P-1.7 পদার্থের গাঠনিক ধর্ম

qqr{frGH }8'rg a qR q$lIT{ fras <q<-c{R{ 6|6 q6f{ foT{"t: O qtEsqTqfrs qrs$r mlcel( qtqrEl "t.zrerr c< T{ Er.{ {s m fr&a 66s rt5.rrfl oth or< sno q-ggqlqR'sqrsd"ITarrar 1q +fu "tnr{< vfsaqHks qls("t {{CErr ffi ett.cs q<( qlgsqqfrq E<g r<(Em F{ e[r$ r 1i1 +6r tnrc{< e"tteret Eq aRr<6rr r-<co "nm lt 1i-g fiq q{${ TFlu qcs affro r 1ii1 <fti mn{< rorr'+t q4n <t qqrcri& 6di r (iv)u{qoffid<mmsfssFqf qFF,fttfipE-{T{sqr{${elrs,{<(q<IFmft{<Tc{IEFrIGrls<rFflIGrr (v) oBrfi-s "mrc{< 6$rq qrg:qHfrs T{y {{CE(T ffi e[56 qai qgcqt"tfrs qffi{ <{ c:rcE({ s{ allrs r e66flqkr ffi{; a qr+'{q -ifu sl<l ftr q€ a &{ dffi< "nmt "l;r9!r {s <{ qX 'it{ or< slrs ffiqks s[;r{Frr cn<{IqR'o <rr c emm: (i) qxfr+ (iil qrr{ffr (iii) qtturci{ ffi{ (iv) {E< (v) s]l{sK srlq{ stsfrs dut: $E< s q<lg< dre< <TctTFs RfrlrsTra <tg< "r<$tr <Rss< calr€ q{g q<NlT< <Rsst-< qs <I e+Ik{ E3;r6{ qr+rsRg qerF {tvrl 1? r+rw vm s qlqrqs qt-Tr+< fi <r fr< @ vm{"r ero c< <+r q$s c{ Errs ql-nfrq a6q <54 1 qmfr+ <sn s|<t I?. ffil|56 q-gF"+ d4 {ffi I cqrqlfr {s.{: <Rssc< fi&x eBnq< QGftq Efq-dr sl}l.rfl qq"d< Bcqr.R.T{|q qi?fs q'{ul{ e- ffifiR FGI er <t esll!-s e- mlg 1E oc< q<< E-sT TflT"I sT qqFsl6{ crl$< or< r qsft< 'i3NI{TCT< {c$ c{ <ltr{ {6s c{ errs c{fi|fr <s-{ <t mMft <fi Em r {E< sffi: {E< crqlfi w<F im-ss qtrn {s e- co srlo{{ +-m r q< Frq EE qKr+< slr<I cs {tr{ ?sl? cn vlrs $g?t {ifr;I{FI| si"l\5k snlEm<Er: Flq+Rw<F' fiqucEs ilr<f aqffi{5{euo*tro fursKistGFsiFisTir sRtEt4{E<6r I ,;,,.-14g: ffifiEpirt];r[q<'Knfr<e<w{q<$eq&TI{6.r-castc,TlqftTT€<rEI srs"l(qQ&t"is<l $F+<g.s{cqr 0 o o qeffi{ oq qnc?i< ortfrtr qt' c<Is CQ M C a CQ M C a CQ M C a CQ M C o CQ M C T o rt ri { s ?t 'l s F "l 'l s $ { 'i { s { 't s DKT I 3 1 1 2 2 2 I 3 2 3 I 2 {rq1l* I I 2 2 q-eq6M l :l Etdtr I I 3 I I 3 I 2 t I 3 14i36 I 2 1 I 4 I I <furc 1 I 3 2 I 3 I 1 3 4r"lt< I 3 3 2 1 2 Tft-sl I 1 I 2 3 3 5 I 1 I 2 fr-{MT{ I 2 2 I 2 2 3 I 4 vwfi'.q I 1 I 2 fr.u.- \oto cl-rq mg "ramq{frsqsqtt qaq qo:uqn-qrc{ c{rl6qft{ E{ r6frrE {frT[q{frussr 'IEq !bb

o o o o o o o q5rrRGrd lEI rtg : i{<It{-oq { QBq"r+ <-c 6s[rll fti-?r \e'fi <q Ec<t't c$< lK & <-q q$fl<q ofl arE TgE {fr "1c-<tfft 1rf< q<Sr ft.r< rx o-m wo 14 fu'bgrfl-o Tg rrd r t{ 1o re : con+ <g-< E"r< cvcotr+ qRllq fi qcfiur sr< {fr ET< r<Te <I slfro qffi qBrr+ ql {T, Er< cli<-eco {5-r<e <rrr Q&qr"r+ fr+r: e{.3.- <ifos 161-< cs +c{m <r S(ftqr "i'fu c$.trlT <-s t{ e&qrlo qr6s Et6s & qer R&qprc ftrff<Tar qrR sfn q<( q{q ftw:1r+w c< Fffi w-r<-< fuffi corr+ qe ers + fr65 rll{ El-r$ qrR qn/\eq;[ {(ur r cslr* e$E (€< qT:F cwFF(aK \s'R A{s qrq W<r-+ sqqftsT <rE r frgc;K {1q.l ML-1T-2 r QBqtto ffi : cq qrql-{ {q q'EKcc]<l {rcat 4fcqt (g qrc'i{ wEqt frr< t* i,l. sn+ eEEr"r+ ilfu <rn r @: cotrnT eoF r€< qFs {li4k ({ "tk+5r sCB sf @ ftm ${ s{ I @ fu ++N (D ?nfi @: <q qrrpr'k a6a fi a6 |q6fp6 "rR-<r6q q& on-+ h6 @ <cn r (iD qfis{ W' <E Erskuld Frq <fr (€-{ sr<r-ur+< tkfit+ qt6 s.r< srr+ stqg{ RfG {ra r 1ii11-v+ @: <fr Ep <rfur <ri-{ fuTR <EK qmsi qrfr<frG cqrs rs-fi q< qTfr< 1ffir qs ,a ,r{6{< f+gfuogorfcEG<ttr 6e< g : Qft qt"to ff rr< rcrt +s< s "r< e1*- ft .sq vtr RTfu cat-x"t }&s r Q&q"r+ e"r+: Q&qt"r+ ffI.l< m$ mrrqt Ts{ ft.u{ e ffi"< q-flTErr eGq"ro eqts <cr r tqi q< a"[t: €Fs efq@aq< c$E'sri RFE rsn31 EIc<< ?q(1 {fl-{< efuqff+ ffn< ar$ 6q fi EGiIrf $-scq sl-dB< ffii fi qtfr ?qrtim w:tF {r Em tt< q< eqtq (r< r rlqt: [y] = [M I, 1 T - 2] o 10+ ete: Q&qr"r+ srm :rc<i gvl ft-w s aw @ qxts €sF << r(,BT r qr$ gs{ ecttq <F | qlEI lYl q< q{fr1| vmw e*e: Q&qt"fo fr+t< TC<r <g< qmsq fr-s{ e q|TsT @ qnvr+ vmw e.UE{FrI srf ,g,frcT erslno<I {{ | Elqt: [Y] qF w{s1 I {(d1lsl: qHEd eqm< ft"tfts <Fn+ qR{Tr\9t TFi I Qft q"r+ ffi : <tm crrr+ con*t <-er.e ro er-<m +r< kls o+ce ftR sM q{ !,]. <er eGA"m ft g-fl fu fr sr{ cF@E{r mtr+<wqns:QGqnoffat<m<i<e<"n{@s?n{rk1G<qtse+Gg<arFrr qrsfi.fir_:rqT{E{qTqrr 3 Q&qrr+sr: {fgd =:' {rf<{q3 C<{]r{ ftvi @ F = e{g' <Et, A = cse-TEI = S-{s ffii qtr\9-4 qrsIi(/ Tq{/ (ITE9' @ r &6fui "i1i<6r L qfi?6{r v qmE{ 1fu1 v qrfrqt$rd e (mfrTT ssi:+) EGIFF ?rR. s< eq-s, ,=%: " qEtsrecits,e=fi:#; [P = Ef'f = Ir TPs]-<t e"[S, n= *:; c{rl[F, c-?l"l e= <lc{E;1=(sE{ fiFr< <ar e1o qq Ek ffi..+Er I {({{lsl, K = ;, K = qts{ aclr6 (Bulk modulus) I t$l

q5l{fr6|d iN eE[ : q{Jl{-oq 3lrprr*rw{{v, " = m = i ; c{{ttrr, D = ffi qtc, a = $tc-d 1ffi 15eftn1 o un-+<?nfi 1fr-<q"r,TE€M: tirw=if =irr ,{tFlqEIr{cR6Effir '" qss \fi$5r{ fr-s{"itu = )"i " i = ;, fuI , R-.Ifr C emft"lfl{: (D "I6iT{, r = l; a"IIn r = l6tFr; r = <-r L = ffis?qd, tenrtd 8lfu6 {sl-{?nfi qrv 6sril ffid( l..-.rd aflrs) o+ "nfr< mbm tUtm<w+ufiokeur"r = f,; os. cFrtrlir frl[TqGR-sEtt = (ii) s-f,c{n{e-s[T< qG qsF cs-q]f,Erfus.lfu = 1ffi = E = r liiq cv<to lR<6r* gsfl-q, W = AA x T; fr?firq AA = m'+rar< 1ffiq sm-qr c+tl-<F$-fl ErE / cqMEFtcs{,frs <I ft'fu-lfu, w = +" (u.t - r) nr. r qr[61, 1,r = TE c+FFcifi ; R = {s c+FR <rFrI{ ; T = 16Er* r ffu'<ar: r = Aafl; CArUrlrl =*fg"l*,*{ = c<I'jitafu, F = qItKE, A = emt<qq6<ffiF dTFGn< {as n clt\rf {qctld ffi'rqI E<tt< w<t'r <lfqkfu c6ffi 61qq v 6qcrf rlbft{ qr-{ Et< B"r< er<tfu IIE lat (viscous force), F = 6rrqv T€r${ ffi r(]fr[r Elsc<r'i ft5 flWE {trs E"lT, qls 6<rf, v - 2"tq'- pr)e . 6{{l'[n, ps = crfFrr< T{g, pr = +<rft< rag ET1$EI-< qlral Tfg\5lrr< {Dl6. E{Fl3t SII, T elsFl Ef'I{lql-Er Cfts|s I R6{, logn = A + i; q{r{, A € B SFF I fltrc-< q;iT. n' = [ \2 !r, 3 ffi1-Eq5qsiffi<qrr{Ect<tq?FFrr{!{ 6$',@. .o,(r'*r) rul r = #' 6r55a 1 = |6fi-q n5qs arEI(; p = \rTrq< q{S, g = qffi \<6f, h = E{ffi{ ql-Kfqq, O = qf{ ffi.f tqritREt qr{ h (+)ve, q<I{fq.t RrE h (-) vel (b) T = ;."". [r << h Er{] 3 tT( q"lts (Y) , vFs;I e"flrF (B) , TCsk ectts (n) q<( 3ipl64.zt q{4.s- (o) q< ft$ {"16 frTs"l: y = 3B(1 - 2r:) = 21171+ o) ; ; = 1+* 4T. p rE

qn{RGla uE rt-g : qsfiEl-o4 a 01. rsr6{t (6< qEr{ ecfe (K) <<i rimlq< (c) vcv IDB'22llAns: al o)C=;KT (d): = 1 oz. { luco< corm for< c+nqt mq6eF cesz [DB'22][Ans: cl Y aeffi66ffiz _l lal (- = -K i;KT (c) L = lY ,^,El ,/ o+x - r.{sJE x 04. 05. 'lTpnffi qfll-(E-< cscE ffiqE "ffi TI? tRB'221 (a) -0.6 (b) -0 1 (c) 0.1 (d) 0.6 {fli{l{: (d); -, a o a', qlTrs{ eqtrs<rrlEt csFF? lctg.B'22llAns: trl IDB'22llAns: bl 0lf-s{ftv{ (oq{qfu{ O) urtt-r (d) MrlT-, lCtg.B'22llAns: bl (b) Tqq< ecrl'.r (d) qtrsq e6tfs (c) 07. rzYI A ,.,F11 ,,,Ell -/ o-x r<tr\2 o'--xt<tre 03. cflc{I (6d qFFk ffiw w cs ft-s{ 4[RTn F<t E{sl6sft<rq? (a)?nfufig--q (c)ErFsqft-st (a) Mr'zT-1 (c) M-1L 1T-1 QGqrlF ftll< x$ qfllv'rsftTffi? (u) tr<-q< q"ltq (c) C(;Wte-l oo. eFF Elrtrd QT( q< s"lFF (9 e FEfr< m{trq foE{ crFrF? [crg.B'22][Ans: a] ,,, "1\ ,,o,'l ,/ I \..-- '-', V @v Frytu .,"1 l, fiEb gw frg* s 1-s'+ r<tre rEtq )5) MCQ: fris<q141rq{ c<f6 q{ e cTt{'{ > fiffi ffi{5q-q w=qlrr "r<-<€t ElF eiad E-g'l Er,€ : 20 m h(, € 1mm2 eqcqcr< creqqRFi? qaF t-Ilcs{ vl6f,{ Errg 20 N <ar smlet {<I {rql r [Y:2 x 1011 Nm-2] os. fiq& <+m ftw rq{E@'< aoAB cFqF-{ fr6i.t s-6n- IBB',22l (a) Qsq q< q"tl-e 61+ffi grc-+m (c) 'EFrtrRI q{'ilE (d)qr-sclssnqfusffi {qI{Ft: (d); "u* qgs6a qftoo ffi = 11 qgo r 6=6 09 . qrF EIr{{ E4Fdr{< Qs( q< eq16 2x 1011 Nm-2 | EI-<E< kf, 15% IR €ce s(q e{e-ft.sifrfts''{r tBB'221 (a) 3x 1011 Nm-2 (b) 6x 1011 Nm-2 (c) 6x 10-11 Nm-' (d) lx 10-11 Nm-z "rTl{ra:gft69g{ont: y=E@ + ft-w = Y x 0.15 = 2 x 1011 x 0.15 = 3 X 1010Nm-2 to. c+tcqt <c< qtfrflifl x €n( fi Q{\9 R€$< 'K nl4f tt. ftg 1fi*t "fifuTEF c{EqTsr{d roz ci{GE F-{CE SE "lRTt"t Elfl E({FI $-:I(s qr<, fi?Ilr{ {frd qEls;r q6lI5 2 x 10e Nm-2? uB'221 (a) 2 x 1010 Nm-2 (b) Z x 10e Nm-, (c) 0.02 x 1010 Nm-z (d) 0.5 x 10-10 Nm-, ,i.Il'rtFt: (c); u = T * p = !l = z'ro'-,'(o r v = Z x IOB Nm-2 = 0.02 x 1010 Nm-z 12. fi efrslrrl {fr mml T€-{ qlsl-r+< qffi qg vno vRce, @6q- (a) x(x-y) (c) - x-y ff<rEz (a)ql$r{ftV{ (c)qlrrs{fuT 13. fr-wqnrffi6$FrF? (a) [Mr1T-2] (c) [MLT-1] IBB'22llAns: dl (b) x + (x-y) (o? IJB'22llAns: bl O)qar{fiT& (Oq1rslfr-{fr IJB'22llAns: al (b) [MLr-,] (d) [M-113T-'z]

ftEd Efr"fcre-{ qtrqtm "r<-<ff tQt ecfd Esd Ets : Z mffi € 1mm2 eyqcs6< CrqEqRfiB qsF tnkg< EIGK alrs 20 N <ar {EFf GrI Ecqt r [Y= 2 x 1011 Nm-2] 14. gk-T<?hdl1frss? ISB,22,cB'2zl (a) 2x 10-am (b) 1.99m (c) 5x 103 m (d) 2 x 10a m ;wI{Fr:(a);v=}=t=*I! = 2xlOrrxtrt0-6 7o" , = 2 x Lo-am 15. E@CE< CE'q{ 2mm2 s €fre"tCFtq]fiIfr "5c{< oue"t 6<z ISB'22, CB'221 17. (a) 1 tlct (b) 2 e"l (c) 3 e6t (d) 4 ecl tFtTtlFI: (a): 1 = I!= 1 4I... lz - F., A, YAAITF'AZ - a .. 1\10_6 - . 2x10-6 "lB-{r{{ q-talE fuE{ 6$,FF SC\9_ "I|6< qI? [Din.B,22][Ans: d] (a) - 0.e (b) 0.1 (c) 0.4 (d) I ft-s{ T{T{ Rfe 6<Gr<< ure ft ffit $L<z lDin.B'221[Ans: a] (a)Q&qt'ro qcfis (b) 'EFrffidqfls (c) olt gu-oro (d) q{s EFEr{frs{{G sI qs,<E ftgfl< ss-s cfF6? IMB,22llAns: bl (a) Nm (b) Nm-' (c) Nm-1 (d) Nm-3 'ilFrrdiT \trfltF< nl;I @FE? [MB'22][Ans: b] 16. 18. 19. 20. ffiqt"rs fu< xc!T?q'(l eqkrt T+l{ sFr-q< c6-s (a) -] < o s 1 (c)1<o<1 (b) -1 < o<1 (d)l<o<2 (b)cr{Et (d)Q&qr"FFol fi'.16-qcfl{E? r"lcttr6t ,,2 \9ts cYcr{"I r") f\t\ gET [DB'191[Ans: bl ctl{l.?I.f ,n, I ) I q;r c?].{l{cr I ,n' l./- V v]-?I 21. 6sir{I (6{sBr[Gt {E< c+tr ofqE&E{z [DB'191[Ans: al (") .r-qBt{ (c) ?sFktrc-t qw{fr6[{ uTI rrel : qrfitE_oct 22. fi&{ "iqt{< qtarEtir {c{r 'it{qR-s w+rfu a"no 23. cT{< Effi 4IE6iF 65ql{ qI EI&-< mro -or{ rotrcr< ql4{r{- (a) o' IRB'l9llAns: dl (b) eo" (c) 90" qc'fst T{ (d) 90" qcE5'l 6<ft 24. fi-cE-{ cot6{r $ftF rlqlfrfu ? lCts.B'l9l {EIE{. (a) dA{ (c){rtfu<El (a) l<9le t"l tri eqr+ IRB'191[Ans: bl o)q{sfl<q (d) cIE n"T 0) ft-s{ (d) Tggl:T aGfIs :{:rt{Fr: (a); fue c+i q'rqr Etr <tft< wltt\5r vlt q< cotc{t qq$ (jtl zs. 1m ftd esEEIGtr LosNm-2 <q ecaM q<?q,{T1h c"FT 0.001m r q<E{ESr e"fl-s $E? [Cts.B,t9l {:n{Fr: (d); t = * = ""9# = 1oB Nm-z [qmGI qs?F CFE',.P=cq {F]-< nl-{ 10s l 26. q&{ qss € qlqk ffiM<q- [Ctg.B,l9][Ans: cl 1iy+mre 1ffi 1i1 1&t+s1ffi (iiO wNftr4lsl \3 )f<"f frru.<mFBc6sr (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii 27 ffid"I6ft{0.06Nm-1qc{Ekr1ffi- 1su,ro1 {fi{l{: (d); dtrr = Iffi ftcur Eft"rr+-< qrrql-rf "rr<ff ffi acr< Ec< me : esF ?sFls irE? <rlq 0.4 mm I qr$ 72 x 10-3Nm-1 1Sn o<f 103kgm-3 ltq< alfusyRiFf qcEI, rrTd F\9- Ei6-stT qlfr Bbr<? {stt{Ft: (c); ,=Y=h=*,4= 0.073469 m <lffi frsqq(Eirffi ts E6-.9]T "ilF E'&<? ISB, l9l {qt{Ft(b); h"1+H=2 . n, = \ = ty r:12 = 0.03673m (a) 10-7Nm-2 (c) 107Nm-2 (a) 60 Nm-1 (c) 0.6 Nm-1 (a) 7.3469 m (c) 0.073469 m (a) 0.00367 m (c) 0.3673 m (b) 10-3Nm-z (d) 108Nm-z (b) 6 Nm-1 (d) 0.06 Nm-1 (b) 0.73469 m (d) 0.00734 m (b) 0.03673 m (d) 3.673 m lsB,r 9l 29. f I I I

qqlzfRcr{ iEotE : qqgA-oq 30. qIEEI ecil-66<r $i<T 6$'FF? SB'19;RB' l7;Ctg.B'17;Ctg.B'17;BB'l7llAns: al (a) ML-1t-1 (c) MF1T 31. qEE;r eql-cs-<q{r{I{fr? IBB'19llAns: al (a) s{(T$EI (c) FT6riir e6lts (b) MLT-I (d) MrlT-' (b) c(Tclsl (<l) i<i-q< eqrt 32 ffi @ r+r qT{ ffig< cqfre< eTF =0.2= [B8',19] 38. dL 'FIT{FI: rc): efT{6d-119;leflE. o = i-DI 2xl o-3x0.25x10-3 +d=5x10-8m -r{cfl"loS(E- ICB'lglJAns: cl (i) FtD € 'llfr{ CFrq 0' < 0 < 90' (ii) qkn € <'I[5-rr 6FCr 0" < 0 < 180' (ii0 FtF € C+r-<tfrrr< c+rq o" < 0 < 90" F6-d rsnBcfrs? (a) i (b) ii v6 = 4iaf 6e1, n = E<tq-< CIUEI,S, p = \9{Fr< T{9, r = qcq<<Icf{q(q@kFT 6E"lG@Fc6-s? ICB'lel c$I{E? ,^,EI/ ffiFlTtu *,ila, tr@ -ru -,EZ ffir{ftu 39. 33. qT{ffi {rrrfFr: r.ll:o =. i:+ + ?q-{f ffix "!T{ ffi ' CESII{flg Qfrqr"restqqc6<qts{, tEt- IBB'r9l [Ans: a] (D oPmrqR {rcat 'lR<\fi E{ 14ewn-+<E tQfusqfr<lfiq ( iii ) firek qEfu< em fig'< +-m frrDTc{FEr6'{? (a) i, ii (b) ii, iii (c) i, iii (d) i, ii, iii r- <-qRFt? <uftom rcq u<6q Ftr&E scr FlEt qr{Ir qa ($ {lQ x E{9 MIF TE Tlci sE? tc{"Iffi T "tf,il{F((nF(.<l IJB'l9llAns: cl Z p tr {:[I{FI: (d}: v" = 3"(P-P') .. ' - e n uto; 40. 6$|(;nEEiKqrR ftWfi,6<+r-<ir*tr<- tCB,tgl (a) {rl{tc(i s'l3r G) ?q'dl< sl< [Ans: cl (c) Efltqlfld s"td lsrq< efl'r6-< qlqt- (a) [Mr1T-'z] (c) [M-11-1T-'z] 1a; erggqrr< vrg&< 'e"i< afl{r+; 1sy; y = I! ='l'#lii' = [Mrr1-21 42. eEPrr{< wt'ltF-it- IDin.B't9l[Ans: dl 19 c+ocQ (iD {Fr -1 qF 0.5 q< Tc{, (iii) {Fr fi ffi Eettqtc{d qdr fr ffi frro-{6ctiFc6-sz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii -:Z1 r rd) l/?I (a) 34. wl{l{: (c); rcr{{ EtF tr "I& EI$r{ r .'. AA = 2{L(L + x) - L2} = Ztx ...W=AAxT=ZLxxT=ZLTx 35. 6Ir{ EEr$ 6sd cqq Et Fr<I q{t Effitr qro (a) W = zLT (c) W = 2LTx EICKq{qvkqr{- 1a1 ffiw,fu fcl 1r(<fte.t (b)w=r (d) w = Lrx UB'l9l[Ans: b] o) T<<c{4 (O tftqF-Dpft$r lcB'l9l (b) [MLr-1] (d) [M-'?r1T-1] 36. n fiuEl e"tlrFRFE {I$({ R $W,fu esB crlFlls]3t <Er v gtBs 6r{ fVrE ft{lftE cf€ <Er F Er{- UB'l9llAns: bl (a) F o( R S<(F (1 (b) F o( R qn(F oC v (c) F <f e<ir x I (d) F o< l q3ip 6q., 37. 2m Ett s 2mm <Il{l(Rfi? ,s$E EtcT< ?6{1 lfr 0.25 mm {6{ s]-iIF< omr( +s g|4 15ar [o = 0.2] (a) 5 x 10-3m (c) 5 x 10-8m (c) lcB'r9l (b) 2.5 x 10-3m (d) 2.5 x 10-sm rElil {R{6? qs,rr ftsi7 "falu-d...

['\ 6rq csB qE< ETrtr< qryffii frv-{-?q.,fr fr-fG GI{ cq"ilffi ErcT' 4.8xl0r' 3.6x 10ro 45 '""\+ *'^2, >I.lTfqq: (d); T = I!!9 ;rh = const. .'. h x 1{s<t( h vs}s.rnn F rrer<{T r Frr< Eft"tc+< strqtm "ra<ff FF effd E-qd qtv : t z ! croosrrl O 0.2 ?ffi@ +:. st<E< B"nqtc+< is(-qr q"[s src? [Din.B'19] (a) 7.2 x loeNm-z (b) 3.6 x 101oNm-, (c) 4.8 x 101oNm-, (d) 1.8 x 1011Nm-2 {:r{tn: (d): v= 9= r'6'rolo1.8 x LOrrNm-? ' lTflE 0-2 ++. omB< eq< ft-w- lDin.B'191 (i) 4.8 x 1010Nm-z-ca cD-6{ 6Ft qr{ Em frrs $(< (ii) 4.2 x 101oNm, qrq EREi q|S Rt& << (iii) 3.6 x 101oNm-2-qi CF({ sT EC{ crlrql frf& !fr< TI frrr< ronB c6'<rz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii {rl<lT: (a); (D {{{q-{ w"i'Ft cft ftVcq Et{ fr(g Tm I (ii) 3.6 x ro10 q< aFt ftVn o"t q{rtft qlit kfG ETr (iii) 3.6 x 1o1o q< s'{ AV"ri qqtft @mw<r*r ffiqrrc ArK lc<r mffi :raqq* sE+ qttr+z [All B,l8llAns: al . s-sn .. "r{ff" ... <.r (ll- (x)- (rrr) - l<rs 6- rdge (EtEc frrr{ 6$FrFcEr? (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii (TIr{I fiffi Wr ?sFt-r +re EftlE "tF< tro 6'y € ?sFrs iffi{ <fi{I( (r) q< Tcti firr< c+rn a{ffic6-oz lAu B,l8l qEIdR'Grd DEI'tg : qqlql-oq 4'7 . esF .e-lCK< q1'CWE< C$-GF{ 1mm2 q<( qrR v< a0 kg r E-frs< qTq fr-5{- (a) 4 x 10-6Nm-2 g) 3.92 x 1o-4Nm 2 (c) 4 x 107Nm-z (d) 3.92 x 108Nm-2 qTt{Fr: (a);qrt{ft\5.'{, P ='C - 4oxeq = 3.92 x 108Nm 2 1x10-6 E<(E 'isqft{ {€-?r w{l' c+nrT cel,fB-s-E c6-sz (6{tt= v, tIfrr\r-l= h) IDB'l7l v r<1 v r<'l tt ,u, l/- ,o, L/ o L---.----- 1GR-r. h oZ.----------., t+{ET, h v r{rl vI<i t_ r \q l./ (d) l\ 04 't*ror, h o L--------------+ "t0nst, h {{t{Fr: (c); E-{r{ ls{ft{ (g {{y{aci E{cs el|trF I EEf'k Efg.f<rl EIS ET I qEtE{ aqtrm fuftg aft 6oFF" IDB,lTllAns: dl (a)o6141<e.fIt (b) iri-e< eqls (c) 'mrrr{dq{qls (d) {({{JEI 50. c$lr{ E<6T Et-< fr&{ sr{{ w1fu-f "l&< kfffi <f{I sq'lqsr<, e li-firfTfls [Rr]'lTllAns: cl 48. 49. (a)Q&q1"F6sT (c)TtEsl @)uQfuqpcq (d) qsTrET o.z cm 1fr o-<t {r-"[ r sz. eSS+tec-"F{c<z st. e$EEIrfi Hr@ o.oz q<( "rt{feg& o.ooz qr{ s< 'ilPrrffi wfllEs\5? (a) 0.00004 (b) 0.000a (c) 0.1 c'flrflT: (c);o=#=0., ftEd Eft1r€d qtintl.$ "r<-<ff ffi er*r< Ec< ntv : 100cm ft( q<( 1 x 10-2cmz er{cqqRF$ qsE Elrffi t{i qT e"fi(F 1.24 x 1011Nm-2 r sr{ dr{ (a) 0.11aJ $) 0.724|' (c) 0.248J (d) 0.2881 {:fi<Ft: 1c;;y7 = 1 ry = ;;1 1.24 x 1011 x 7 x 10-2 x 19 +; (o?"1{ = O.24Bl 53. qI$Tq- lctg.B'171 (D frrTtic= o.ooz (ii) ft-E{ = 2.48 x 108Nm-2 (ti)ft-wx@ frru-drdrBq6o? (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii qqlqlq; 16;;l = 0.002,:: 2.48 x 108Nm-2 IRB'l7l (d) 10 lCtg.B'l7l r'i=Nl )b8 "rffir+*qq*troripru.fi... (I

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N 03. fiFrc;Kq1{FsEcq@qt"lsfu<:rl$ [Ans. d] 04. fr[G-{ 6$I{ ilFtrd 6str{t $Et 6i? (a) QrR. e"fl-O (c) {Pulil ecil-e , - ?Erf qga ' ' msr1{$lE . - <ra6i ffvn ' ii-<!r FIflE (a) 1os Nm-2 (c) 1011 Nm-z (")Y=+ Icln=lA€ (a)q{frsTr{ (c)ftrql{-frc4Fr ., . qlqEi Agl ' ' qlTE4 r{{l19 'rT{ffi ' 'cErlrFrf]v (b) \fliE{ e'fl's (d)llwfl<w{4ls (b) 10-11 Nm-z (d) 10-s Nm-'z (b)B=* (dto=I* 05. Tfl{f{: G); I'Rrfltr< q1{e <sl Etr ?qr6< wt'tl-vl firrd 6$t-{F< ftFqlffisl q{fct+t c<Ff? t.lns. al (a) t91s (b) <F1-< (c) slill (d) Btq 108 Nm-z ftw al.ql't rm ft( qsBEtr{dffi, 1fr c"m ro-3 m I El-<F{ tn\ ecltrF ss? q:rT{Fr: (c): y = iP = -J!a = lgrr y.-z .. 1O-. / | 07. foT< 6rFrtr@"FFE1<wrq6+ qft-c<qz lAns. cl 08. G c?r s<6r fifi +i5(-o &qtr ietrq< csGT'-'t{ 6$t6t- (a) dlII 90' (b) El{ 0' [Ans. d] 11. (c) 90" - q< cE[T <9 (d) 90' - qF 6Em AIE +tu s RBa 4l<CEd Gs1-g -"i{ 6fi6Br qF- [Ans. bl (a) 0" (b) El{ 139' (c) 90" (d) 8" 100 g v[<-<r qsF {g "ttfr< qc{l fvllr gI-{ B"Fl fu'sf<s :r+q o.ss t N Er{ fig rq qr<- [Ans. b] (a) 9.81N (b) 0.981 N (c) 1.962 N (d) 0 q-c"lFflR qterEEr rv-+r< rnqcs ft <r{? [Ans. d] 09. 10. (b) q-{C{Gil<qq (d) \e-1;rs1-;1 €{Fm 31tr{ 13. 12. "flfr{ q6F T{r<Fl<<{-{rS ff <(q? lAns. cl (a)\{]qfr+<q{ (b)ml{lfr{fi (c) frr9Il{-frr"tl{T{-{ (d) {]Er Tffi r+nF< mm smsm €{Fm <at ftqFtFP tAns. bl (a)GtfrTN€ @lk{"m${fi O)qfurq{qt{<{{ (c) frfr€{ "F{t"X{Tfi (d) q:a< 1<{ltd {tr{ Irtut I I cm{Rura oxorg 16. [Ans. bl (a) 7.35 x 10-3 Nm-1 (b) 72 x 10-3 Nm-1 (c) 550 x 10-3 Nm-1 (d) 6.314 x 10-2 Nm-1 .,c-rq \e Ta{ fit{< airffi< -"r,{Fr"t ftaD-{ c.$I-{E qrq s-fi "ltil{, s61 "fq|{ro &sTk< TIZ [Ans. d] (a) 0" (b) 40' (c) 60' (d) 120' "ufi-{ E K qrB l-'qTcE< 6s Ffi {FFl< Fl{6l- (a) ltfr"< T6lt'r 0)ffi<E(El1 tms.al (c) "1fi-< qqg t-"ffcu= !{q< cucr s:r E€{R Tl<nt t a. <rq< rlz-c{ zg'c' EI"N|qT{ {ifr{ \5EE1a sE E[<? e€ E"[h]r+< Ze-R lx qcm ?q6 rr Efcr-< hcf{ fie"t ft-g <it-m( >r stm< qc(+ qre e q{F sk EGM s<rFI l{\5k s )T slcK?qdl E}rl3r(*r \5qqlE se? (a) same (b)2 @: {: rfFI: (d}: t}=Lr4=21,'l =a \ Ll'ti t,,T t Hl' re r <rlclc(< qstr slcr< E"[hlc{< tn eqm y r EIc<< h'6 : e<r om( i e-+ <o tm eqw +o qc<? <oi tu)Y (c) 2Y :r{T{t{: (b); Fffi S"nqlr{d sft-rd irs-q< e.tl-s F< {({1I I r+e mtn6< str qofi <e- [Ans. c] (b) cluEf (o1ffir{ (b) 73.5 dyne/cm [Ans. b] (d) 7.35 N m (d) 8 (d) 4Y O)qlE?rd (d)ql{sl{<E lAns, cl 19. 20. 21. r+. nF-<dBnmffiz 15. (d) 'fifr{ cfg\g-R slircor rz. ronB4Eft{<fl$<q{{? (a) "I&qfu (c)ffiq"rcq (a) 735 dyne/cm (c) 73N m (a)qGo(<E (c),rvrfuT{ TirRFr: (d); EF &a *itd< w5 {[{r qF{ct <Er q ql'rrffi <Err srt {ritc{< qt( {c{I qm'(q <e EE {(cfu({r nfr p a<i b {cfl@r{ ft-E{ s fqG< fi{ E{, Er< erE<Tcvq60qP6{at- lAns. bl (u)p:u (b)pab (")p"i (d)p (,1b 23. snqEi1fr6"rffiEdt{- (u)lfrftr (b)t{c{ (c) Bt'q "tET (d) k{ cm )bb \\\ ifurl<qs,r+E'@{arFot... (I

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qqF[Ru|d aEl rtst : ol{Ifig-oq ! .'t'<o"irt, E1g;AVo =; = s.8B x 107Nm-2 qtfr?n-{r, L = qm ffir$, I = s x o.oolo= 9 x 1o-sm @=i=qx1lo-s=1g-s Trdt\, {{ffd <I{qs sr<F ?-ttrsr ;N I 03. qsB S-'flrsB glrird ?q(r 2 m, ef@m-{ (EFF6I 1mm2 ,q<( qr{ftg{ 4.76 x 107 Nm-z r sRF< cF $rs z kg s? lstrq sfcrir ffir 2 x 10-a m 1fr 'tmr eQ sarq st<Fm q{ qfr Aa-r6? {d{ <rftIfiFB Tglslr qqn, t{( q< efl6, Y = "lr-ff = +g = s.8s x 10r2Nm-2 ' lTfls 4 rads-l 6{Crt T{1Is Crkq \rffi ftrV +r r (tf) Effidt{c-q< r.ttrF fi{T{{r (s) EIrtr 6s{fr09 oiraft vt Efrer$ qtctc< flfies'ffitf{ cst{E q-Ns I I vmoffi, m=2kg L=2m A=1mm2=1x10-5m2 l=2x1O-am .'.Y=1.96x1011 Nm-z .'. sr<F< tsr cr ectls e6{l 1.96 x Nm-2 E srq-fiffi, q{qq, F = Eq(qcq-< crcrEq x qrrqftv{ =(1 x 10-6 x 4.76 x L07) = 4.76 x 70 N=47.6N cI{6{qftT cdft'f 6otti<q, m.;.zr = 47.6=to = -,@ 1.= l1 12x2 ' .'.o=3.45rads-1 .l qrR Tq 47.6N q< qII >n(lE 3.45 rads-1 c6fto c<r"l$Tril+q<rft-gBft"rr+ 4 rads-l 6{crl X 6{kE El< frrs crftq | (Ans.) 04. ,ss6tqftcsirE|r{{ffi,2mqR<ittlmmrror<E<b,Ft0NqdTEGrFtTirllrp6q,{affiIfr'fl'{1lels Etftrdt{t(,{T aotts Y = 2 x 1011 Nm-2 I ('t) Eftqpq-trytmqrft ffi'$r ffiqt"tfi(rv-q r O \offid sckr.t 6ETqslq,,,q{-$qEsnrft€{fu q6{616q{qr{ ilFlF+s-Eqfrrf{.ttfansFrEct€ I 8 I un<<Hi, L = zm;H11fr qrqr t; <rtc, d = <TtrTrt. r = 0.5mm = 0.5 x 10-3 m = 5 x 10-am E{6<EI,F=10N qfi, fu(q< E.fq, Y = * = 2 x 1011 Nm-2 ICtg.B'221 8 Y= Fl _ mgl Al fir2xAl 2x9.8x2 1x1o-6x2x1o-4 t-Es<-l 1 mm 9rlrlI ,FL p<t?n61fr <rat, t = t.273 x lo-a m nx(sxro-+12;2116rr = L.273 x 70-a m

qql{aErfl dEI ctst : qqlg-o{ qcFIqmst, V = nrzl = Tr x (5 x 10-a)2 x 2 = 7-570796 x 70-6 m3 \01-{Ei?T6fi, t = L.273 x 1o-a m q<E< Scf<r"f cT.E Erl_sIq, .W=lrVrVr(i)' =!xL570796x10-6x Zxt0L1 x(rg, )'I = 6.3638 x 10-4 I qk q€s \ffs\9-r{ cfts Ilfu qr4l, , = it H' = ! x z x 1f x (Y:zlY:)'z = 4.0513 x 702 I r=5x10-am('d'ere) {flEW<f,f: w= jx ft-wxqtnqxft-f& 1 __ F I =-xVX;xr. 1 ,, F L L I =-XVX-X-X-X- 2AILL =ixv"i"(i)' =lxvxYx(i)'r<r<tv=ftr 05. ,4sF Auf,{d Ek A {|d q}rc s|{ 9. 23 x 104 N I ct str{d ?,r=di TdFrd rq qrTFt {-<I qc6T ,{< ?c'6 t0% lfr 4F q<( TFt 5% Em 'll{r I q'rd qTF AEIFT \'lil B TEr Eq[qrq"{ (EIqE 10-6 m2 q<(k(i 0.3 m I B sttrir{ 9:F eilrg 10 kg vct-zt <€ 6ic{ {r{t6 4 rads-l cfifts Ffucs {il6n {s?r E{ I IBB,22| ('t) A9l66,ilwffidqflsi:s?fr4{T-dr e ({) A € B Efrd-?r {c{l.6sF{FqR-$E-{ qFtz ffi&oRav"r*rEfr{r{c?tl$il I 8 f Esr-l glrf,{qlft'ffi= L Elffi qlft {,1-q = D nadJffi<-6{, I = L x 1oolo = 0.1 L "rfi qk{6{, d = D x (-5olo) = -0.05D tcrrcqgeH co1.6{1q, EE ffi1-6{ 1t.i1-q-sl 9 -o.os9 .'. l]rrrr{< s{oflE, o = -i = - .fI = 0.5 (Ans.) Bft1r+ a sm cqRfu- "r{M Eati rt allolg ei Effd E-s{ fi€$ qsr a-rr r 06. 6 m hr{I{ q{\ s.6 ,, <if{E(T .s{F iatt(ET q{\ qfi ,q<fi ft{k vtCT{ cF st(s zs xg v* 1tfrm fire vtra-* E E E q{n, w = vx u<I, GF g\9-flq =Elrtrdql!\$r, eF-s q|{Isn rrft6 *Ifu qdR, dlB TE-srq 1e qs-s qFEr* rfts -tG-< w1"nu Vr<-< vr<-sl r na6 q{<.lfilqrq 0.026 m (l\ 0.325 m ,fl\3Tt crtq I EjtrsrEtr+*t{\ q* QqFr 2 x 1011 Nm-2 | ttl Eftto< *rttrs< EIr{{ <1ffi 8.58 y lQ-a 66 {frt 6af6ai,fimr+* s{-{"I\' fi{TF-d I (q) Eft,tm:a srdsrsd rr$' csFF c<Ft QBt"rs? 'tfi&-$slcr RHq.I {-d I uB'221 \, 8 ttns<vtr<<m(Em, d = -8.58 x 1o-a mm Q-,itre< snrrsnryt{, o = 0.6 mm t-"itre< str< ?16, 1= 6m t-nrc< EIr+d?Ffu eFrl<rq, I = 0.026 m _q -a.sax1o-4 "xt{6ffi w{'llE, " = f = - --+- = 0.33 L6 IMffi tob

qqMfrurd !E qE : q{fl{-oq E ftct<El6{<t{( q< scil6qR, Y, = # = qlr fuEr Elrrd fu i e< efls qret, Y, = 2 x 1011 Nm-'z [qetEq-s'gaBrt{tr<, I = H = cq$rtq, v, > v, rvtRt*flvr<ftQ&qrr+r oz. qvF {v{stm r0 kg srf|Elffid{m q<bi{TGe.t € <rl{&r-WdlrtEr r lcB'221 {lY trro<wtte g; AI 7x 1010 Nm-z F'E t 1.5x 1010 Nm-z Cu l3X 1O1o Nm-z (rt) E-6 {1v?rEtFd "r.FrcFr q.fllsTE? F) Eft"rsqgka {s<vrdF+ftrtM? rtlfi&-rfiAloq{s Ft{-rqstqsll€ r 8 I um*ffi, 25x9.8x6 rx(0.6x10-3),x0.325 =4x1oeNm-2 25x9.ax5 nx(o.6x1o-3)2x0.026 = 5 x 101oNm-21 E "rtrF fi's$ cltr vt?Qrs. qqmfr4tc+ lq< {{r EFr {E?r EId A fr(T?sR oa. q+Fql1fiFtrRTdsrin-<br{r z m, qqcqcqr cFFrEr 1 mmz q<(wr qsFFt{TfiAv'cil$fuffiElaah{, 2.25 m, qWqfiT (iEFF?T 0. 90 mm2 r vtr 5E< arcf:Brc' 20 N lEI EGtFf TIIFI rFtFdFC:r 0.2 mm s 0.19 mm Hrlfrtrr lDin.8'221 ('t) crtfifuT{ str*< q& c+-s qtnvr{ qfts.ifu ffi qd r 8 qi{fosfs fl?Frr{< q;teug - cSqrl{flE q"F, Efrtrdqtfr ffir, L = Lo ; qffioffii, Y = zl,o ?tdi flfr<6{, aL=tt -L = 2Lo - Lo = Lo sfc-<<ffi<rfq, p = oo ;{ffi<ltc, o'= ioo sl(<it<,Iprn qR(6, AD = D' -, = iro - D, = -? __l_ -!s qil;I, q]r'{r;r{ s1'fl8, 6 = --l; = 1= g.25 L. ..' 't!Prr{(qt4e Ec-{t 0.25 qlT$qlfr,fu(q<E.tt6, v = * ?q,fi{fr$fi, t=zL-L=L qeFr.y=** ='olt,Yt l m= rokg . ftru{ ".(})_,r_ lg= s.a,*._, y=Lz4.7sx* l.=L- "12 R-E EftT{ <l1c D ,{3r fl{ Bfr cryFs <{I+q<qgr ({) qrtfiFutcffi {cq{t{q fr{trfi{+rqQB-qPr$smftffi "tfuiq6?'tfiGsfrrss.t"I{oa\5Eo qts r

qn{frg|a otr rrg : qq[{-o,t I cne*wrq, qr<-< Hl, t = zm EWqCq-{ ffiE'S-{, A = Lmm2 : 1 x 10-6m2 E{@ <Fr, F = 20N ffiifi, I = 0.2 mm = 0.2 x 1o-3m q<s?Fqlr\rTrq&sqfu, u = ix igr x@ =;";-:=;r;fl*x 02x10-3 - 1000J (Ans.) E qiqfrfiRTn<cscE, laI,F=20N brdI, L, = 2m GGFIEEI,AT=1x10-6m2 ?q'fi $, tr = 0.2 mm = 0.2 x 10-3m .'. &Gsr"rs E"trq, y, = # =;#,,o,!:1fi- = 2 x 1011 Nm-z wfqfrfutra-< wcaf +f{q GtIr{k TrE, Lz = ?.zS m Az = 0.9 mm2 = 0.9 x 10-6m2 {4, F = 20N bT'fi fi, Iz = 0.19 mm = 0.19 x 10-3 m @qrr+ e"rw, y, = X=,,-"::i;;*10- = 2.63 x 1011Nm-2 {g.{T( qrEfrhTft{d cl'tat <'ffu c{"ffr{R FrE @'rsEf yr, i[ y1 q{ cEr{ FFf I qdR, QE-qf,|-fgI 6{rg Crfe I 09. qllE-{T 0.3 m q{I q:R 10-6 m2 q@rq-{ ffirsqFFt} EEmr qrF efrs 10 kg sr{-{ qsF rRIm c<r 1crcrt {ElslrqrvffiiuenqkTdc.{qqv{4.8 x 107 Nm-z r IMB'221 ({) rfliF<swqrqffic*r \e (q) Eft,trr< strlB {{Gx +u c<cut a*rr iFit I q'c'{ ft-s-{ = 4.8 x 107 Nm-2 efq@(q-{ mFE = 10-5 m2 q'{fiffi.qftfiu{= w€ clrqtE?c# + qrrqnq = q}lq 4Vq " qqtwn< ffi'sq = 4.8 x 107 x 10-6 = 48 N ..q<E<qcEfi +s N .'1,E.s sts, \'kE{\5FR<q 48 N rsErEd co-s{ft<-qq{qrqq[,lstI{sFqrqtumEftca<tm r <R, v c<{ g*tc{ uktr ftrg <tr< r TSts<,m=10k9 Effitr?qtf,r=0.3m "fi,+=48+vlnffrr.z.r-, .'. ERE c{hT 1.2ms-1 crcet {<tF fu sr{ r eoB 1p waaTa qss 200 cm ?qf e 1 mm2 gqsqqfrffi EIB &{ Eqklrtr Er; A € B lFnr wdcam fr.D 10 kg itrd \'d lErhFt r{rsl I Trq A vEtR{ Wt 7o/o c r sRF< bR6 Bolo 1fr C"tA r 19 = 9.8 ms-zl I [DB,rgl (0 B EfrEd qrr{rqtasr+< fis-<,tfu +sZ e F) I'm{6Tqcilc'r<sdhn61fr'**o*trr-qrecitr6{{r{irrq-6Efr,r(s-*qrqlrs{rne.selrqftH<.tqqr a frrv$r<?<rHrt t-rt E E 10. IEq qffi+* qsnr&ga.F{FT|...

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E E 15. qril{Fiwd }Eqc 14.,s<iEffqEtGrd€'f{10NTEqrfir'tEtrtrdffirlfrE{O.1mmr<ffi{1fr<6T{dk+reqrQffir{q<( fre.f ri-{k,fu q"{ q$fr src? w{fiTt t in{r tfr wt r (rt) Efr"mr-dsqT\oTr<-{ffiiR{&,"1w+trffi<r<r [BB'r9l ({) EfttTBfrFlv<ffid{R'{66d'fftni.tt1fi&-+qr<frmq"tqdr 8 T-Eslq, w =)rt =)x 10 x 0.1 x 10-3 = 5 x 10-41 (Ans.) y = I!q"n. y, =y.=FrLr-Ful ^ '-'2 Ar . - Arrr o,i-F. =rr ii=Fr'(;) = F1'22=4 x10N=40N ... <ffid 1Ri\r'{ = (40 - 10) N = 30 N qF{q 'fifi-d eqRsrq.e=ffi{ 5 cm &ndr* erBETrrcq{qfr.s q.{qm {vt e"trsvqcEtr q<"rd ,ttF.rs qsF 6qRl-?r otFl?FTa CErv frr* qrstrt'I 'rR{Ief <'Tr4r r "rtr<Gcs et "ttfi-< Etqrrqi {&rs qFfli€ q+t c{Fr6r{, qryfrrT qlsr{ t nRfl"f T-{r{t I tcB,lgl ('t) {lTdEfdBrFE,lt?yqr9ftifiqFt{{qcrFtF-{[1fi{TF-{r e ({) gft,fr+,-d @tint fficr efm 6<Ff "It\Bnt{r{? 'flffG-rfrlH\r"l{{Rlr{rlvhsEt€ I 8 t BER-I qlrqTlffi, "nfi< TStn r = 0.072 Nm ... r = rI = F = Tt' = o.o72x(2x0.05)=7.2x10-3N(Ans.) Qlsc-fft. v" = 4-'e 16 - 6.-.1 ' 9I' EI"iTrql <lVrE sel q <rn <tft t< v'tffiu qllcr: r qdtq, 11 ffif o-<r< v. q< qk<<q I q?FI qT<l ffi, re-{FK 6sct, log4 = 4a! ; fl{t6, A, B qa<ro r qdlq, g;f"FIlEt <lV({ n qn I.FI Elc "[r< I qfi n qR TF RIC C'lFr v6 €T {l{ {lp6{ r qdtq, frfrs ffirq vc c<Fl <r< r Y qfiqu,rtu' zm ?qr(rd € 0.Bmm qq[wq-d ljt{RFta rxr0iNm'l---Z- o1\1o"rl---Z EF E{ en sk 6\3rI Erafir vl3r Efra Fq, " #o ffiH#HhPffi Fq-$frrEeFFF.IF-dtERrE- [Din.B,rg] Q&{'loffTlrrr$rxqrdfq-)q$IcrcdtorfuE.tB-de1frfl.tsszffiFdr e @vn-<-<wv con6qR'{Qeq1"rsqffie-rRr*s.t{q<ipltqdr 8 t-EEr l )r EIc< qs-s qHsr{ cRE1fu, wu = ] " ftq x @ = ()" rx 1013 x 10,) I = 101sJ ,. ){ slr<qfuE mlB.t&, w = Wy x V = Wy x nr2 x L = 101s x 3.L4t6 x(*i4)' r, = 1005312000 1 (Ans. ) rrU<tr<@q"f+e.$S, Yr = =?I'!" p,,-, = 2 x 1011Nm-2 \rvkicrQ&{'rse6f$ y, ErE. w= 1,, vzat' = y^ = 1!II =*##ffi =L3sz6xro1? .r y2 > y,;e{Ie, i{q-{DqR-fqfrEf;r t -' Atz 17. ,ssF Fet(-q 80 gm Et Elcttcat 2 cm ln(l Eqk"t Es q]\ 600 gm sT DtqtFr 8 cm ffir EcF"t In r qtft E_s, ft{q q1 {Fr{qF qro 1 cm ?q6 el{Eit "tdrs.t F-drst r (it) FE1 s-{6E-{c1q**, "'-'Er-rrir-r -r'{L'{ 11 YsrL.rl I [Din'B'191 ({) q'{ftBETEr-Td m@ft{tfrdqfi6s-rB-<fi-m1fin6,ffr{s"t€rR{rtfirE1rrualqqqIErr.no, I E E 16. ('l) ({) E E fui r{f]o

qcFffrgla !E qE : q{Jl{-oq (-Ft N E 18. I e"m<-r, Fr = mrg = (,|*' e.s) = 0.784 Mt, x, = g'92- <rm {qrdrrc zmm € 4mm Rti q< e.tt$ = 2 x 10uNm-2) I ('t) .cqr sRf{,4Fo cBvr{ Qffi fr{-{ <'- t s-€< J [ >tur<E<e+oqssrlRffi = i x ftw,@ = ;, i, i = ;': >. * = 1 2 qFil qIcE, ftE( $<-r = kr {6{,Fr = krxr =t kr = * = # ". kr = 39.2 Nm-1 (Ans. ) qFll3t, F2 = lgn x9.8N = 5.88N;xz = 0.08m.r U, =; = "*l* = 73.5Nm-1(Ans.) elcFr 6srq, fr{(rm t cm ffi em|*c"kt Trq qR6s.lfu, q = i, k1 x x2 = $xzs.zx (o.or)'?)I = 1.e6 x 10-sl ftfts ffirE, ftRrs< tcm ?ndI Erflnc{< I'aE cftqrc-.tfu, wr=)xk2xx2 ={!"rr.sx (0.01)'z}J = 3.675 x 10-31 [R.s. otF eB14r skq q4tr Fa(rsd fr$( &.?rcF-ir {Fr qsFt qll rl !F q.lFw{ ciro lm iqr6-d q{q uqffiffd EF El(ird EFr{fiT T@slrs 0. 05kg s3 lqttrrl crqt I Eliersrd lAll B'l8l 1 F2 I m2p2 -X-=-X-------:t- 2 A'zY 2 (rnd,)'xy o.os2x9.B2 I ? L E 19. E E 20 15 10 5 0 = 0.0608 I (Ans. ) frqq-$trrAvtrrdqfiHI 1m q<tEqoqfis cETE 1mm2 rq'RfrrrF 2m hrr6<eqr{d S{t'itffid ts( - qr €cttq 1.2x1011Nm2r ER EEr ,4$F qretsEs otbt q<( q"RE qks Q&-qfr+r E{@ <cErir cft{ qir Etr{ ?q{ryCr cr{trE Grs qqFfs ccrq r A € B EP stririr qrF firr <v q+tr c<Rnro cirq qqir sRF ftr{ Et 6r{frr{ d\3Tt Cr{t I IDB'171 8 (t A sf<Ed S"ltqlGrd ts(-q< a"tts fi{T ir-{ I $ sld EBd 6sHFr$ 6qrt irtcu' <Fqr{ +-{t B'H}ERRrrqr< frrdTccrt Ttsm rvEs Ete r L s_sdJ ffi?ndt, l = rm, E@Cq< ffi-qir-{, A = 1mm2 = 10-6m2 I dI{F ECE, | = -*- rrn-' ...t*iereons, " = i i = #,#*Nm-2 = z x 1011Nm-2 'rt'qrs, Eel{ \rlr<<r fui e< e"ffs, yo = 2 x 1011Nm-2 Efr"f+ <o, B sl-r{d tfi. q< e"[s , ye = 7.2 x 1011Nm-2 A sIG-?r ?hdI, LA = 1m B sk<mHi, Le = zm A Effi qks QBqfqs r wrcq<, B EEIF qfts c{fi | {qdR A € B \5ktir {{cq[q3r ffits-{ I{tf@6q Ao € AB q6q, * > r .. q+t "rRqH drfl<lf I qn qdl, ;. Fo = Aoyo a Fs = AeYeli " 3= *#rF =+ =+x '?''oll' '1 -3 =:.ss *9 " " - LB rB ABYB La Fa AB l.2x10" =F = 3.3s xF I Fe AB Aa As - A EII<T ft_E{ = 3.33 x B sfGR ftV{ C{q qsE?Ffi s{t<r"l A \9-fcr FFI{E4C'I, iott eF 6<FrT{ Tqsfto "n<r<r {.c-dtq, bl{F strq A sEr € <}qk +,lcq s Ek {r<qtd q-$ EGs r {6T F(N I rElq a.)8 \\ 'tffi-{dqEr$Rw+trst.. e

qET{frsr{ uEI ,rg : q<fi{-oq tr E 29. Q& sl{ erEl{k6l{ ErrtF 1 0 0 cm Ert € 4mm2 efqrqrq-< ,qrE strtrd frE EIrs sl{ 1frar o< tn6 "tGr<61 s "rl"{ rffiq< "tt5 fiq q<r sr* <nnft frft6a aaa 6a q-6 qAsrr A<r {R<6{ 1e "tti ifu4 <*6q-m 5o7n s 60lo 'fi€$ c{cq r qBt Qr{ frft lErE, q[s {rrd {r | @I{rd B"tE q(drq yq qr{rq I [\'fr{{ tR-qR e"ftKi y= 2x 1011Nm-2] ('t) Eftflrs <fls st<F*?q(r romm Ifr rr{r\9= ss sR Epfl.g qrfl (q) freld Efu-d {cfi,{fur ffi&+sfrq {ffi si r ailt ch€ll qlcq, qrs{?h6, L = loocm = 1m efq(Qfq-< 6S-<Tal, A = 4mmz = 4 x 10-5m2 ts(,{< eqls, Y = 2 x 1011Nm-2 EI.<< ?6,fi fi, I = 10 mm = 10 x 10-3m;EIItr{'tv{, m =? srq-+ qrfi , T = y i = rn = I41 - 2x1o11x41lo--ix1ox 10{ kg = 816.33kg ff ,o]=*vo=fi=to.oo h,fi'@,T=sy"=*=o.os -4 ...1rprdjrq{4\o-, " = -} = 19T = +r.z - 0.05 69, vtr<tffi, -1 <o<o.s 1wr, Q&< G"ru r(,{R Vq qkq i Rfr< Efu <$d r 21 2mm € 4mm <rlrrK rg q&{ffi< 1fisf< qoB1pq<qr+<slqlc1tqErEl-dSficuv&q eq-{ e6f"f T-dld Trqmrqqq{r_rfr sq$R ?n='fi $< co g6m<t qrql r ffi{'sKF{'RpTtriir qflE 0. 4 r I crs.B. r 7 | t"D laGl*sktr<Hl 5ol0 1fts-dtccq<Tm(FETg1.q"ffr{firfuFdr s rty ffits-<Er<qE<*<r'conBc<Frnruvrp{O-+frrawmmqn 8 t_s-s<J ch€{I !flra, ftqTErr<-<'ilFrtrK q{ej'l-, o = 0.4 ?hrfr ffi, ll = sv" = 0.0s ; 'rH ffi, 19 =z Ad 91T<IEIB, " = -t =f = -+= 0.4 x 0.0s = -,0.02= -2o/o ,.4tqt42vogFr"n6<L I cqs$ qrq, ){ Ell-fr {irn(, r, = ?-- = 1mm; lT El6fi Vlril(, rr]mm = Vn11 "\ =) {r{$fr, q<c.R<?q{l = L,lqIrdI sd = m,a<(slrffiffir1fr.<qt+ml, e r, l, s l, .'. 1, =1t, ="=1 l-1 <R, sma:r< tri e< a6lls {[email protected]{ y1 € y2 = # " 2 = (f)',. f = e), . : =J = v, = ly, " rr sr<F c<ft ffiqrr+ r IRB',t Tl \9 8 lsB'l7l tr E II )1 i'-J I .yr c$E Etrr r oLe s{ 1El6{R {',rq@ B"ficFr Y-qT CFI qrmtuc 7 x 101oNm-2 6rSt 11. 5 x 101oNm-2 E.Frt 13 x 1010Nm_2 t91s 20 x 1010Nm_2 ('f) (s) Efr 'rc<;-a str<-* "m-c-ffd q.fltrs{ ff{ fr{T sr I slGtlr <,t{ D = 4.22 x 10-2mm c[E sft{rs( vq] qcs qfr FtHt ${frq lsFw RNs I I "t5lrd{ tskz 'tlffe{ ffi? 8 m: l0Kg -$til

qHdfrg|d DErrfE : o[<]T{t_o< E E 7 4( (tl) ,s< q{fr1 q( <?'tfi@,i= r (1 sc-',] $Fr, D = 4.22 x 7O-2 mm;qFrf(, r =2.77x 10-2 mm = 2.11 x 10-5 m s<,m=10kg 1x... e{rq = y<ce, # = v x i + y = H = ;#*t+ Nm-2 = 7 x 1010 Nm-2 23. Lm2 66-q''q-{RFl?e!\8mm1+rg<f+<cafi< frco<"16 IT qisrr*qEfrrrBqrr<"lrt<qErlloI<trd <i<6qffiFfisErfBrq<<r<6q rfit+ I x 101oNm-2 1 IBB'l7l ('t) Eft"l(sBBRsced-<<is6-{@0.3qr{ssrsTqr{H$<rsqr{? e $ csrr 8. sNsm-z rflEEfir {q[rlit EiIcffi 2mm Xe sr{<' B"R qt FI Frd 500ms-1 c<ct qlbQq +-*re {:rFt<{ {r{FlTtrc\9-cr{ft? nsEsEt\3 I 8 r^-:-------\ L s-s<_J A*< m+n, A = 1mz; <<6@,e = 0.3; <r+6 eq|s, n = 8 x 1010 Nm-2 ... EI$ri{E€, F = nAo = (8 x 1010 x 1 x 0.3)N = 2.4 x 1010N E{FK {fg9, }fq,J, n = 8.5 Nsm-2 (Tc"K dfu. gI - soo ms | - soo ms--' = 2.5 x l.os s-l dx 2 mm 2/LO' )m 5$< m+o, A = 1m2 ... EmM+{<EI F qc{, p = nAa,t = (8.5 x 1 x 2.5 x 10s)N = 2.125 x 106N W<t\ Es&slq eLTTqft'{ <EI }FIl{ qtl I tr E ("t) (s) 8 ( EEKI tg( q< s"tls, Y = 1011 Nm-z rbl I nvn<<h,fiFqf'1i = z.s x 1o-4; fte-ffi< ... B EI616 qs-s qmv6 cftE 1&, E=1xyx O' =)"1011 x (2.5 x L0-a)21 = 3125y \ 24. qrEz50Neqn-<stfr{vqqsr<l-?rxy{{Ftmf<lFvm,tsBqrfiq{gfrsvr4lqf[ltqrrerTttrrq fiqlfil Erscq (qftrffi q-{ql) r s&F sl[lil €f@Iq-i 2.5 x 10-4,4 qr{<r 0.8m FErdrd, <|ff 1.2m fbr6K I fBre-dtR q<e.tt$ = 2 x 1o11Pa PErryatsi-qq tql(s = 1 x 1011 Pa 0.8 m l.2 m x B Elrfir q+?Fqf{sr{qfts.tfufi{TF-d I <16fi r{ttrrt slg Fft fi[ Cr{, srEa Ti I csEFFr 2.5 x 10-7m2,8 Et(<-{ hT6 frt&' IJB'l7l \)s ", qffi"{dqvrmBEl7"rqE{t... l-r;. ::

qqHfru|a )EI era : 0[16l{-0rl E s.i.o RF m tr( q< qcfsfrFi] sr< frfrrq cr{@ c<rt s'td Eel' tr( q< a"tte (v"o) c* +-<t <c< r <fr, L. s r,, Hrr< EQE sn cqq qrcq lloi{ sWwE< mElrrq = A (<i €[e p <q frr{ letF@c{ t, e t, efqtRs qs r FP $I{CaI,Yr =rr-=11 =}ev, =*-lr=* h6"^ q<lY""={=r=Ji ' L t"q^ (r1;I. l=1,+1. = FL = "+FLr= L =Lr+L, ' Y"qA YrA YzA Yeq Yr Yz ffis{t qICE, Etclst dtB?Rdi, I = 2m; Fiv-ffii \T(.1, Lr = 0.8m; ffifl< 9(rt, L2 = l./rn Pf,,c-r+< tgr e< s"ttq, yr = 1011pa; ftrc-{ tT( q< E.f6,yz = 2x t0\1pa "9q1Q<qq< €qr$,v* = Lft + fi) 1 = 7.43x 1011 Nm-2 c{rQ, <N 'ltrl<r{({6\rIr{dts\ qi Eqr6 <Ft, orca e<Q&wrsEr cFf €<(T:rfr[qr< r A € B EE E-{dT ,fEI{ {tg6s qag {etl4r{ 1000 kgm-3 E 800 kgm-3 r eFtor a € B B\r-T U{IEI q[g ftR C5'{t CrtsI VkElt qrSrl't {{t|-E;aq 236x!O2 ms-l s 4x10zms-1 16bn zz x 1o-3 Nm-1 (R g = 9. g ,.-2, (fl Efta-qrs s16* Bltcqlt crs eT@ <cr q< :rFr R{R € r $ Eft"nrr-d 6{rqf E{.rF 6ftqE? ffiG-+ frr*sr"fd ct{lrq Etsrf{ enF: 25. sraq q'qfr"+vir< E"tr* Elnnt sq r {r< 4mm <lFIk(< € 7. 8 x 103 kgm-3 {{q< er;G 6{fql{ c"tFr{rs a [A v-drqlT IcB'17] 8 E 26. $bn zz x 1o-3Nm-1 | (,! Eftaq-q rv 6o51uvtrrffi +r r (q) Efr"trqd 6ffi {fi-< sr"Nqm 6{rint qBrqdr<< fr-d-ffi&-{vtnfrr$s.t F.{ r [Din.B'17] 8 I .g-tr<<?nfi, l=0.1m a u<rn-< 16Ef+, r = 72 x 10-3 Nm-1 .1 el$BFrqFs€, F =T x2l = (7ZxLO-3 x2x0.1)N =0.0144N A E{rffi T{Y, pn = 1000 kgm-3 B sTFFt S{9, pB = 800 kgm-3 <r+< q{9, ps = 7.8 x 103kgp-: {ffid<1l-ffi r = 4mm = 4 x 10-3m A Uf6{ gfgGFI, vA = 2.36 x 102 ms-1 € B E{FI qlg(-{ l, vs = 4 x 102 ms-1 {r{ $R, A € B s{F]-< {r€\5I Qcf$ {qll@C{ Ia ie Is I ...6^ = 2.'(p,-po)g = 2 x(4x 10-3 ), g:Bl:1_q3_-1000)xe.8 Nsm_2 = 1.004x 10_3Nsm_2 '^ 9vn 9x ... r.,, = a1&:eeE = 2x(4x 10-3)i!1gll03-800)xe.8 Nsm-2 = 6.098 x 10-4 Nsm-2 c{q A s-{Flir fiEst a"i'$ cFt, or{g A ufiE 6Ft ffU, I q€qtsfil-dr..tB 'ltR-< ffit qsfteEclqFF<V ffit{,ifro5oqer s&F 6FFfdn1q s x 10-7m r ffi< EiFr q[s 0.1m h'0(Fr rE

qqF[Fiu|a oEI rt3tr : q<rrT_oq efBffi<+nf(,. = t"';o - = 2.5 x 1o-7m qr{ $R, W mbR <ilfi ( = & <v csftk qI{s-{ = 10 tr aF mtrt< wqq +1nR3 = 10 x1nr3 + R3 = 1013 e l = ffir = 5.386 x 10-7m 33 .'. <15 C+tl< <I1rI, D = 2R = L.0772 x l0-6m cqtB c+Fm <n m(, . = 2.5 x 1o-7m TVGTR<lFI( R = 5.386 x 1o-7m .. 10trAEc+ftTi 'I&'E[s<(EFIE, A1 -- L0x41r.r2 = 10 x4nx (2.5x 10-7)2 m2 = 7.854x L0-r2m2 f EWmtf<$-sfq<6EFFEI, Az = 4nR2 =4Trx(5.386x 70-7)2 = 3.65x10-12m2 .1 qq afr.{lT lfsffid 6E's-{ T'c{cq r {qft 1fu fruf" Er< r 'fifu "I6tT{, T = 72 x 10-3 Nm-1 .. fi'IroIfu,w = TAA = 7 ?. x L0-3 (7.854 x 10-12 - 3.65 x 7o-12)l = 3.03 x 10-13J c{lQ .l&E{o <{, frrEF{s RtR ef'NlEf alb Rtr{q"i{tElqc'fsl${ qr{ I a cQ: c{6ffi ergf't e EEe-dqsEI{Es eft e {$tBg-{ + 01. {qdRqrtqnr<APi1cEFeg6@e-sq6{\ster qsErs c+rqtfrre<\w{,FFsr<ftq?sqr E{HErrl CfrF {trq 4969 "" s6q qfte, q{{ qTF 'fl@T RfiD frBt EtFt-?r ces-d 6m m'st Er{t e{-{ sfiaFr €"R eTS fi"i th C"nq 4.9 x 10sNm-2 qR qhE{ (|{ CafcT 3999 cc ErEtr tc{'rdfiT s sr<Prq Frffi qtas-{ Q&qrr+ wttr+ron 1.96 x 10eNm-2 € 1.62 x 10eNm-21 ('t) <Frqevrrffi qFlvrfrT&ffi r-* r (s) cs Efitrd s"rd {ftsqT-dtqrd cqF [ *m*ase=ffi='o.*#"= ! *"***, - =i=+= 4.e x 10s *T = r.so, 10e Nm-z {I c$rilFr{d qiN-{ Q&-q"ro e"ttro< wtr r .'. s+qfr cor<tfrq r 02. IiF qT|{ iq({rr Ek A € B qtr $l{ $tEFrT 1x 10-3m q<( 4 x 10-3m tEE{\diGF TqFI{{Skt bHCE A q<HrIft s- qFtn6Ifraur<etRrYr = 2x1011Nm-2 r (rt) A qGir ?q{, 1 0olo 1fr(g qr{lqfu fr Vr-+q qR fi 4r <r< r (rr) A € B q'r{T{rl(rc+nFq['irlTs FFtQe'{'ls ,tlReaRffi.tiFGrrEFrr<rGrtr (-E* -l I = 0.11 ; y = # = ft-w = v x @ = v, i = v, f = (2,. 1st. x 0.1) Nm-z = 2 x 1010 Nm-2 {k Q&qf,lo E"Irs mft, vt< Qfrqt"lo-"-l c<ft r e c< QGqrr+ ectFr = 2 x 1011Nm-2 B q< YB = F.F = -,--l+.- L'r Fr Lr 4x(rx1o-3)'z aB rB *{^'J) :"='i fr ?ffi=Yexo25 /r xro-3\' tyi-l\./ .'. B q< Qfrq1'rc\i1 A qcatsts'{ l E E I ?E:q? rtfifu$frzH{"tEl\e csrrtfr{{lqrft{ I 8 f-E"r l 2.5 x 10-4 I 8 E E rEm \5t