tw``n G fnk J. [a` jfijuiftdon ds kon` dn ta` hoiiowdnb st`ps.

(d) [fm` jurr`nt D `nt`rdnb hrolFfnk fssul` dt to spr`fk ov`r f a`ldspa`rdjfi surhfj` dn ta` giojm.

(dd) Jfijuift` hdìk@(r) ft kdstfnj`r hrolFgy usdnb Oal's ifw @ C , wa`r`C ds ta`

jurr`nt p`r undt fr`f ftr.(ddd) Hrol ta` r k`p`nk`nj` oh@(r), ogtfdn ta` pot`ntdfiX(r) ftr.(dv) W`p`ft (d), (dd) fnk (ddd) hor jurr`ntDi`fvdnbKfnk sup`rpos` r`suit horF K

4. X l`fsur`k g`tw``nGfnkJds 3

(F)

D D

f f g

(G)

D D

f f g

(J)

7 7D D

f f g

(K)

7D

f g

65. Hor jurr`nt `nt`rdnb ftF, ta` ì`jtrdj hdìk ft f kdstfnj`rhrolFds 3

(F)71

D

r

(G)

7D

r

(J)

77

D

r

(K)

7;

D

r

66. Fn ì`jtrdj kdpoi` oh i`nbta 6 jl ds pifj k wdta ta` fxds lfmdnb fn fnbi` oh :5 to fn ì`jtrdj hdìk oh str`nbta; 6

65 NJ

. Dh dt`xp`rd`nj`s f torqu` oh65 7Nl , ta` pot`ntdfi `n`rby oh ta` kdpoi` ds 3

(F) 5.7;0C (G) ;7 ;0 65. C (J) 5.57;0C (K) ;7; 0 65. c

67. F sflpi` ohAJibfs ds pifj`k dn fn ì`jtrdj hdìk oh ; 6: 65 NJ . [a` kdpoi` lol`nt oh `fja AJiloi`jui` ds :58 65 Jl .

[a` lfxdlul torqu` taft jfn fjt on f loi`jui` ds 3

(F):; 7 67 65 J lN (G) :;7 65 Nl (J) 7861 65 Nl (K) :; 7 65 0 65. J Nl

6:. Kdpoi` ds pifj`k pfrfiiì to ta` ì`jtrdj hdìk. DhVds ta` worm kon` dn rotftdnb ta` kdpoi` gy 85 , ta`n worm kon` dn rotftdnb dt gy

615 ds 3

(F) 7R (G) :R (J) ;R (K) R/ 7

6;. Fn ì`jtrdj kdpoi` afs f pfdr oh `qufi fnk opposdt` podnt jafrb`s fnkq q s`pfrft`k gy f kdstfnj` 7x. [a` fxds oh ta` kdpoi` ds

k`hdn`k fs =(F) kdr`jtdon hrol posdtdv` jafrb` to n`bftdv` jafrb`(G) kdr`jtdon hrol n`bftdv` jafrb` to posdtdv` jafrb`(J) p`rp`nkdjuifr to ta` idn` codndnb ta` two jafrb`s(K) p`rp`nkdjuifr to ta` idn` codndnb ta` two jafrb`s krfwn ft ta` j`ntr` fnk podntdnb kownwfrk kdr`jtdon.

60. Fn ì`jtrdj kdpoi` jonsdsts oh two opposdt` jafrb`s `fja 5 50. J s`pfrft k gy ;5 ldn. [a` kdpoi` ds pifj`k dn fn undhorl xt`rnfi

ì`jtrdj hdìk oh 8 665 NJ . [a` lfxdlul torqu` `x`rt`k gy ta` hdìk on ta` kdpoi` ds 3

(F):8 65 N l (G) :: 65 N l (J) :60 65 N l (K) :6 0 65. N l


13/18

Xdkyflfnkdr Jifss`s

XLJ/@i`jtrostftdjs 0; AR[-8/Uaysdjs





On` jorr`jt optdon.

6. [a` i`jtrdj hdìk dnt`nsdty @, ku` to fn i`jtrdj kdpoi` oh lol`nt p , ft f podnt on ta` `quftordfi idn` ds 3

(F) pfrfiiì to ta` fxds oh ta` kdpoi` fnk opposdt` to ta` kdr`jtdon(G) p`rp`nkdjuifr to ta` fxds oh ta` kdpoi` fnk ds kdr`jt`k fwfy hrol dt(J) pfrfiiì to ta` kdpoi` lol`nt(K) p`rp`nkdjuifr to ta` fxds oh ta` kdpoi` fnk ds kdr`jt`k towfrks dt

7. Fn ì`jtrdj kdpoi` ds pifj`k ft fn fnbi` oh :5 to f non-undhorl ì`jtrdj hdìk. [a` kdpoi` wdii `xp`rd`nj`.

(F) f trfnsiftdonfi horj` oniy dn ta` kdr`jtdon oh ta` hdìk(G) f trfnsiftdonfi horj` oniynf kdr`jtdon norlfi to ta` kdr`jtdon oh ta` hdìk.(J) f torqu` fs wìi fs f trfnsiftdonfi horj`(K) f toqu` oniy

:. Fn ì`jtrdj kdpoi` oh lol`nt U ds pifj`k ft ta` ordbdn fionb ta` x-fxds. [a` ì`jtrdj hdìk ft f

podntU, waos` posdtdon v`jtor lfm`s fn fnbi` wdta ta`x-fxds, wdii lfm` fn fnbi`

(F) (G)

(J) (K) 7

Rdta ta`x-fxds, wa`r`6

7tfn tfn .

;. [a` rftdo oh ì`jtrdj hdìk on ta` fxds fnk ft `quftor oh fn ì`jtrdj kdpoi` wdii g` 3(F) 6 3 6 (G) 7 3 6 (J) ; 3 6 (K) 6 3 ;

0. Fn ì`jtrdj kdpoi` ds sdtuft`k dn fn ì`jtrdj hdìk oh undhorl dnt`nsdty@waos` kdpoi` lol`nt dspfnk lol`nt oh dn`rtdf ds D. Dh ta`kdpoi` ds kdspifj`k sidbatiy hrol ta` `qudidgrdul posdtdon, ta`n ta` fnbuifr hr`qu`njy oh dts osjdiiftdons ds 3

(F)

6 7/p@

D

(G)

: 7/p@

D

(J)

6 7/D

p@

(K)

6 7/U

D@

*8. F spa`rdjfi l`tfi saìiFoh rfkdusWFfnk f soidk l`tfi spa`r`Goh rfkdus G FW W fr` m`pt hor fpfrt fnk `fja ds bdv`n jafnb`

+V. Now ta`y fr` jonn`jt`k gy f tadn l`tfi wdr`. [a`n

(F) 5dnsdk`F@ (G) F GV V (J) F G

G F

W

W

(K) on surhfj on surhfjGF@ @

2. F aoiiow l`tfi spa`r` oh rfkdus 65jlds jafrb`k suja taft ta` pot`ntdfi on dts surhfj` g`jol`s 15X. [a` pot`ntdfi ft ta` j`ntr` ohta` spa`r` ds 3

(F) 15X (G) 155X (J) 1X (K) z`ro

1. Out oh two jopp`r safp`s oh ta` sfl` sdz`, xds aoiiow wadi`yds soidk. Dh ta`y fr` jafrb`k ft ta` sfl` pot`ntdfi, waft jfn g` sfdkfgout ta` jafrb`s on ta`l?(F) Jafrb` on gota ta` spa`r`s ds z`ro (G) Jafrb` on gota ta` spa`r`s ds `qufi(J) Zpa`r`ywdii afv` lor` jafrb` (K) Zpa`r`xwdii afv` lor` jafrb`

4. [a` rftdo oh lol`nt oh fn ì`jtron fnk proton wadja fr` fjjì`rft`k hrol r`st gy f pot`ntdfi kdhh`r`nj` 05Xds 3

(F) `

p

l

l(G) `

p

l

l(J)

p

`

l

l(K)

p

`

l

l


14/18

Xdkyflfnkdr Jifss`s


65. [wo podntsUfnkVfr` lfdntfdn`k ft ta` pot`ntdfis oh 65 fnk ;X X r`sp`jtdvìy. [a` worm kon` dn lovdnb 655 ì`jtrons hrol

UtoVds 3

(F)6264 65 C (G) 624 85 65. C (J) 687 7; 65. C (K) 687 7; 65. C

66. [a` ì`jtrdj pot`ntdfi ft fny podntx,y,zdn l`tr`s ds bdv`n gyX< :x7. [a` ì`jtrdj hdìk ft f podnt (7, 5, 6) ds 3

(F) 667Xl (G) 68Xl (J) 68Xl (K) 667Xl

67. Dk`ntdhy ta` wronb stft`l`nt.(F) [a` ì`jtrdjfi pot`ntdfi `n`rby oh f syst`l oh two protons safii dnjr`fs` dh ta` s`pfrftdon g`tw``n ta` two ds k`jr`fs`k.(G) [a` ì`jtrdjfi pot`ntdfi `n`rby oh f proton - ì`jtron syst`l wdii dnjr`fs` dh ta` s`pfrftdon g`tw``n ta` two ds k`jr`fs`k.(J) [a` ì`jtrdjfi pot`ntdfi `n`rby oh f proton - ì`jtron syst`l wdii dnjr`fs` dh ta` s`pfrftdon g`tw``n ta` two ds dnjr`fs k.(K) [a` ì`jtrdjfi pot`ntdfi `n`rby oh syst`l oh two ì`jtrons safii dnjr`fs` dh ta` s`pfrftdon g`tw``n ta` two ds k`jr`fs`k .

6:. [wo jafrb`s fnkq q fr` m`pt fpfrt. [a`n ft fny podnt on ta` rdbat gds`jtor oh idn` codndnb ta` two jafrb`s.

(F) ta` ì`jtrdj hdìk str`nbta ds z`ro(G) ta` ì`jtrdj pot`ntdfi ds z`ro(J) gota ì`jtrdj pot`ntdfi fnk ì`jtrdj hdìk str`nbta fr` z`ro(K) gota ì`jtrdj pot`ntdfi fnk ì`jtrdj hdìk str`nbta fr` non-z`ro

6;. Zlfii krops oh ta` sfl` sdz` fr` jafrb`k toXvoit `fja. Dtnsuja krops jofi`sj` to horl f sdnbi` ifrb` krop, dt pot`ntdfi wdii g` 3(F) Xn (G) X/n (J) Xn6/: (K) Xn7/:

60. [ar`` jafrb`s 5 fnkV q q fr` pifj`k ft ta` v`rtdj`s oh fn

dsosjì`s rdbat fnbi` trdfnbi` fs dn ta` hdbur`. [a` n`t ì`jtrostftdjpot`ntdfi `n`rby ds z`ro dhV5ds `qufi to 3

(F);q

(G)7

:7

q

(J) 7q (K) q


15/18

Xdkyflfnkdr Jifss`s






6. [a` worm kon` dn grdnbdnb f undt posdtdv` jafrb` hrol dnhdndty kdstfnj` to f podnt ft kdstfnj` Qhrol f posdtdv` jafrb`V dsR.

[a`n ta` pot`ntdfi ft ta` podnt ds 3

(F) RV

Q(G) R (J)

R

V(K) RV

7. [a` ì`jtrdj pot`ntdfi dnsdk` f jonkujtdnb spa`r`(F) dnjr`fs`s hrol j`ntr` to surhfj` (G) k`jr`fs`s hrol j`ntr` to surhfj`(J) r`lfdns jonstfnt hrol j`ntr` to surhfj` (K) ds z`ro ft `v`ry podnt dnsdk`

:. [a` kdspifj`l`nt oh f jafrb`Vdn ta` ì`jtrdj hdìk 6 7 : ds@ ` d ` c ` m r fd g c . [a` worm kon` ds 3

(F) 6 7V f` g` (G) 7 7

6 7V f` g`

(J) 76 7 7V ` f g (K) 7 76 7V ` ` f g

;. Jafrb` +q fnkq q fr` pifj`k ft podnts F fnk G r`sp`jtdvìy

wadja fr` f kdstfnj` 7Ifpfrt,Jds ta` ldk-podnt g`tw``nFfnkG.[a` worm kon` dn lovdnb f jafrb` +Vfionb ta` s`ldjdrji`JWKds 3

(F)5;

qV

I(G)

57qV

I(J)

58qV

I(K)

58qV

I

0. Ndk`ntdjfi krops oh l`rjury fr` jafrb`k sdluitfnòusiy to 65X. Ra`n jolgdn`k to horl on` ifrb` krop, ta` pot`ntdfi ds hounk to

g` ;5X, ta` vfiu` ohNds3(F) ; (G) 8 (J) 1 (K) 65

8. [a` ì jtrostftdj pot`ntdfi n`rby g tw``n proton fnk ì`jtron s`pfrft`k gy f kdstfnj` 6 ds 3(F) 6:.8`X (G) 72.7`X (J) 6;.;`X (K) 6.;;`X

2. [wo jafrb`sq6fnk q7fr` pifj k ;5jlfpfrt, fs saown dn ta` hdbur`. F tadrkjafrb`q:ds lov`k fionb ta` frj oh f jdrji` oh rfkdus ;5 jlhrolJtoK. [a`

jafnb` dn ta` pot`ntdfi `n`rby oh ta` syst`l ds :

5;q

m

, wa`r`mds 3

(F) 1q7(G) 1q6(J) 8q7(K) 8q6

1. Fionb ta`x - fxds, tar`` jafrb`s fnk7 7q q

q fr` pifj`k ft 5x x f fnk 7x f r`sp`jtdvìy. [a` r`suitfnt ì`jtrdj pot`ntdfi

ft f podntUiojft`k ft f kdstfnj`rhrol ta` jafrb` q f r ds ( 5 ds ta` p`rldttdvdty oh hr`` spfj`)

(F)7

5;

fq

r(G)

7

:5;

qf

r(J)

7

:5

;

;

ff

r

(K)5;

q

r


16/18

Xdkyflfnkdr Jifss`s


4. [wo jonj`ntrdj spa`r`s oh rfkddWfnkrafv` sdldifr jafrb`s wdta `qufi surhfj` k`nsdtd`s ( ). Raft ds ta` ì`jtrdj pot`ntdfi ft

ta`dr jollon j`ntr`?

(F) 5/ (G) 5

W r

(J)

5W r

(K) Non` oh ta`s`

65. Hdnk ta` pot`ntdfi ft ta` j`ntr` oh f squfr` oh sdk` 7 7l . Radja jfrrd`s ft dts hour jorn`rs jafrb`s 8

6: 65q J ,

8 87 :: 65 ; 65q J q J

, 8; 2 65q J .

(F);7 2 65. X (G) :6 0 65. X (J) 7: 65 X (K) :0 65X

66. Hdbur` saows tar`` spa`rdjfi fnk `qudpot`nt surhfj` F,G,fnk J rounk f podnt jafrb` q. [a` pot`ntdfi kdhh`r`nj`

F G G JX X X X . Dh 6 7fnkt t g` ta` kdstfnj` g`tw``n

ta`l. [a`n 3

(F) 6 7t t (G) 6 7t t

(J) 6 7t t (K) 6 7t t

67. Hdbur` saows tar`` podntsF,GfnkJdn f r`bdon oh undhorl ì`jtrdj hdìk @. [a` idn`FG ds p`rp`nkdjuifr fnkGJ ds pfrfiiì to ta` hdìk idn`s. [a`n wadja oh ta` hoiiowdnbaoiks book?

(F) F G JX X X (G) F G JX X X

(J) F G JX X X (K) F G JX X X

wa`r` XF,XGfnkXJr`pr`s`nt ta` ì`jtrdj pot`ntdfi ft ta` podntsF,GfnkJr`sp`jtdvìy

6:. [wo tadn wdr` rdnbs `fja afvdnb f rfkdusWfr` pifj`k ft f kdstfnj` k fpfrt wdta ta`dr fx`s jodnjdkdnb. [a` jafrb`s on ta` two rdnbsfr` fnkq q . [a` pot`ntdfi kdhh`r`nj` g`tw``n ta` j`ntr`s oh ta` two rdnbs ds 3

(F)

75;

qW

k

(G)

7 75

6 6

7

q

W W k

(J) z`ro (K)7 75

6 6

;

q

W W k

6;. [a` pot`ntdfi to wadja f jonkujtor ds rfds`k, k`p`nks on(F) [a` flount oh jafrb` (G) Bòl`try fnk sdz` oh ta` jonkujtor(J) Gota (f) fnk (g) (K) Oniy on (f)

60. Dn ta` hdbur`, f proton lov`s f kdstfnj`kdn f undhorl ì`jtrdj hdìk @fs saown dn ta` hdbur`. ko`s ta` ì`jtrdj hdìk ko f posdtdvòr n`bftdv` worm on ta` proton? Ko`s ta` ì`jtrdj pot`ntdfi `n`rby oh ta` proton dnjr`fs` or k`jr`fs` ?(F) N`bftdv`, dnjr`fs` (G) Uosdtdv`, k`jr`fs`(J) N`bftdv`, k`jr`fs` (K) Uosdtdv`, dnjr`fs`


17/18

Xdkyflfnkdr Jifss`s






On` jorr`jt optdon.

6. [a` hdbur` saows ì`jtrdj pot`ntdfi X fs f hunjtdon ohx, Wfnm ta`hour r`bdons fjjorkdnb to ta` lfbndtuk` oh x-jolpon`nt oh ta`ì`jtrdj hdìk@wdtadn ta`l, br`ft`st hdrst

(F) ; 7 : 6@ @ @ @ (G) 7 ; 6 :@ @ @ @

(J) 6 7 : ;@ @ @ @ (K) 6 : 7 ;@ @ @ @

7. Rorm r`qudr`k to s`t up ta` hour jafrb` jonhdburftdon (fs saown dn ta` hdbur`) ds 3

(F)

7

55 76. q / f(G)

756 74. q / f

(J)7

56 ;6. f / f

(K)7

57 17. q / f

:. Dn ta` hoiiowdnb kdfbrfl ta` worm kon` dn lovdnb f podnt jafrb` hrol podntUto podntF,GfnkJds r`sp`jtdvìy fsRF,RGfnkRJ, ta`n 3

(F) F G JR R R (G) 5F G JR R R

(J) F G JR R R (K) F G JR R R

;. [a` podnts r`s`lgidnb `qufi pot`ntdfis fr` 3

(F) UfnkV

(G) ZfnkV

(J) ZfnkW

(K) UfnkW

0. Jafrb` Z 7 fnkq q q id` ft ta` v`rtdj`s oh f trdfnbi`. [a` vfiu` oh@fnkXft ta` j`ntrdok oh `qudift`rfi oh `qudift`rfi trdfnbi`

wdii g` 3

(F) 5 fnk 5@ X (G) @< 5 fnkX< 5 (J) 5 fnk 5@ X (K) 5 fnk 5@ X

8. [a` rfkdus oh nujiùs oh sdiv`r (ftoldj nulg`rS< ;2) ds 6;: ; 65. l . [a` ì`jtrdj pot`ntdfi on ta` surhfj` oh nujiùs wdii g` 3

(F)86 44 65. X (G) 87 44 65. X (J) 8: 44 65. X (K) Nfl` oh ta`s`

2. F aoiiow jonkujtdnb spa`r` ds pifj`k dn fn ì`jtrdj hdìk prokuj`k

gy f podnt jafrb` pifj`k ftUfs saown dn hdbur`. I`t F G JX X X g`

ta` pot`ntdfis ft podntsF,GfnkJr`sp`jtdvìy. [a`n

(F) J GX X (G) G JX X

(J) F GX X (K) F JX X


18/18

Xdkyflfnkdr Jifss`s


1. F spa`rdjfi krop oh l`rjury afvdnb f pot`ntdfi oh 7.0 X ds ogtfdn`k fs f r`suit oh l`rbdn` 670 kropi`ts. [a` pot`ntdfi oh fjonstdtu`nt kropi`ts wouik g` 3(F) 6.5X (G) 5.0X (J) 5.7X (K) 5.6X

4. F aoiiow l`tfi spa`r` oh rfkdus 0jlds jafrb`k suja taft pot`ntdfi ft dts surhfj` ds 65X. [a` pot`ntdfi ft ta` j`ntr` oh ta` spa`r` ds3(F) S`ro (G) 65X

(J) sfl` fs ft podnt 0jlfwfy hrol ta` surhfj` (K) sfl` fs ft podnt 65jlfwfy hrol ta` surhfj`

*65. Radja oh ta` hoiiowdnb stft`l`nt(s) ds(fr`) jorr`jt ?

(F) Dh ta` ì`jtrdj hdìk ku` to f podnt jafrb` vfrd`s fs 70r dnst`fk oh 7r , ta`n ta` Bfuss's ifw wdii stdii g` vfidk.(G) [a` Bfuss's ifw jfn g` us`k to jfijuift` ta` hdìk kdstrdgutdon frounk fn ì`jtrdj kdpoi`(J) Dh ta` ì`jtrdj hdìk g`tw``n two podnt jafrb`s ds z`ro sol`wa`r , ta`n ta` sdbn oh ta` two jafrb`s ds ta` sfl`(K) [a` worm kon` gy ta` `xt`rnfi horj` dn lovdnb f undt posdtdv` jafrb` hrol podnt Fft pot`ntdfiXFto podntGft pot`ntdfi

dsG G FX X X

66. [a` Bfussdfn surhfj` hor jfijuiftdnb ta` ì`jtrdj hdìk ku` to f jafrb` kdstrdgutdon ds 3(F) Fny surhfj` n fr ta` jafrb` kdstrdgutdon(G) Fiwfys f spa`rdjfi surhfj`

(J) F syll`trdjfi jios`k surhfj jontfdndnb ta` jafrb` kdstrdgutdon, ft v`ry podnt oh wadja ì`jtrdj hdìk afs f sdnbi` hdx`kvfiu`

(K) Non` oh ta` bdv`n optdons.

67. F podnt jafrb` oh 6 1. J ds ft ta` j`ntr` oh jugdjfi Bfussdfn surhfj` 00 jlon `kb`. Raft ds ta` n`t ì`jtrdj hiux tarouba ta`

surhfj`?

(F)0 7 66 5 65. N l J (G) 0 7 6: 5 65. N l J

(J)0 67 5 65. N l J (K) 0 7 6; 5 65. N l J

6:. F kdsj oh rfkdus;

fafvdnb f undhorliy kdstrdgut`k jafrb` 8Jds pifj`k dn ta`x-ypifn` wdta

dts j`ntr` ft 5 5

7

f

. F rok oh i`nbta f jfrrydnb f undhorliy kdstrdgut`k jafrb` 1J ds

pifj`k on ta` x-fxds hrol;

fx to

0

;

fx . [wo podnt jafrb`s 2 fnk :J J fr` pifj`k ft

: :5 fnk 5

; ; ; ;

f f f f

r`sp`jtdvìy. Jonsdk`r f jugdjfi surhfj` horl`k gy sdx surhfj`

7 7 7

f f fx y z . [a` ì`jtrdj hiux tarouba tads jugdjfi surhfj` ds 3

(F)5

7J

(G)

5

7J

(J)

5

65J

(K)

5

67J

6;. [a` ì`jtrdj jafrb` fr` kdstrdgut`k dn f slfii voiul`. [a` hiux oh ta` ì`jtrdj hdìk tarouba f spa`rdjfi surhfj` oh rfkdus 65jlsurrounkdnb ta` totfi jafrb` ds 75Xl. [a` hiux ov`r f jonj`ntrdj spa`r` oh rfkdus 75jlwdii g` 3(F) 75Xl (G) 70Xl (J) ;5Xl (K) 755Xl

60. Dh ta` ì`jtrdj hdìk ds bdv`n gy 0 ; 4d c m , ta` ì`jtrdj hiux tarouba f surhfj` oh fr`f 75 undt iydnb dn ta` T-S pifn` wdii g` 3(F) 655 undt (G) 15 undt (J) 615Xl (K) 755Xl

jee 2014 booklet6 hwt electrostatics

Documents