Physics Chapter 11 Answers

Imlptar <
Ls l ilr brlkas, tma c`rias rasp`fsgbna c`r brlkgfh lra lppngad lt hrùfd navan. Tma iaftar `c jlss `c tma ilr gs wann lb`va tma hrùfd, m`wavar. Tmarac`ra, tma brlkgfh c`rias axart l t`rqua lbùt tma iaftar `c jlss tmlt tafds t` r`tlta tma cr`ft `c tma ilr d`wfwlrd. Tmgs, gf turf, ilusas lf gfiralsad upwlrd c`ria t` ba axartad by tma cr`ft sprgfhs, uftgn tma fat t`rqua litgfh `f tma ilr raturfs t` zar`.

4.

Tma c`ria tmlt liianarltas l j`t`riyina gs l c`rwlrd c`ria lppngad lt hrùfd navan. Tma iaftar `c jlss `c tma j`t`riyina, m`wavar, gs lb`va tma hrùfd. Tmarac`ra, tma liianarltgfh l iianarltgfh c`ria axarts l t`rqua `f tma iyina tmlt tafds t` r`tlta tma cr`ft wmaan upwlrd.

3.

I`fsgdar lf lgrpnlfa pr`pannar `r l iagngfh clf tmlt gs oust stlrtgfh t` r`tlta. Gf tmasa ilsas, tma fat c`ria gs zar` bailusa tma iaftar `c jlss gs f`t liianarltgfh. M`wavar, tma fat t`rqua gs f`fzar` lfd tma lfhunlr liianarltg`f gs f`fzar`.

=.

L ilr liianarltgfh cr`j rast gs f`t gf stltgi aqugngbrguj bailusa gts iaftar `c jlss gs liianarltgfh. Ygjgnlrny, lf lgrpnlfa pr`pannar tmlt gs oust stlrtgfh up gs f`t gf stltgi aqugngbrguj bailusa gt mls lf lfhunlr liianarltg`f.

<5.

Was. Xmaf lf lgrpnlfa ‗s afhgfa stlrts up cr`j rast tma pr`pannar mls l f`fzar` r`tltg`fln liianarltg`f, tmùhm gts trlfsnltg`fln liianarltg`f gs zar`.

<2.

Tma tlgn r`t`r `f l mangi`ptar mls l m`rgz`ftln lxgs `c r`tltg`f, ls `pp`sad t` tma vartgiln lxgs `c tma jlgf r`t`r. Tmarac`ra, tma tlgn r`t`r pr`duias l m`rgz`ftln tmrust tmlt tafds t` r`tlta tma mangi`ptar lbùt l vartgiln lxgs. Ls l rasunt, gc tma lfhunlr spaad `c tma jlgf r`t`r gs gfiralsad `r dairalsad, tma tlgn r`t`r ilf axart lf `pp`sgfh t`rqua tmlt pravafts tma aftgra mangi`ptar cr`j r`tltgfh gf tma `pp`sgta dgraitg`f.

<4.

F`. Gc tma dgvar ‗s gfgtgln lfhunlr j`jaftuj gs zar`, gt just stly zar` ufnass lf axtarfln t`rqua lits `f mar. L dgvar faads t` stlrt `cc wgtm lt nalst l sjlnn lfhunlr spaad, wmgim ilf tmaf ba gfiralsad by c`ndgfh gft` l tuikad p`sgtg`f.

Y`nutg`fs t` Ur`bnajs lfd I`fiaptuln Axarigsas <.

Ugitura tma Ur`bnaj? Tma c`ria gs lppngad gf l dgraitg`f parpafdgiunlr t` tma mlfdna `c tma wrafim lfd lt tma afd `c tma mlfdna. Ytrltahy? Qsa aqultg`f <<-< t` cgfd tma c`ria cr`j tma kf`wf t`rqua lfd tma nafhtm `c tma wrafim. Y`nutg`f? Y`nva aqultg`f <<-< c`r C C ?

τ : r ( C sgf ν ) τ <1 F ⋁ j C : : : 35 F r sgf ν ( 5.21 j ) sgf 75µ

Gfsghmt? L n`fhar wrafim ilf axart l nlrhar t`rqua c`r tma slja ljùft `c c`ria.

2.

Ugitura tma Ur`bnaj? Tma waad gs punnad by axartgfh l d`wfwlrd c`ria `f tma afd `c tma t``n mlfdna. Ytrltahy? Yat tma t`rqua `f tma t``n aquln t` tma c`ria axartad by tma waad tgjas tma j`jaft lrj lfd s`nva c`r tma c`ria. Y`nutg`f? Y`nva aqultg`f <<-< c`r C C ?

τ : Cw aaaa dr w aaaa d C waad :

τ r waad

:

<.29 F ⋁ j 5.545 j

: 9< F

Gfsghmt? Tma t`rqua just ba tma slja avarywmara avarywmara `f tma t``n. Tmarac`ra, tma mlfd just just axart l <.29 F ⋁ j 5.22 j : 1.3 F c`ria c`ria t` pr`duia pr`duia l 9<-F c`ria c`ria lt tma waad. Tma c`ria gs juntg juntgpngad pngad by l clit`r clit`r `c 22 4 : 1.1. I`pyrghmt © 25<5 Ualrs`f Aduiltg`f, Gfi. Lnn rghmts rasarvad. Tmgs jltargln gs pr`taitad ufdar lnn i`pyrghmt nlws ls tmay iurraftny axgst. F` p`rtg`f `c tmgs jltargln jly ba rapr`duiad, gf lfy c`rj `r by lfy jalfs, wgtmùt parjgssg`f gf wrgtgfh cr`j tma pubngsmar.

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Oljas Y. Xlnkar, Umysgis Xlnkar, Umysgis,, 4tm Adgtg`f

Imlptar <
9.

Ugitura tma Ur`bnaj? Tma lrj axtafds ùt agtmar m`rgz`ftlnny `r lt s`ja lfhna ban`w m`rgz`ftln, lfd tma waghmt `c tma tr`pmy gs axartad strlghmt d`wfwlrd `f tma mlfd. Ytrltahy? Tma t`rqua aqulns tma j`jaft lrj tgjas tma c`ria lii`rdgfh t` aqultg`f <<-9. Gf tmgs ilsa tma j`jaft j`jaft lrj gs tma m`rgz`ftln dgstlfia dgstlfia batwaaf tma smùndar smùndar lfd tma mlfd, lfd tma c`ria gs gs tma d`wfwlrd waghmt `c tma tr`pmy. Cgfd tma m`rgz`ftln dgstlfia dgstlfia gf alim ilsa lfd juntgpny juntgpny gt by tma waghmt `c tma tr`pmy t` t` cgfd tma t`rqua. Gf plrt (b) tma m`rgz`ftln dgstlfia gs r⊡ : r i`s ν : ( 5.351 j ) i`s 22 22.1µ : 5.117 j. Y`nutg`f? <. (l) Juntgpny tma j`jaft lrj by tma waghmt?

τ : r⊡ jh : ( 5.351 j ) (<.3< kh ) ( 7.=< j/s2 ) : 7.13 F ⋁ j

2. (b) Juntgpny tma j`jaft lrj by tma waghmt?

τ : r⊡ jh : ( 5.117 j ) (<.3< kh ) 7.=< j/s2 : =.=9 F ⋁ j

(

)

Gfsghmt? Tma t`rqua `f tma lrj gs raduiad ls tma lrj gs n`warad. Tma t`rqua gs axlitny zar` wmaf tma lrj gs vartgiln.

4.

Ugitura tma Ur`bnaj? Tma lrj axtafds ùt agtmar m`rgz`ftlnny lfd tma waghmt `c tma irlb trlp gs axartad strlghmt d`wfwlrd `f tma mlfd. Ytrltahy? Tma t`rqua aqulns tma j`jaft lrj tgjas tma c`ria lii`rdgfh t` aqultg`f <<-9. Gf tmgs ilsa tma j`jaft lrj gs tma m`rgz`ftln dgstlfia batwaaf tma smùndar lfd tma mlfd, lfd tma c`ria gs tma d`wfwlrd waghmt `c tma irlb trlp. Y`nutg`f? Juntgpny tma j`jaft lrj by tma waghmt?

τ : r⊡ jh : ( 5.85 j ) ( 9.3 kh ) ( 7.=< j/s2 ) : 21 F ⋁ j

Gfsghmt? Gc tma jlf baft mgs anb`w lfd brùhmt mgs mlfd up faxt t` mgs smùndar, tma t`rqua `f tma smùndar wùnd ba zar` but tma c`ria `f mgs mlfd wùnd rajlgf 91 F `r 8.7 nb.

1.

Ugitura tma Ur`bnaj? Tma bgiaps jusina, tma waghmt `c tma lrj, lfd tma waghmt `c tma blnn lnn axart t`rquas `f tma c`ralrj ls dapgitad lt rghmt.

Ytrltahy? Qsa aqultg`f <5-9 t` datarjgfa tma t`rquas pr`duiad by tma bgiaps jusina, tma waghmt `c tma c`ralrj, lfd tma waghmt `c tma blnn. Yuj tma t`rquas t`hatmar t` cgfd tma fat t`rqua. Lii`rdgfh t` tma sghf i`fvaftg`f, t`rquas gf tma iùftarinìkwgsa dgraitg`f lra p`sgtgva, lfd tm`sa gf tma inìkwgsa dgraitg`f lra fahltgva.

Y`nutg`f? <. (l) I`jputa tma gfdgvgduln t`rquas usgfh aqultg`f <5-9 lfd suj tmaj?

τ bgiaps : r⊡ C : ( 5.5281 j ) (<2.3 F ) : 5.948 F ⋁ j τ c`ralrj : r⊡ jh : ( 5.<85 j ) (<.25 kh ) ( 7.=< j/s2 ) : − 2.55 F ⋁ j τ blnn : r⊡X blnn : ( 5.945 j ) (<.42 F ) : −5.4=9 F ⋁ j

∜τ : τ bgiaps + τ c`ralrj + τ blnn

: +5.948 − 2.55 − 5.4=9 F ⋁ j : −2.<4 F ⋁ j















Imlptar <
3.


Ugitura tma Ur`bnaj ? Tma ldunt pusmas d`wfwlrd `f tma nact sgda `c tma taatar-t`ttar lfd tma imgnd sgts `f tma rghmt sgda ls dapgitad gf tma cghura? Ytrltahy? Ilniunlta tma t`rquas axartad by tma waghmt `c tma imgnd lfd tma c`ria `c tma plraft‗s mlfds lfd suj tmaj. Tma sghf `c tma fat t`rqua gfdgiltas tma dgraitg`f gf wmgim tma taatar-t`ttar wgnn r`tlta. Y`nutg`f? <. (l) Cgfd tma t`rqua tma imgnd axarts `f tma taatar-t`ttar.

9. (b) Rapalt stap 2 wgtm tma faw r ⊡ c`r tma ldunt? 4. (i) Rapalt stap 2 wgtm tma faw r ⊡ c`r tma ldunt?

r ⊡ imgnd

C ldunt

jimgnd h

τ imgnd : r⊡ imgnd jimgnd h τ imgnd

2. Cgfd tma t`rqua axartad by tma plraft lfd suj tma t`rquas t` cgfd tma dgraitg`f `c trlvan?

r ⊡ ldunt

: − (<.1 j ) (<3 kh ) ( 7.=< j/s2 ) : − 291 F ⋁ j

τ ldunt : r⊡ ldunt C ldunt : ( 9.5 j ) ( 71 F ) : 2=1 F ⋁ j . Mara τ ldunt + τ imgnd 6 5 s` tma taatar-t`ttar wgnn r`tlta iùftarinìkwgsa lfd tma imgnd wgnn j`va up. τ ldunt : r⊡ ldunt C ldunt : ( 2.1 j ) ( 71 F ) : 29= F ⋁ j . Mara τ ldunt + τ imgnd 6 5 s` tma taatar-t`ttar wgnn r`tlta iùftarinìkwgsa lfd tma imgnd wgnn j`va up. τ ldunt : r⊡ ldunt C ldunt : ( 2.5 j ) ( 71 F ) : <75 F ⋁ j . Mara τ ldunt + τ imgnd > 5 s` tma taatar-t`ttar wgnn wgnn r`tlta inìkwgsa lfd tma imgnd wgnn j`va d`wf.

Gfsghmt? Tma plraft wùnd mlva t` axart tma 71-F c`ria axlitny 2.4= j cr`j tma pgv`t p`gft gf `rdar t` blnlfia tma taatar-t`ttar. Xa baft tma runas c`r sghfgcgilft cghuras snghmtny t` j`ra alsgny i`jplra i`jplra tma jlhfgtudas `c tma t`rquas.

8.

Ugitura tma Ur`bnaj? Tma r`tltgfh systajs sm`wf lt rghmt dgccar `fny gf tmlt tma tw` spmargiln j`vlbna jlssas lra p`sgtg`fad agtmar clr cr`j tma lxgs `c r`tltg`f (nact), `r falr tma lxgs `c r`tltg`f (rghmt). Ytrltahy? Qsa Fawt`f‗s Yai`fd Nlw t` axpnlgf tma j`tg`f `c tma mlfhgfh waghmt lfd t` lfswar tma i`fiaptuln quastg`f. Y`nutg`f? <. (l) Tmara just ba l fat d`wfwlrd c`ria `f tma jlss bailusa gt liianarltas d`wfwlrd. Xa i`finuda tmlt tma tafsg`f gf tma strgfh `f tma nact-mlfd r`tltgfh systaj gs nass tmlf tma waghmt `c tma jlss lttlimad t` tmlt strgfh.

liianarltas d`wfwlrd. Ytltajaft G gs clnsa clnsa bailusa l > h , lfd stltajaft GG 2. (b) Tma bast axpnlfltg`f gs GGG. Tma jlss liianarltas gs clnsa bailusa tma strgfh dàs f`t cunny supp`rt tma jlss. Gfsghmt? Lntmùhm tmara gs l Fawt`f‗s Yai`fd Nlw c`r r`tltg`f, gf tmgs ilsa gt dàs f`t manp yù t` datarjgfa tma tafsg`f gf tma strgfh.

=.

Ugitura tma Ur`bnaj? Tma r`tltgfh systajs sm`wf lt rghmt dgccar `fny gf tmlt tma tw` spmargiln j`vlbna jlssas lra p`sgtg`fad agtmar clr cr`j tma lxgs `c r`tltg`f (nact), `r falr tma lxgs `c r`tltg`f (rghmt). Ytrltahy? Qsa Fawt`f‗s Yai`fd Nlw t` axpnlgf tma j`tg`f `c tma mlfhgfh waghmt lfd t` lfswar tma i`fiaptuln quastg`f. Y`nutg`f? <. (l) Tma jlss gf tma nact-mlfd systaj dr`ps wgtm l sjlnnar liianarltg`f tmlf tma jlss gf tma rghmt-mlfd systaj. Tmgs jalfs tmara gs l sjlnnar fat c`ria `f tma nact-mlfd jlss. Xa i`finuda tmlt tma tafsg`f gf tma strgfh `f tma nact-mlfd r`tltgfh systaj gs hraltar tmlf tma tafsg`f gf tma strgfh `f tma rghmt-mlfd r`tltgfh systaj.
















Imlptar <
7.

Ugitura tma Ur`bnaj? L t`rqua r`tltas yùr b`dy lbùt `fa `c tmraa dgccaraft lxas `c r`tltg`f? ilsa L, lf lxgs tmrùhm yùr spgfa; ilsa B, lf lxgs tmrùhm yùr mgps; lfd ilsa I, lf lxgs tmrùhm yùr lfknas. Ytrltahy? I`fsgdar tma j`jaft `c gfartgl `c yùr b`dy c`r alim `c tma tmraa lxas gf `rdar t` datarjgfa tma rlfkgfh `c tma lfhunlr liianarltg`fs. Y`nutg`f? Tma j`jaft `c gfartgl gs hraltast wmaf j`ra jlss gs lt l hraltar dgstlfia cr`j tma lxgs `c r`tltg`f. Curtmarj`ra, tma hraltar tma j`jaft `c gfartgl tma sjlnnar tma lfhunlr liianarltg`f pr`duiad by l hgvaf t`rqua. Ilsa L wùnd i`rrasp`fd t` tma sjlnnast j`jaft `c gfartgl lfd ilsa I wùnd i`rrasp`fd t` tma nlrhast j`jaft j`jaft `c gfartgl. Xgtm tmasa `bsarvltg`fs gf jgfd, jgfd, wa lrrgva lt tma c`nn`wgfh c`nn`wgfh rlfkgfh? ilsa I > ilsa B > ilsa L. Gfsghmt? L sprgfhb`lrd dgvar ilf raduia mgs j`jaft `c gfartgl by iurngfh tghmtny gft` tma tuik p`sgtg`f, raduigfh tma dgstlfia batwaaf mgs b`dy‗s jlss lfd mgs lxgs `c r`tltg`f.

<5. Ugitura tma Ur`bnaj? Tma t`rqua lppngad t` tma bgiyina wmaan ilusas gt t` r`tlta wgtm i`fstlft lfhunlr liianarltg`f. Ytrltahy? Ilniunlta tma j`jaft `c gfartgl `c tma wmaan usgfh G : jr 2 (Tlbna <5-<) lfd tmaf usa Fawt`f‗s Yai`fd Nlw c`r r`tltg`f (aqultg`f <<-4) t` datarjgfa tma lfhunlr liianarltg`f.

μ :

Y`nutg`f? Y`nva aqultg`f <<-4 c`r μ ?

τ G

τ

:

2

jr

:

5.78 F ⋁ j kh ) ( 5.91 j) ( 5.81 kh

2

: << rld/s 2

Gfsghmt? T` axart l 5.78 F¸j t`rqua `f l 5.91-j wmaan yù faad `fny lppny l tlfhaftgln c`ria `c 2.= F `r <5 ùfias.

<<. Ugitura tma Ur`bnaj? Tma iagngfh clf r`tltas lbùt gts lxgs, dairalsgfh gts lfhunlr spaad lt l i`fstlft rlta. Ytrltahy? Datarjgfa tma lfhunlr liianarltg`f usgfh aqultg`f <5-3 lfd tmaf usa aqultg`f <<-4 t` cgfd tma j`jaft `c gfartgl `c tma clf.

G :

Y`nutg`f? Y`nva aqultg`f <<-4 c`r G G ?

τ μ

:

τ

Δχ Δt

:

τ Δt

Δχ

:

( − 5.<25 F ⋁ j ) ( 22.1 s ) : ( 5 − 2.81 rld/s )

5.7 5.7=2 kh kh ⋁ j2

Gfsghmt? Crgitg`f i`fvarts tma clf‗s gfgtgln kgfatgi afarhy `c <2 G χ χ5 2 : 9.<5 O gft` malt. R`tltg`fln w`rk w`rk wgnn ba axljgfad axljgfad

gf j`ra datlgn gf saitg`f <<-=. <2. Ugitura tma Ur`bnaj? Tma ID r`tltas lbùt gts lxgs, gfiralsgfh gts lfhunlr spaad lt l i`fstlft rlta. Ytrltahy? Datarjgfa tma lfhunlr liianarltg`f `c tma ID usgfh aqultg`f <5-<< lfd gts j`jaft `c gfartgl (tralt gt ls l dgsk) cr`j Tlbna <5-<. Tmaf usa aqultg`f <<-4 t` cgfd tma t`rqua axartad `f tma ID.

μ :

Y`nutg`f? <. Y`nva aqultg`f <5-<< c`r μ ?

2

( 415 rav/jgf Ø 2υ rld rav Ø < jgf 35 s ) − 52 : 2 ( 9.5 rav Ø 2υ rl rld rav )

χ 2 − χ 52

2Δν

: 17 rld/s 2

( 5.5<8 kh ) ( 5.535 j) : 9.<Ø <5−1 2

2. Qsa Tlbna <5-< t` cgfd G : <2 JR ?

G : <2 JR 2 :

9. Lppny aqultg`f <<-4 dgraitny?

τ : G μ : ( 9.<Ø <5−1 kh ⋁ j2 ) ( 17 rld/s 2 ) : 5.55<= F ⋁ j

2

< 2

kh ⋁ j2

Gfsghmt? Tma ID tlkas 5.=5 s t` liianarlta t` gts cgfln lfhunlr vanìgty, liiùftgfh c`r s`ja `c tma danly batwaaf wmaf yù prass „pnly‚ lfd wmaf yù cgrst malr tma jusgi.

<9. Ugitura tma Ur`bnaj? Tma nlddar r`tltas lbùt gts iaftar `c jlss, gfiralsgfh gts lfhunlr spaad lt l i`fstlft rlta. jlss J lfd lfd nafhtm N nafhtm N tmlt gs r`tltad lbùt gts Ytrltahy? Qsa Tlbna <5-< t` cgfd tma j`jaft `c gfartgl `c l ufgc`rj r`d `c jlss J 2 < iaftar `c jlss? G : <2 J N . Tmaf usa aqultg`f <<-4 t` cgfd cgfd tma raqugrad t`rqua t` pr`duia tma liianarltg`f. liianarltg`f. Y`nutg`f? <. Qsa Tlbna <5-< t` cgfd G

<

J N2

G

<

J N2

<

( = 42 k ) ( 9 <1 )

2

3 73 k

2
















Imlptar <
<4. Ugitura tma Ur`bnaj? Tma wmaan r`tltas lbùt gts lxgs, dairalsgfh gts lfhunlr spaad lt l i`fstlft rlta, lfd i`jas t` rast. Ytrltahy? Qsa Tlbna <5-< t` cgfd tma j`jaft `c gfartgl `c l ufgc`rj dgsk lfd ilniunlta G ilniunlta G . Tmaf usa aqultg`f aqultg`f <5-<< t` cgfd tma lfhunlr liianarltg`f cr`j tma gfgtgln lfhunlr lfhunlr spaad lfd tma lfhna tmrùhm wmgim tma wmaan r`tltad. Qsa G Qsa G lfd lfd μ t`hatmar gf aqultg`f <<-4 t` cgfd tma t`rqua axartad `f tma wmaan. Y`nutg`f? <. (l) Qsa Tlbna <5-< t` cgfd G : <2 JR ? 2

G : <2 JR 2 : χ 2 − χ 52

< 2

2 ( 3.4 kh ) ( 5.8< j ) : <.3 kh ⋁ j2 2

2. Y`nva aqultg`f <5-<< c`r μ ?

μ :

9. Lppny aqultg`f <<-4 dgraitny?

τ : G μ : (<.3 kh ⋁ j 2 ) ( − 5.<1= rld/s 2 ) : − 5.21 F ⋁ j

2Δν

:

52 − (<.22 rld/s )

2 ( 5.81 rav Ø 2υ rld ra rav )

: − 5.<1= rld/s2

4. (b) Gc tma jlss `c tma wmaan gs dùbnad lfd gts rldgus gs mlnvad, tma j`jaft `c gfartgln wgnn ba iut gf mlnc (dùbnad bailusa `c tma jlss, iut t` l cùrtm bailusa `c tma rldgus). Tmarac`ra tma jlhfgtuda `c tma lfhunlr liianarltg`f liianarltg`f wgnn gfiralsa gc tma crgitg`fln t`rqua rajlgfs tma slja, lfd tma lfhna tmrùhm wmgim tma wmaan r`tltas bac`ra i`jgfh t` rast wgnn dairalsa. Gfsghmt? Gc tma j`jaft `c gfartgl gs iut gf mlnc, tma lfhunlr liianarltg`f wgnn dùbna t` −5.92 rld/s2 lfd tma lfhna tmrùhm wmgim tma wmaan r`tltas wgnn ba iut gf mlnc t` 5.9= rav. Tmgs gs bailusa tma wmaan mls nass r`tltg`fln gfartgl but tma crgitg`fln t`rqua rajlgfs rajlgfs tma slja. Xa baft tma runas c`r sghfgcgilft cghuras gf stap 2 t` lv`gd rùfdgfh arr`r gf stap 9.

<1. Ugitura tma Ur`bnaj? Lf `boait i`fsgsts `c tmraa jlssas tmlt ilf ba r`tltad lbùt lfy `c tma x tma x,, y, y, `r z lxas, z lxas, ls sm`wf gf tma cghura lt rghmt. Tma z Tma z lxgs lxgs plssas tmrùhm tma `rghgf parpafdgiunlr t` tma pnlfa `c tma cghura. Ytrltahy? Ilniunlta tma j`jafts `c gfartgl lbùt tma x tma x,, y, y, lfd z lfd z lxas lxas usgfh aqultg`f <5-<=, lfd tmaf lppny aqultg`f <<-4 t` cgfd tma raqugrad t`rqua t` hgva tma `boait lf lfhunlr liianarltg`f `c <.25 rld/s2 lbùt tma vlrgùs lxas. Nat j< : 7.5 kh, j2 : <.2 kh, lfd j9 : 2.1 kh. Y`nutg`f? <. (l) Ilniunlta G x usgfh

G x : j< r<2 + j2r22 + j9r 92

aqultg`f <5-<=?

: ( 7.5 kh ) (<.5 j ) + 5 + 5 G x : 7.5 kh ⋁ j2

2. Cgfd τ x usgfh aqultg`f <<-4?

τ x : G xμ : ( 7.5 kh ⋁ j 2 ) (<.25 rld/s 2 ) : << F ⋁ j

9. (b) Ilniunlta G y usgfh

G y : 5 + 5 + ( 2.1 kh ) ( 2.5 j ) : <5 kh ⋁ j2

aqultg`f <5-<=?

2

2

4. Cgfd τ y usgfh aqultg`f <<-4?

τ y : G yμ : (<5 kh ⋁ j2 ) (<.25 rld/s 2 ) : <2 F ⋁ j

1. (i) Ilniunlta G z usgfh

G z : ( 7.5 kh ) (<.5 j ) + 5 + ( 2.1 kh ) ( 2.5 j ) : <7 kh ⋁ j2

aqultg`f <5-<=? 3. Cgfd τ z usgfh aqultg`f <<-4?

2

2

τ z : G z μ : (<7 kh ⋁ j2 ) (<.25 rld/s 2 ) : 29 F ⋁ j

Gfsghmt? Xmaf tma lxgs `c r`tltg`f plssas tmrùhm l plrtgiunlr jlss, tmlt jlss dàs f`t i`ftrgbuta t` tma j`jaft `c gfartgl bailusa r : r : 5. Tma j`st t`rqua gs raqugrad raqugrad t` r`tlta tma jlssas lbùt tma tma z z lxgs lxgs bailusa tmlt lxgs plssas tmrùhm tma nalst ljùft `c jlss (`fny tma <.2-kh jlss).
















Imlptar <
<3. Ugitura tma Ur`bnaj? Lf `boait i`fsgsts `c tmraa jlssas tmlt ilf ba r`tltad lbùt lfy `c tma x tma x,, y, y, `r z lxas, z lxas, ls sm`wf gf tma cghura lt rghmt. Tma z Tma z lxgs lxgs plssas tmrùhm tma `rghgf parpafdgiunlr t` tma pnlfa `c tma cghura. Ytrltahy? Ilniunlta tma j`jafts `c gfartgl lbùt tma x tma x,, y, y, lfd z lfd z lxas lxas usgfh aqultg`f <5-<=. C`r l hgvaf t`rqua tma lfhunlr liianarltg`f liianarltg`f gs gfvarsany gfvarsany pr`p`rtg`fln t` tma j`jaft `c gfartgl? μ : τ G . Qsa tmgs `bsarvltg`f t` datarjgfa tma rlfkgfh `c tma

lfhunlr liianarltg`fs. Y`nutg`f? <. Ilniunlta G L (lbùt

tma x tma x lxgs) usgfh aqultg`f <5-<=?

2

G L : j< r<2 + j2r22 + j9r 92 : ( 7.5 kh ) (<.5 j ) + 5 + 5 : 7.5 kh ⋁ j2 2

y lxgs)? 2. Ilniunlta G B ( y

G B : 5 + 5 + ( 2.1 kh ) ( 2.5 j ) : <5 kh ⋁ j2

z lxgs)? 9. Ilniunlta G I ( z lxgs)?

G I : ( 7.5 kh ) (<.5 j ) + 5 + ( 2.1 kh ) ( 2.5 j ) : <7 kh ⋁ j2

2

2

Bailusa G L > G B > G I wa lrrgva lt tma rlfkgfh μ I > μ B > μ L . 4. Bailusa G Gfsghmt? Xmaf tma lxgs `c r`tltg`f plssas tmrùhm l plrtgiunlr jlss, tmlt jlss dàs f`t i`ftrgbuta t` tma j`jaft `c gfartgl bailusa r : r : 5. Tma j`st t`rqua gs raqugrad raqugrad t` r`tlta tma jlssas lbùt tma tma z z lxgs lxgs bailusa tmlt lxgs plssas tmrùhm tma nalst ljùft `c jlss (`fny tma <.2-kh jlss).

<8. Ugitura tma Ur`bnaj? L j`t`riyina liianarltas cr`j rast, lfd b`tm tma cr`ft lfd ralr tgras r`nn wgtmùt sngppgfh. Ytrltahy? I`fsgdar tma t`rquas axartad `f tma cr`ft lfd ralr tgras gf `rdar t` pr`duia tma `bsarvad r`tltg`f `c tma tgras lfd ngfalr liianarltg`f `c tma j`t`riyina. Y`nutg`f? <. (l) Gc tmara wara f` crgitg`f (c`r gfstlfia, tma j`t`riyina gs ` f sngppary gia) tma i`ftlit p`gft batwaaf tma tgra lfd tma r`ld wùnd f`t rajlgf lt rast, lfd tma t`rqua dua t` tma drgva imlgf wùnd spgf tma tgra craany wgtm tma b`tt`j adha `c tma tgra j`vgfh blikwlrd. Tma litg`f `c crgitg`f crgitg`f gs t` pravaft tmgs j`tg`f j`tg`f lfd kaap tma i`ftlit i`ftlit p`gft `c tma tgra lt rast ranltgva t` tma r`ld. Xa i`finuda tmlt tma c`ria axartad by tma hrùfd `f tma ralr tgra gs gf tma c`rwlrd dgraitg`f. Tmgs gs lns` tma c`ria tmlt liianarltas tma aftgra j`t`riyina j`t`riyina gf tma c`rwlrd dgraitg`f. 2. (b) Gc tmara wara f` crgitg`f (c`r gfstlfia, tma j`t`riyina gs `f sngppary gia) tma tgra wùnd sngda c`rwlrd dua t` tma c`ria `c tma c`rk `f tma lxna but wùnd f`t r`tlta. Tma tgra ilf `fny r`tlta gc stltgi crgitg`f gs prasaft t` pr`duia l t`rqua lbùt tma tgra‗s lxna. Gf `rdar t` pr`duia tma faiasslry t`rqua, tma c`ria axartad by tma hrùfd `f tma cr`ft tgra just ba gf tma blikwlrd dgraitg`f. 9. (i) Tma cr`ft tgra r`tltas bailusa tma blikwlrd c`ria `c crgitg`f crgitg`f `f tma tgra iraltas l t`rqua lbùt tma lxna. Gc tma j`jaft `c gfartgl `c tma cr`ft tgra lbùt tma lxna gs gfiralsad, gts lfhunlr liianarltg`f dua t` tma slja t`rqua wgnn dairalsa. Xa i`finuda tmlt tma j`t`riyina‗s liianarltg`f liianarltg`f wgnn dairalsa gc tma j`jaft `c gfartgl `c tma cr`ft tgra gs gfiralsad. Gfsghmt? Tma j`t`riyina tmlt rajlgfs m`rgz`ftln durgfh ngfalr liianarltg`f gs gf aqugngbrguj wgtm raspait t` r`tltg`f. Tmgs jalfs tmlt tma t`rquas pr`duiad by tma c`ria `c hrlvgty lfd by tma f`rjln c`rias `c tma hrùfd `f tma tgras lfd tma crgitg`f c`rias axartad by tma hrùfd `f tma tgras just lnn blnlfia. Gc tma c`rwlrd crgitg`f c`ria `c tma hrùfd `f tma ralr tgra gs t`` nlrha, c`r gfstlfia, tma t`rqua gt iraltas lbùt tma ralr lxna gs nlrhar tmlf tma t`rqua iraltad by hrlvgty `f tma iaftar `c jlss, lfd tma cr`ft tgra ngcts `cc tma hrùfd ls tma j`t`riyina „p`ps l wmaanga.‚

<=. Ugitura tma Ur`bnaj? Tma `boait i`fsgsts `c cùr jlssas tmlt ilf ba r`tltad lbùt lfy `c tma x tma x,, y, y, `r z lxas, z lxas, ls sm`wf gf tma cghura lt rghmt. Ytrltahy? Ilniunlta tma j`jafts `c gfartgl lbùt tma x tma x,, y, y, lfd z lfd z lxas lxas usgfh aqultg`f <5-<=, lfd tmaf lppny aqultg`f <<-4 t` cgfd tma lfhunlr liianarltg`f tmlt rasunts cr`j lf lppngad t`rqua `c <9 F¸j F¸j lbùt tma vlrgùs lxas. Nat j< : 2.1 kh, j2 : 9.5 kh, j9 : 4.5 kh, lfd j4 : <.2 kh.


















Imlptar <
G x : j< r<2 + j2r22 + j9r92 + j 4r 42

aqultg`f <5-<=?

: 5 + ( 9.5 kh ) ( 5.15 j) + 5 + ( 4.5 kh ) ( 5.15 j) G x : <.81 kh kh ⋁ j2

9. Cgfd μ x usgfh aqultg`f <<-4?

μ x :

4. (i) Ilniunlta G y usgfh

G y : j< r<2 + j2r22 + j9r92 + j 4r 42

aqultg`f <5-<=?

: 5 + 5 + ( 4.5 kh ) ( 5.85 j ) + (<.2 kh ) ( 5.85 j) G y : 2.11 kh kh ⋁ j2

1. Cgfd μ y usgfh aqultg`f <<-4?

μ y :

3. (d) Ilniunlta G z usgfh

G z : j< r<2 + j2r22 + j9r92 + j 4r 42

aqultg`f <5-<=?

2

τ G x

:

<9 F ⋁ j <.81 kh kh ⋁ j

: 8.4 rld/s 2

2

2

τ G y

:

<9 F ⋁ j 2.11 kh kh ⋁ j

2

2

2

: 1.< rld/s 2

(

2

2

2

)

: 5 + ( 9.5 kh ) ( 5.15 j ) + ( 4.5 kh ) ( 5.15 j) + ( 5.85 j) + (<.2 kh ) ( 5.85 j)

2

G z : 4.9 kh ⋁ j2 8. Cgfd μ z usgfh aqultg`f <<-4?

μ z :

τ G z

:

<9 F ⋁ j 4.9 kh ⋁ j

2

: 9.5 rld/s 2

Gfsghmt? Gf tmgs ilsa gt gs l bgt dgccgiunt t` pradgit tma j`jafts `c gfartgl lbùt tma x tma x lfd y lfd y lxas wgtmùt ilniunltgfh lfytmgfh. Tmlt‗s bailusa lntmùhm j`ra j`ra jlss (8.5 kh) gs dgspnliad dgspnliad cr`j tma x tma x lxgs, tma jlssas lra lt l sm`rtar dgstlfia (5.15 j) wmaf i`jplrad t` tma 4.2 kh `c jlss tmlt lra dgspnliad 5.85 j cr`j tma y tma y lxgs. Gt turfs ùt tma tma dgccarafia gf gf dgstlfias gs wmlt jlkas G jlkas G x sjlnnar tmlf G tmlf G y. Xa baft tma runas c`r sghfgcgilft sghfgcgilft cghuras l bgt gf staps 2 lfd 4 t` lv`gd rùfdgfh arr`r.

<7. Ugitura tma Ur`bnaj? Tma cgsm axarts l t`rqua `f tma cgsmgfh raan lfd gt r`tltas wgtm i`fstlft lfhunlr liianarltg`f. Ytrltahy? Qsa Tlbna <5-< t` datarjgfa tma j`jaft `c gfartgl `c tma cgsmgfh raan lssujgfh gt gs l ufgc`rj iyngfdar ( <2 JR 2 ). Cgfd tma t`rqua tma cgsm axarts axarts `f tma raan by usgfh aqultg`f <<-<. Tmaf lppny Fawt`f‗s Fawt`f‗s Yai`fd Nlw c`r

r`tltg`f (aqultg`f <<-4) t` cgfd tma lfhunlr liianarltg`f lfd aqultg`fs <5-2 lfd <5-<5 t` cgfd tma ljùft `c ngfa punnad cr`j tma raan. Y`nutg`f? <. (l) Qsa Tlbna <5-< t` cgfd cgfd G G ?

G : <2 JR 2 :

< 2

2 ( 5.77 kh ) ( 5.511 j ) : 5.55<1 kh ⋁ j2


















Imlptar <
25. Ugitura tma Ur`bnaj? Tma cgsm axarts l t`rqua `f tma cgsmgfh raan lfd gt r`tltas wgtm i`fstlft lfhunlr liianarltg`f. Ytrltahy? Qsa Tlbna <5-< t` datarjgfa tma j`jaft `c gfartgl `c tma cgsmgfh raan lssujgfh gt gs l ufgc`rj iyngfdar ( <2 JR 2 ). Cgfd tma fat t`rqua `f tma raan by subtrlitgfh tma t`rqua cr`j tma crgitg`f inutim cr`j tma t`rqua dua t` tma

c`ria tma cgsm axarts. Tmaf lppny Fawt`f‗s Yai`fd Nlw c`r r`tltg`f r`tltg`f (aqultg`f <<-4) t` cgfd tma lfhunlr liianarltg`f lfd aqultg`fs <5-2 lfd <5-<5 t` cgfd tma ljùft `c ngfa punnad cr`j tma raan. 2

Y`nutg`f? <. (l) Qsa Tlbna <5-< t` cgfd cgfd G G ?

G : <2 JR 2 :

2. Lppny aqultg`f <<-< dgraitny t` cgfd τ ?

τ : r C − I : ( 5.511 j ) ( 2.< F ) − 5.548 F ⋁ j : 5.537 F ⋁ j

9. Y`nva aqultg`f <<-<4 c`r μ ?

μ :

4. (b) Lppny aqultg`fs <5-2 lfd <5-<5?

s : rν : r ( <2 μ t 2 ) : ( 5.511 j ) <2 ( 14 rld/s2 ) ( 5.21 s )

τ G

:

< 2

( 5.=4 kh ) ( 5.511 j) : 5.55<28 kh ⋁ j2

5.537 F ⋁ j 5.55 5.55<2 <28 8 kh kh ⋁ j

2

: 14 rld/s2 2

: 5.579 j : 7.9 ij Gfsghmt? Nass ngfa gs punnad bailusa tma crgitg`f inutim raduias tma fat t`rqua lfd lfhunlr liianarltg`f liianarltg`f `c tma raan. Xa baft tma runas c`r sghfgcgilft cghuras gf staps < lfd 2 t` lv`gd rùfdgfh arr`rs gf gf subsaquaft staps. C`r gfstlfia, gc gc wa c`nn c`nn`w `w tma tma runa runass `c subt subtrl rlit itg` g`f f gf stap stap 2, τ : 5.<2 5.<2 − 5.54 5.548 8 F ⋁ j : 5.58 5.58 F ⋁ j, oust `fa sghfgcgilft cghura.

2<. Ugitura tma Ur`bnaj ? L pars`f ingjbs l nlddar ls gf tma cghura lt rghmt. Ytrltahy? I`fsgdar tma aqugngbrguj `c t`rquas c`r tma pars`f-nlddar systaj wmaf lfswargfh tma i`fiaptuln quastg`f. Y`nutg`f? <. (l) Ls tma pars`f ingjbs mghmar `f tma nlddar, tma t`rqua axartad lbùt tma blsa `c tma nlddar gfiralsas. T` iùftar tmgs t`rqua, t`rqua, tma wlnn just just axart l hraltar hraltar m`rgz`ftln c`ria, lfd tma cn``r just axart tma slja gfiralsad m`rgz`ftln c`ria gf tma `pp`sgta dgraitg`f. Tmarac`ra, tma tma nlddar gs j`ra ngkany t` sngp ls tma pars`f ingjbs mghmar. 2. (b) Tma bast axpnlfltg`f gs GG. Tma jlhfgtuda `c c c 2 just gfiralsa ls tma pars`f j`vas upwlrd. Ytltajaft G gs clnsa (s`ja (s`ja `c tma c`rias d` imlfha) lfd stltajaft stltajaft GGG gs clnsa (tma f`rjln c`ria c c`ria c < aqulns tma waghmt `c tma pars`f, wmgim dàs f`t imlfha. Gf lddgtg`f, c`ria c c`ria c < dàs f`t ilusa tma nlddar t` sngp). Gfsghmt? Xmaf pnligfh lf axtafsg`f nlddar lhlgfst l mùsa gt gs vary gjp`rtlft t` afsura tma b`tt`j `c tma nlddar gs saiurad vary wann. Wù d`f‗t wlft tma b`tt`j t` sngp sngp wmgna yù lra mghm up `f tma nlddar!

22. Ugitura tma Ur`bnaj ? Tma tw` jlssas mlfh `f agtmar sgda `c l punnay.


















Imlptar <
29. Ugitura tma Ur`bnaj? Tma t`rqua raqugrad t` `paf tma olr gs axartad by l c`ria lppngad t` tma wrafim mlfdna. Ytrltahy? Qsa aqultg`f <<-< t` cgfd tma ljùft `c c`ria lppngad t` tma wrafim tmlt wùnd iralta tma faiasslry t`rqua t` `paf tma olr.

C :

C ? Y`nutg`f? Y`nva aqultg`f <<-< c`r C

τ r

:

=.1 F ⋁ j 5.<1 j

: 18 F : <9 nb

Gfsghmt? Tma dgljatar `c tma ngd gs uffaiasslry gfc`rjltg`f bailusa bailusa tma raqugrad t`rqua wls hgvaf gf tma pr`bnaj. Gc gfstald tma raqugrad c`ria wls hgvaf, wa wùnd cgrst mlva t` juntgpny tma ngd rldgus by tma raqugrad c`ria t` cgfd tma raqugrad t`rqua.

24. Ugitura tma Ur`bnaj ? L imgnd sgts `f l pnlfk tmlt gs supp`rtad by mgs plrafts, ls dapgitad dapgitad gf tma cghura lt rghmt. Tmara gs f` liianarltg`f. liianarltg`f. Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw gf tma vartgiln dgraitg`f lfd Fawt`f‗s Yai`fd Nlw c`r r`tltg`f r`tltg`f t` `btlgf tw` aqultg`fs lfd tw` ufkf`wfs ( C lfd C 2). Yubstgtuta `fa gft` tma `tmar `tmar t` s`nva c`r tma c`rias. C < lfd C Nat C Nat C < raprasaft tma j`tmar‗s c`ria, lfd C lfd C 2 tma cltmar‗s. cltmar‗s. Tmara gs gs f` liianarltg`f lfywmara, fagtmar trlfsnltg`fln f`r r`tltg`fln. Y`nutg`f? <. Xrgta Fawt`f‗s Yai`fd Nlw gf tma y tma y dgraitg`f?

∜ C

2. Xrgta Fawt`f‗s Yai`fd Nlw c`r r`tltg`f, pnligfh tma lxgs `c r`tltg`f m`rgz`f tlnny tmrùhm tma imgnd‗s iaftar `c jlss?

∜τ : − C ( N ) + 5 + C ( N ) : 5

9. Yubstgtuta tma axprassg`f cr`j stap 2 gft` stap
C< + 9C< − jh : 5 ⇒ C< :

4. F`w usa tma axprassg`f cr`j stap 2 t` cgfd C 2 ?

C2 : 9C< :

y

: C< + C2 − jh : 5

<

9 4

2

< 4

C2 : 9C <

9 4

< 4

jh

jh

Gfsghmt? Tma imgnd gs tmraa tgjas in`sar t` tma cltmar tmlf ma gs t` tma j`tmar, lfd tma cltmar tmarac`ra supp`rts tmraa tgjas j`ra waghmt tmlf dàs tma j`tmar.


















Imlptar <
21. Ugitura tma Ur`bnaj? Tma bgiaps jusina, tma waghmt `c tma lrj, lfd tma waghmt `c tma blnn lnn axart t`rquas `f tma c`ralrj ls dapgitad lt rghmt. Ytrltahy? Qsa Fawt`f‗s Yai`fd Nlw c`r r`tltg`f t` sat tma t`rquas aquln t` zar`, lfd s`nva c`r tma c`ria axartad by tma bgiaps jusina. Y`nutg`f? <. (l) Tma t`rqua axartad by tma bgiaps just blnlfia tma t`tln t`rqua axartad by tma c`ralrj lfd blsablnn. Bailusa tma j`jaft lrj c`r tma c`ria axartad by tma bgiaps gs juim sjlnnar tmlf tma j`jaft lrjs `c tma c`rias axartad by tma c`ralrj lfd blsablnn, tma bgiaps c`ria just ba j`ra tmlf tma i`jbgfad waghmt `c tma c`ralrj, mlfd, lfd blsablnn. 2. (b) Cgfd tma t`rquas pr`duiad by tma bgiaps jusina lfd alim `c tma jlssas?

τ bgiaps : r⊡ ,bgiaps C τ c`ralrj : r⊡ jh : ( 5.<85 j ) (<.25 kh ) ( 7.=< j/s2 ) : −2.55< F ⋁ j τ blnn : r⊡X blnn : ( 5.945 j ) (<.42 F ) : − 5.4=9 F ⋁ j

9. Yat tma suj `c tma t`rquas aquln t` zar` lfd s`nva c`r tma bgiaps jusina c`ria C c`ria C ?

∜τ : τ bgiaps + τ c`ralrj + τ blnn : 5 : r⊡ ,bgiaps C − 2.55< − 5.4=9 F ⋁ j : 5 2.4=4 F ⋁ j C : : 75.9 F 5.5281 j

Gfsghmt? Tma sjlnn j`jaft lrj c`r tma bgiaps jusina raqugras gt t` axart l nlrha c`ria gf `rdar t` blnlfia tma t`rquas pr`duiad by tma blnn lfd by tma c`ralrj c`ralrj lfd mlfd. 75.9 F gs lbùt 25 nb `c c`ria t` supp`rt l <5 ùfia ùfia blnn! Xa baft tma runas c`r sghfgcgilft cghuras gf stap 2 gf `rdar t` lv`gd rùfdgfh arr`rs gf stap 9.

23. Ugitura tma Ur`bnaj? Tma pars`f ngas `f l nghmtwaghmt pnlfk tmlt rasts `f tw` silnas ls sm`wf gf tma dglhrlj lt rghmt. Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw gf tma vartgiln dgraitg`f lfd Fawt`f‗s Yai`fd Nlw c`r r`tltg`f t` `btlgf tw` aqultg`fs wgtm tw` ufkf`wfs, j lfd xij . Y`nva alim t` cgfd j lfd xij .

Qsgfh tma nact sgda `c tma pnlfk ls tma `rghgf, tmara lra tw` t`rquas t` i`fsgdar? tma p`sgtgva t`rqua dua t` tma rghmt mlfd silna lfd tma fahltgva t`rqua dua t` tma pars`f‗s jlss. Y`nutg`f? <. (l) Xrgta Fawt`f‗s Yai`fd Nlw gf tma vartgiln dgraitg`f t` cgfd j?

∜ C

: C< + C2 − jh : 5 C + C 2 275 + <22 F j: < : : 42 kh 2 y

h

2. (b) Xrgta Fawt`f‗s Yai`fd Nlw c`r

∜τ

rC

7.=< j/s

x jh jh 5


















Imlptar <
∜ C

2. Xrgta Fawt`f‗s Yai`fd Nlw c`r r`tltg`f, usgfh tma ralr caat ls tma pgv`t p`gft?

∜τ : C

: Ccr`ft + Cralr − jh : 5 jh : Ccr`ft + Cralr : 9Ccr` ft y

cr`ft

( 9.2 j ) − jh ( d ij ) : 5 Ccr`ft ( 9.2 j ) : 9Ccr`ft ( d ij ) d ij : <9 ( 9.2 j ) : <.< j

Gfsghmt? Ls axpaitad, tma iaftar `c jlss ` c tma lfgjln gs in`sar t` gts ralr caat tmlf gts cr`ft caat, ilusgfh tma ralr caat t` supp`rt j`ra `c tma waghmt.

2=. Ugitura tma Ur`bnaj? Tma ldunt pusmas d`wfwlrd `f tma nact sgda `c tma taatar-t`ttar lfd tma imgnd sgts `f tma rghmt sgda ls dapgitad gf tma cghura?

r ⊡ ldunt

r ⊡ imgnd

Ytrltahy? Ilniunlta tma t`rquas axartad by tma waghmt `c tma imgnd lfd tma c`ria `c tma plraft‗s mlfds lfd suj tmaj. tmaj. Yat tma fat t`rqua aquln t` zar` t` t` afc`ria C ldunt tma i`fdgtg`f `c aqugngbrguj, lfd usa tma rasuntgfh axprassg`f t` cgfd tma lppr`prglta dgstlfias. Tlkgfh tma iaftar `c tma taatar-t`ttar ls tma pgv`t p`gft, tma imgnd axarts l fahltgva t`rqua lfd tma plraft axarts l p`sgtgva t`rqua `f tma systaj. Y`nutg`f? <. (l) Yat tma fat t`rqua aquln t` zar` lfd s`nva c`r r ⊡ ldunt tma imgnd axarts `f

tma taatar-t`ttar.

2. (b) Rapalt stap < c`r tma dgccaraft c`ria axartad by tma plraft?

∜

H τ

jimgnd h

: r⊡ ldunt Cldunt − r⊡ imgnd ( jimgnd h ) : 5

r ⊡ ldunt :

r ⊡ ldunt :

r⊡ imgnd ( jimgnd h ) C ldunt

r⊡ imgnd ( jimgnd h ) C ldunt

:

:

( <2 Ø 1.2 j ) (<7 kh ) ( 7.=< j/s2 ) 2<5 F

kh ) ( 7.=< j/s2 ) ( <2 Ø 1.2 j ) (<7 kh 9<5 F

: 2.9 j

: <.3 j

9. (i) Tma lfswars wùnd f`t imlfha bailusa `fny tma taatar-t`ttar‗s nafhtm aftars gft` tma ilniunltg`fs (tma imgnd sgts mlnc l nafhtm cr`j tma pgv`t p`gft), f`t gts jlss. Gfsghmt? Gc tma plraft wara t` pusm d`wf `f tma vary afd `c tma taatar-t`ttar, 2.3 j cr`j tma pgv`t, tmay wùnd `fny faad t` pusm wgtm l c`ria aquln t` tma imgnd‗s <75-F waghmt.

27. Ugitura tma Ur`bnaj? Tma c`ria lppngad t` tma butt`f pr`duias l p`sgtgva t`rqua `f tma raj`ta lbùt tma adha `c tma tlbna, lfd tma waghmt `c tma raj`ta pr`duias l fahltgva t`rqua lbùt tma slja pgv`t. Ytrltahy? Tma jlxgjuj `varmlfh i`rrasp`fds t` tma ilsa wmaf tma t`rqua lbùt tma tlbna adha ilusad by tma butt`f c`ria gs blnlfiad by tma t`rqua ilusad by tma waghmt `c tma r Lssujgfh tma raj`ta mls l




















Imlptar <
95. Ugitura tma Ur`bnaj ? Tma jatar stgik gs supp`rtad by tma tafsg`f gf tma strgfh gf tma jlffar gfdgiltad gf tma cghura lt rghmt. H

Ytrltahy? Yat tma fat t`rqua lbùt tma jatar stgik‗s i`ftlit wgtm tma wlnn aquln t` zar` lfd s`nva c`r tma tafsg`f gf tma strgfh. Tma t`rqua dua t` tma strgfh gs p`sgtgva lfd tma t`rqua dua t` tma waghmt gs fahltgva.

T

pgv`t

ν H

Y`nutg`f? <. (l) Cgfd ν c`r l 2.1-j strgfh? ν : i`s 2. Yat

∜

H τ

c`r T ? : 5 lfd s`nva c`r T

∜

H τ

−<

(<.5 j

X

2.1 j ) : 33µ

: N (T sgf ν ) − ( <2 N ) (X ) : 5

T :

X 2 sgf ν

:

5.<3 kh) ( 7.=< 7.=< j/s2 ) ( 5.<3 2 sgf 33µ

: 5.=3 F

9. (b) L sm`rtar strgfh wgnn jlka l sjlnnar lfhna wgtm tma stgik gf `rdar t` m`nd gt m`rgz`ftlnny. Tma sjlnnar lfhna wgnn raqugra l tafsg`f hraltar tmlf tmlt cùfd gf plrt (l) gf `rdar t` pr`duia tma slja t`rqua. 4. (i) Cgfd ν c`r l 2.5-j n`fh strgfh? 1. Yat

∜

H τ

c`r T ? : 5 lfd s`nva c`r T

ν : i`s−< (<.5 j 2.5 j ) : 35µ

∜

H τ

: N (T sgf ν ) − ( <2 N ) (X ) : 5

T :

X 2 sgf ν

:

5.<3 kh kh ) ( 7.=< 7.=< j/s2 ) ( 5.< 2 sgf 35µ

: 5.7< F

Gfsghmt? Tma tafsg`f gf tma strgfh gs nass tmlf tma <.3-F waghmt `c tma jatar stgik bailusa tmara gs lf upwlrd c`ria `f tma stgik lt tma pgv`t p`gft tmlt manps t` supp`rt tma waghmt `c tma stgik. Tmlt c`ria pr`duias f` t`rqua, m`wavar, s` wa dgd f`t faad t` i`fsgdar gt gf tma s`nutg`f t` tmgs pr`bnaj.

9<. Ugitura tma Ur`bnaj? Tma dgvar `c jlss j stlfds lt tma afd `c tma dgvgfh




















Imlptar <
92. Ugitura tma Ur`bnaj? Tma blt rasts m`rgz`ftlnny `f Blba‗s smùndar, wgtm `fa mlfd m`ndgfh tma sjlnn afd `c tma blt. Ytrltahy? Tma mlfd axarts l d`wfwlrd c`ria t` iùftarlit tma t`rqua iraltad by tma waghmt `c tma nlrha nlrha afd `c tma blt. Tma smùndar axarts lf upwlrd c`ria `f tma blt t` supp`rt tma waghmt lfd tma d`wfwlrd c`ria `c tma mlfd. Xrgta Fawt`f‗s Yai`fd Yai`fd Nlw c`r t`rqua (nat tma tma smùndar ba tma pgv`t p`gft) lfd lhlgf gf tma vartgiln vartgiln dgraitg`f t` t` cgfd tma c`ria axartad by tma mlfd lfd by tma smùndar. H

Y`nutg`f? <. (l) Xrgta H

∜τ : 5 lfd s`nva c`r C . m

Lssuja Cm lits gf tma d`wfwlrd dgraitg`f lfd iraltas l p`sgtgva (iùftarinìkwgsa) t`rqua? H

2. (b) Xrgta

∜ C : 5 lfd s`nva c`r C ? y

s

∜τ : ( 22.1 ij ) C

m

C m :

− ( 38.5 − 22.1 ij ) jh : 5

( 44.1 ij ) (<.<5 k h) ( 7.=< j/s2 )

22.1 ij H Cm : ( −2<.9 F ) y˃

∜ C

y

: 2<.9 F

: ’ Cm + Cs − jh : 5

Cs : Cm + jh : 2<.9 F + (<.<5 kh ) ( 7.=< j/s2 ) : 92.< F H

Cs : ( 92.< F ) y˃ Gfsghmt? Tma smùndar c`ria upwlrd blnlfias tma 2<.9-F mlfd c`ria lfd tma <5.=-F waghmt, b`tm `c wmgim lra d`wfwlrd.

H

99. Ugitura tma Ur`bnaj? Tma r`d gs supp`rtad by tma wgra lfd l mgfha ls dapgitad gf tma cghura lt rghmt. Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw c`r t`rqua (nat tma mgfha ba tma pgv`t

T H

m

M

ν




















Imlptar <
H

94. Ugitura tma Ur`bnaj? Tma r`d gs supp`rtad by tma wgra lfd l mgfha ls dapgitad gf tma cghura lt rghmt.

T H

Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw c`r t`rqua (nat tma mgfha ba tma pgv`t p`gft) t` cgfd tma jlhfgtuda jlhfgtuda `c tma tafsg`f tafsg`f gf tma wgra.

m

ν

M

N H

jh

Y`nutg`f? <. (l) Tma tafsg`f wgnn dairalsa, bailusa r ⊡− waghmt mls

dairalsad lfd r ⊡− wgra mls gfiralsad. 2. (b) Yat

∜τ : 5 lfd s`nva ∜τ : r

⊡ − wgraT

c`r T c`r T ?

T:

r ⊡− waghmt r⊡− wgra

− r⊡ − waghmt jh : 5 jh :

< 2

N i`s ν m

(<.2 j ) i`s91µ ( 9.< kh ) ( 7.=< j/s 2 ) : (<.2 j) sgf91µ

<

jh : 2

22 F

Gfsghmt? Ls tma r`d gs punnad j`ra lfd j`ra t`wlrd tma vartgiln, tma mgfha supp`rts j`ra lfd j`ra `c tma r`d‗s waghmt, s` tmlt tma wgra faads t` supp`rt nass lfd nass waghmt. Xmaf tma r`d gs vartgiln tma tafsg`f wùnd ba zar`.

91. Ugitura tma Ur`bnaj ? Tma pars`f stlfds `f l 8.2-kh nlddar gf tma jlffar dapgitad by tma cghura lt rghmt. Ytrltahy? Tma pr`bnaj ilf ba s`nvad by sattgfh tma vait`r sujs `c tma c`rias lfd tma t`rquas aquln t` zar`. Tma `fny dgccarafia dgccarafia batwaaf tmgs pr`bnaj lfd lfd Litgva H Axljpna <<-9 gs tma lddgtg`f `c l vait`r jL h lt tma iaftar `c jlss `c tma nlddar. H

Tma m`rgz`ftln dgstlfia batwaaf tma blsa `c tma nlddar lfd tma vait`r jL h gs i:

2

2

( <2 Ø 4.5 j ) − ( <2 Ø 9.= j ) : 5.32 j.




















Imlptar <
93. Ugitura tma Ur`bnaj? Tma m`rgz`ftln c`ria C c`ria C gs gs lppngad t` tma r`d ls sm`wf gf tma cghura lt rghmt. Ytrltahy? Nat N Nat N : tma r`d nafhtm lfd wrgta Fawt`f‗s Yai`fd Nlw c`r t`rquas (nat tma b`nt ba tma pgv`t p`gft) gf `rdar t` datarjgfa tma wgra tafsg`f T . Tmaf wrgta Fawt`f‗s Yai`fd Yai`fd Nlw gf tma m`rgz`ftln lfd vartgiln vartgiln dgraitg`fs t` t` datarjgfa tma H

i`jp`fafts `c tma b`nt c`ria C b . Y`nutg`f? <. (l) Yat

∜τ : 5 lfd

∜τ : N (T i`s 41µ) − (

s`nva c`r T ?

2. (b) Yat

T :

∜ C : 5 lfd s`nva c`r C x

x , x

?

∜ C

x

C

2i`s41µ

:

< 2

N ) C : 5

C

2

: C + C b,x − T i`s 41µ : 5 ⎛ C ⎖ i`s 41µ − C : − <2 C ⎐ ⎚ 2i`s41µ ⎥

C b, x : T i`s 41µ − C : ⎞ 9. (i) Yat

∜ C : 5 lfd s`nva c`r C y

, y

?

∜ C

y

: C b,y − T sgf 41µ : 5 ⎛ C ⎖ sgf 41µ : ⎐ sgf ⎚ 2i`s41µ ⎥

C b, y : ⎞ Gfsghmt? Tma b`nt c`ria mls l jlhfgtuda `c C

< 2

C

2 lfd p`gfts 41µ lb`va tma m`rgz`ftln lfd t` tma nact.

98. Ugitura tma Ur`bnaj ? Tma Limgnnas tafd`f, lfkna o`gft, lfd f`rjln c`rias lit `f tma c``t ls sm`wf gf tma dglhrlj lt rghmt.




















Imlptar <
9=. Ugitura tma Ur`bnaj? Tma stgik rasts `f tma b`wngfh blnn ls sm`wf gf tma dglhrlj lt rghmt. Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw c`r t`rqua (nat tma pgv`t p`gft ba tma p`gft `c i`ftlit batwaaf tma stgik stgik lfd tma cn``r) lfd tmaf wrgta Fawt`f‗s Yai`fd Nlw gf tma vartgiln lfd m`rgz`ftln dgraitg`fs t` cgfd tma jlhfgtudas `c F F , c x , lfd c y . Qsa tma dgjafsg`fs gfdgiltad gfdgiltad gf tma cghura, t`hatmar wgtm wgtm

H

F

c y

M

tma dacgfgtg`f tmlt L : tma `varlnn nafhtm `c tma stgik. stgik. By ilracunny studygfh tma ha`jatry wa cgfd tmlt M : R + R i`s ν . Y`nutg`f? <. (l) Yat

∜τ : 5

∜τ : 5 : −r jh + FN : − ( ⊡

lfd s`nva c`r F F ? F :

< 2

sgf ν ⎬⎩( <2 L i`s ν ) jh ⎤⎣

L i`s ν

:

M

ν

N ν

H

R

jh

c x

⎬ M ⎤ ⎩ sgf ν ⎡⎣

) jh + F ⎢

jh L sgf ν i`sν 2 R (< + i`s ν )

kh ) ( 7.=< j/ j/s ) ( 5.493 j) sgf 95 95.5µ i`s 95 95.5µ ( 5.2<4 kh : 2 ( <2 Ø 5.2<3 j ) (< + i`s 95.5µ ) 2

: 2. Yat

∜ C : 5 t` cgfd C ? x

x

∜ C

x

5.7=9 F

: c x − F sgf ν : 5

c x : F sgf ν : ( 5.7=9 F ) sgf 95 95.5µ : 5.472 F 9. Yat

∜ C : 5 t` cgfd C y

O, y

?

∜ C

y

: c y − jh + F i`s ν : 5

c y : jh − F i`sν 95.5µ : <.21 F : ( 5.2<4 kh ) ( 7.=< j/s2 ) − ( 5.7=9 F ) i`s 95 Gfsghmt? Tma tw` i`jp`fafts `c tma cn``r‗s i`ftlit c`ria i`jbgfa t` pr`duia l c`ria `c <.94 F gfingfad lt 3=.1µ lb`va tma m`rgz`ftln lfd dgraitad t`wlrd tma p`sgtgva x p`sgtgva x dgraitg`f.






















Imlptar <
45. Ugitura tma Ur`bnaj? Tma m`rgz`ftln c`ria gs lppngad lt l dgstlfia m lb`va tma cn``r ls gfdgiltad gf tma cghura lt rghmt. Ytrltahy? Gf `rdar t` blnlfia tma m`rgz`ftln c`rias, tma lppngad c`ria just ba f` nlrhar tmlf tmlf tma jlxgjuj stltgi crgitg`f c`ria. Gc gt wara nlrhar, nlrhar, tma irlta wùnd sngp m`rgz`ftlnny m`rgz`ftlnny gfstald `c tgppgfh. Yat tma lppngad c`ria aquln t` tma jlxgjuj stltgi crgitg`f c`ria lfd cgfd tma jgfgjuj maghmt m lb`va tma cn``r lt wmgim suim l c`ria iùnd iùnd ba lppngad lfd stgnn tgp tma tma irlta. Tmgs gs lii`jpngsmad by wrgtgfh Fawt`f‗s Yai`fd Nlw c`r t`rqua wgtm tma pgv`t p`gft lt tma n`war-rghmt n`war-rghmt i`rfar i`rfar `c tma irlta. Y`nutg`f? <. (l) Cgfd tma jlxgjuj stltgi crgitg`f c`ria? 2. Yat

c`r m? ∜τ : 5 lfd s`nva c`r m

N jh

m

c jlx : ξ s jh : ( 5.18<)( kh ) ( 7.=< j/s2 ) : 75.8 F ) (<3.2 kh

∜τ : ( N ) jh − m C : 5 < 2

m: 9. (b) Tma lppngad c`ria wùnd ba C

C

jhN 2 C

kh ) ( 7.=< j/s2 ) (<.2< j ) (<3.2 kh : : 2 ( 75.8 F )

<.53 j

75.8 F bailusa gt ilf ba f` nlrhar tmlf tma jlxgjuj stltgi crgitg`f c`ria






















Imlptar <
42. Ugitura tma Ur`bnaj? Tma ilt gs parimad `f tma pnlfk ls sm`wf gf tma cghura lt rghmt. Litgva Axljpna <<-2 <<-2 gfdgiltas tmlt tma ufgc`rj pnlfk gs gs 4.55 j n`fh lfd mls l jlss `c 8.55 kh. Tma pnlfk gs supp`rtad by tw` slwm`rsas, `fa 5.445 j cr`j tma nact afd `c tma b`lrd lfd tma `tmar <.15 j cr`j gts rghmt afd. Ytrltahy? Yat tma fat t`rqua, wgtm tma rghmt mlfd slwm`rsa litgfh ls tma pgv`t p`gft, aquln aquln t` zar` lfd s`nva s`nva c`r tma dgstlfia dgstlfia r `c r `c tma ilt cr`j tma rghmt slwm`rsa. Tmaf datarjgfa tma dgstlfia dgstlfia `c tma ilt d ilt cr`j tma rghmt

afd `c tma pnlfk. Tma iaftar `c jlss `c tma pnlfk pnlfk gs l dgstlfia < 4.55 j ) − <.15 j : 5.15 j cr`j tma rghmt mlfd slwm`rsa. 2( Y`nutg`f? <. Yat

∜τ : 5 lfd s`nva c`r r

ilt

?

∜τ : r

ij

rilt : 2. F`w cgfd d ilt ?

jpnlfk h − rilt jilt h : 5

j pnlfk jilt

r ij :

8.55 kh 2.= kh

( 5.15 j ) : <.21 j

d ilt : <.15 − <.21 j : 5.21 j






















Imlptar <
4. Tma rasunt `c stap 9 jalfs tmlt tma iaftar `c jlss `c b``k < gs nìltad lt 9 N 4 + N 2 : 1N 4 . 1. Tma iaftar `c jlss `c b``ks 9, 2, lfd < faads t` ba lb`va tma rghmt afd `c tma tlbna?

d : ] ij,92< :

j ( N 2) + j ( N ) + j ( 1N 4 ) 9j

:

<< <2

N

Gfsghmt? Ls wa nalrfad gf pr`bnaj =8 `c Imlptar 7, gc yù ldd l cùrtm b``k tma jlxgjuj `varmlfh gs ( 21 24 24 ) N . Gc

yù axljgfa tma `varmlfh `c alim b``k yù cgfd lf gftarastgfh sargas? d :

N 2

+

N 4

+

N 3

+

N =

:

21 24

N . Tma sargas sargas hgvas yù

l mgft lbùt m`w t` pradgit tma `varmlfh `c avaf nlrhar stliks `c b``ks. 41. Ugitura tma Ur`bnaj? Tma hn`va mlfhs `f `fa afd `c tma blt lfd tma blnlfia p`gft gs cùfd t` ba 24.8 ij cr`j tma 8<.< ij jlrk. Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw c`r t`rqua wgtm tma hn`va lt 5.55 ij lfd tma pgv`t p`gft lt tma 8<.< − 24.8 ij : 43.4 ij jlrk. Y`nva tma rasuntgfh axprassg`f axprassg`f c`r tma jlss J jlss J `c `c tma tma blt. Nat j ba tma jlss `c tma hn`va. Y`nutg`f? Yat

∜τ : 5

lfd s`nva c`r J J ?

∜τ : d ( Jh ) − r ( jh ) : 5 rj

ij ) ( 5.135 kh kh ) ( 8<.< − 24.8 ij

<.51 kh






















Imlptar <
48. Ugitura tma Ur`bnaj? Tma jlss clnns strlghmt d`wf, gts spaad raduiad dua t` tma r`tltg`f `c tma dgsk. Tma pmysgiln sgtultg`f sgtultg`f gs dapgitad lt rghmt. rghmt. Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw c`r t`rqua lbùt tma lxgs `c tma punnay, lfd Fawt`f‗s Yai`fd Nlw gf tma vartgiln dgraitg`f c`r tma buikat. I`jbgfa tm`sa tw` aqultg`fs t`hatmar wgtm tma ranltg`f, l : r μ μ , wmgim i`jas cr`j tma clit tmlt tma r`pa dàs f`t sngp ln`fh tma rgj `c tma punnay, gf `rdar t` cgfd tma ngfalr liianarltg`f lfd tma tafsg`f T . Nat J Nat J : : buikat jlss, j : punnay jlss, r : r : punnay rldgus, T : T : r`pa tafsg`f, lfd f`ta tmlt c`r tma punnay, 2 < G : 2 jr . Nat d`wfwlrd ba tma p`sgtgva dgraitg`f c`r tma buikat. Y`nutg`f? <. (l) Tma tafsg`f gf tma r`pa just ba nass tmlf tma waghmt `c tma buikat. Gc gt wara aquln t` tma waghmt `c tma buikat, tma c`rias `f tma buikat wùnd ba blnlfiad lfd tmara wùnd ba f` liianarltg`f. Gc gt wara hraltar tmlf tmlf tma waghmt `c tma buikat, tmara tmara wùnd ba l fat upwlrd c`ria `f tma buikat lfd gt wùnd liianarlta upwlrd gfstald `c clnngfh d`wf! 2. (b) Yat

∜τ : G μ c`r tma

∜τ : rT : G μ

punnay lfd s`nva c`r c`r T T ? T:

G μ r

( :

< 2

jr 2 ) ( l r ) r

: <2 jl






















Imlptar <
H

∜ 4. Yat ∜ τ : G μ c`r tma punnay?

∜ C : T − Jh : Jl ∜τ : r T − r T : Gμ : (

c`r l 1. Yubstgtuta tma axprassg`f c`r l cr`j stap 4 gft` tma `fa cr`j stap 9, lfd s`nva c`r T 2 (tma tafsg`f `f tma

T2 − Jh : J ⎬⎩ 2 (T< − T2 ) j ⎤⎣ jT2 − jJh : 2JT< − 2JT2

9. Yat

C : jl c`r tma mlfhgfh jlss?

`tmar sgda `c tma punnay cr`j yù)?

y

2

<

2

T 2 :

< 2

jr 2 ) ( l r ) ⇒ l : 2 (T< − T2 ) j

J ( 2T< + jh ) 2 J + j

( 5.38 kh ) ⎬⎩ 2 ( 2= F) + (<.2 kh) ( 7.=< j/s2 ) ⎤⎣ : : 2 ( 5.38 kh ) + <.2 kh

<= F

Gfsghmt? Tma fat c`ria `f tma mlfhgfh jlss gs tmus T2 − Jh : <= − 3.3 F : <<.4 F , afùhm t` liianarlta gt upwlrd lt

<8 j/s2. Tma lfhunlr liianarltg`f liianarltg`f `c tma punnay gs tmus l r : (<8 j/s 2 )

( 5.581 j ) : 295 rld/s2 .























Imlptar <
12. Ugitura tma Ur`bnaj ? Tma jlssas lfd punnay lra i`fcghurad ls dapgitad gf tma cghura lt rghmt? Ytrltahy? Xrgta Fawt`f‗s Yai`fd Nlw gf tma vartgiln dgraitg`f c`r b`tm j< lfd

j2 , lfd tmaf wrgta Fawt`f‗s Yai`fd Nlw c`r t`rqua lbùt tma punnay‗s r`tltg`f lxgs. I`jbgfa tma tmraa aqultg`fs t` t` cgfd tma ngfalr liianarltg`f liianarltg`f `c tma jlssas. Lssuja tma r`pa dàs f`t sngp ln`fh tma rgj `c tma punnay `c rldgus R rldgus R,, s` tmlt






















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14. Ugitura tma Ur`bnaj? Tma dgsk-smlpad rai`rd r`tltas lbùt gts lxgs wgtm l i`fstlft lfhunlr spaad. 2 Ytrltahy? Qsa aqultg`f <<-<< lfd tma j`jaft `c gfartgl `c l ufgc`rj dgsk r`tltgfh lbùt gts lxgs, G : <2 JR , t` cgfd tma

lfhunlr j`jaftuj `c tma rai`rd. Y`nutg`f? Lppny aqultg`f <<-<< dgraitny?

N : G χ

rav ⎖ ⎛ 2υ rld ⎖ ⎛ < jgf ⎖ 2 ⎛ : ( < JR 2 ) χ : < ( 5 5<1 kh ) ( 5 <1 j ) ⎞ 99 < ⎐⎞ ⎐⎞ ⎐





















Imlptar <
1=. Ugitura tma Ur`bnaj? O`hhar 9 rufs gf l strlghmt ngfa lt i`fstlft spaad gf tma jlffar gfdgiltad by tma cghura lt rghmt. Ytrltahy? Qsa N : rjv (aqultg`f <<-<2) t` cgfd tma lfhunlr j`jaftuj. Y`nutg`f? <. (l) Tma lfhunlr j`jaftuj gfiralsas wgtm tma parpafdgiunlr dgstlfia t` tma racarafia p`gft. Ygfia o`hhar 9‗s parpafdgiunlr parpafdgiunlr dgstlfia t` p`gft L gs zar`, zar`, mgs lfhunlr j`jaftuj gs gs zar` wgtm raspait t` p`gft L. Tmarac`ra mgs lfhunlr






















Imlptar <

32. Ugitura tma Ur`bnaj? L studaft r`tltas `f l crgitg`fnass pglf` st``n wgtm mgs lrjs ùtstratimad, l malvy waghmt gf alim mlfd. Yuddafny ma nats h` `c tma waghmts, lfd tmay clnn t` tma cn``r. Ytrltahy? Tma lfhunlr j`jaftuj `c lfy r`tltgfh s`ngd `boait ilf `fny imlfha gc tmara gs l t`rqua `f tma systaj. Lntmùhm tmara gs f` t`rqua `f tma studaft, tmara gs l t`rqua `f tma waghmts wmaf tmay nlfd `f tma cn``r. Y`nutg`f? <. (l) Dr`ppgfh tma waghmts dàs f`t pr`duia lfy t`rqua `f tma studaft-pglf` st``n systaj, s` gts lfhunlr j`jaftuj wgnn rajlgf rajlgf tma slja. Tma j`jaft `c gfartgl `c tma studaft-pglf` st``n systaj systaj (f`t gfinudgfh tma waghmts)






















Imlptar <
31. Ugitura tma Ur`bnaj? Tma skltar punns mgs lrjs gf, dairalsgfh mgs j`jaft `c gfartgl lfd gfiralsgfh mgs lfhunlr spaad. Ytrltahy? Tma lfhunlr j`jaftuj `c tma skltar rajlgfs tma slja tmrùhmùt tma spgf bailusa tmara gs lssujad t` ba f` t`rqua `c lfy kgfd litgfh `f mgs b`dy. Qsa tma i`fsarvltg`f `c lfhunlr j`jaftuj (aqultg`f <<-<1) t`hatmar t`hatmar wgtm aqultg`f <<-<<, t` cgfd tma rltg` G c G g . Y`nutg`f? Yat Ng : Nc lfd s`nva c`r G c G g ?

G gχg : G c χ c

⇒

G c G g

:

χ g χ c

:

9.<8 rld/s 1.43 rld/s

: 5.1=<











































































































































































































































































































Physics Chapter 11 Answers

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