P-1.4 নিউটনিয়ান বলবিদ্যা

q$Fil og frO6franil"rRrn cgaMfrsrra oxrg I qt qfi-cr-{ fr'ro <q<qqrq< c<tV Er:r< foesq: qw]T sws (Moment of Inertia): 6sfr{t !r ftl cslrfi qrs-d Ekqlr{ 36m e&F r"tr< w € \Ts clrf qrE< dcurFd E? E{cV< 3d1 qcps5ag qqBrs Q q6lr-g ft"irs .h ftiir qvq{ sErrF <r6t r ugsm erro e+E asr'{k TlFt r estr Fr66{ ,a<rtfirs object afr{rrq qg.-\e-R sFl-f 6qFt ?{{ | wr<'t esB F?< <Ift r qt en 6ql't <I ftmt'f e?-< frsm qs r ffi-+ s<r-<r"r< }tc<sqft{q" C$,6EI, m1d' * m2i' : mri, +mri2 I q{r{ 6{crldE,rr$ i s i vrr<-*rmr qRF$, x-qrF € y-qs TnFr< 'jalF 'llFF.et< s<r<ruf< cC<TfftEEk {E ErnFt sirF Ec< I x-qfEFiI E{I, m1u1x + m2u2x = m1v1x + mzv2x y-qfS-d gi{I, mrury * m2ur, = m1v1y + m2v2y o erF rs r"rl ffir agt q&rr Drq, e-{{ cqb iffi = L<FIT "tffi + cdft+,tfr.tRn r ftg q ffir +r< Tlqr{ qffr{ fiE {fr{frr = kFfs'tffi' r o qcq.-{ sl{<r = cqrsrr{l eFE {r{< qE x TEEr{-< ftXIr<rf< {{,-<ff 4t Edg r o 1r = o e< q-$ &IE Tq q$A fraru fr{tftq Erq qm-n mrotr+ esE{ qlt s"r< lt< cqr"rrrr< q,rFr <r elir omcetBqc\g-qr{r rfiF{t, (p - e < R < p + e)r o tan 0 = a, "*, e cr{f {tmrrd ficq EEt m{r< qry<ff 6{rlct I 6ir{g Equation € (FFt m a( 6Ft6{I term 6Q sttqfrs-<1.e<tFtr o "r(T(: q& qq {:rG< u-{I Tss crrc+t <e fufi sr< T€? ot&-d e5tq e {rt"m qffi <.-<tro cisro <I q({d q6E r o lrqdt e-sk- tilQB-qr"mc$( (ii)qeGqnsq$d O Q&'EI"r-s {(${:m wr(< lr< @ T{i< v1rqk 6{'t s1ffis e[r<r qftq <-sq6< cflb dffi cr<ftg a[56 of ccq{rs t{ Qfrlq1"rs cqT( <r{ r o o o o IN] ffiF6 cQ M C a CQ M C a CQ M C a CQ M C a CQ M c a o rl rf s a rl rl E + iI rl \ F { rt s F { rl s DI{-T 3 2 I I 3 2 I I I 5 2 1 3 2 2 2 I 2 ) ffflrtl I 1 8 I I 5 2 q<rq a{g I 1 4 Dtqln I 2 I 5 2 3 2 2 4 I I 6 1 3 14(d6 2 I 4 1 I 7 3 1 I 2 <k"ttq I I 1 4 2 I I 3 2 2 3 I I I 2 {fiK 1 I I 5 2 2 2 6 2 I 3 I I 4 Tfrdl 1 2 ) I 2 3 3 2 2 5 2 I 3 I 4 f6;nq$ 2 1 1 7 l 2 2 2 6 2 2 2 2 3 I I 2 qaffiiq 2 I ,| I 2 2 2 6 fr.u.-{o\oqlrqcT6"fAstffi 7- rs qrg{ Er$ flhtE(g '3IsT s{IoE E{r

qn{F'crfl oEI rrJI : slEIt{-o8 O qRFqf"ls' q(q(: G ,Rrl6ft "frd @ <u "rd-tr<< wtc+ {s cc$ qrB Ts{rq 6qF atfrs ffi, a cc{r{< "R {€ EE< vtr"tfu c<"t 5 q$ q<( T€qrer{ {rsrft "K {gd mF utffi cc<fu E{ {|, str{, cQ&qplF q(q( <rE r O qRFrs@'lslr(rrd:cstiErcd<'ta<-e1frae+<cr"Er*t(calrsfrR{<c*<l*,ft-EwrvrftqT<gEE< \Tl.6qfu 6<'t q(qrft qt6iq q[6qfur 6{cii (Ers r{ q{, sTr<F q(FFF @qrro {|( <ro r O qi''{I&"s q(q(: q$lEtft{ <g EEr qlr"ifr-r nfu<'t qi{r& qtrt 's "Ir< cst TdErsr[ rcrR< Er{ ,h tqtsro q<5qtfu{q(qd<r{r O ffi;I I skg sr+* q{E {g 2ms-1 6{tr't x q.F TjrFK qrrr 3kg E-rfi clm+F Rd rero {iFf {tr;t I rrlqrd er* skg sGrd T€F x \qrFd ,ttBt 30' 6Ftc.t 1ms-1 6[?t Eq[s {tGF',l 3kg T€E{ 6{C'f{ fi{ e ft-+ ro qcq? 5o1n. g(r{[tR qi<sEt IE q$tft , x-\5rF T<r{< E9rf$ frCT, ln4ua cos 0o * 0 = meve cos 30o * msvs cos q m,ur-m.vr cos30o ., Vb COS (O mB - sx2-sx1xcos30o = 1.gg996ms-1 ......... (i) 3 yqs<irFrdBql$ifrr{, mA mAuA sin 0o + 0 = meve sin 30o * (-msvs sin g) . mrv^ sin 30. Srr.] + vBsing =;= 0.8333 '.......'(ii) .'. (ii)+(i): tarup = 9.441+ q =23.79" .'. (ii)'z+ (i)'zF'r{'{tt, .. vB cos2 rp t vB sin, <p = (0.833)2 + (1.88995)2 = vfl(cosz rp + sin2 q) = 4.200 ; vs = 2.066ms-1[cos2 q * sin2 <p = 1] 2.066ms-1 6{ctt, x-q(ffi qtrat 23.8" mtrct frrE< fr'r{r r (Ans. ) O Special Tips: qF{ qsE sffi Shortcut Method yER I MCe F TfE irlrq ft6{ r vl-<t written qftFk Answer checking €i ffi@ qq Method bl rFt tretptrt. Vector and Complex Numbers (T Gl.f ftR properties same. Momentum q<t (-<6{it vector t 4Tbt 2D plane ( ft$ vector aIFFFl EIfqTfS complex numbers <Ifo-T RItl R(-lttt <'GI resultant complex number gcll resultant vector B{ {Ft s fi-$ 6{< Fdt rIFt l 9k complex numbers q< q?FBI calculation calculator qi complex mode -€t ${tfiatr qTE $R{ <fr, vector 4i {FI s fi-E (modulus & argument) qfIS qRF complex number q< € polar form (< (FfE r, z 0 (modulus, argument) \qI(E | \5fEf caEIFI sGI Cq!I{, vector € complex numUers Esat JIFtIgfrs {q w1vtfrmt"t<rr anyways, E'lf*< Maa Ef <r<rQ ffi clear (6{- 2D plane 4 linear momentum conservation S{{Ift, mada + mgis = maia + msis .........(i) qrF qrqTrs complex number <FII6{lit flFrt, 'x' € 'y' axis set Ge) @ 0. + e sGI qI€ r 'x'*1, q146"6q ffi {{r{ argument Rrr< r-<f-st r Now, (i) mada vector F{ polar complex number form RC{' I + r Angle sign (ii)mBiB=0x3=0 (iii) m6i6 = (5 x 1)z.300 (iv) msis = 3 x (vBzO) Look at the figure: Y qr{ s-d, A FrFlFK tltfi< I A fi-rn B eFrs ttt+ +-<r qrqr r c$r(< eBr A s B x qrqr{ {ttal :l?Fq'(:t 30" s 9 6{lct Bq"fX e<r+ r qEfCq-?nS c(sr({ "lir B aF{ r{('F EIr s rp (olqB frfu <td(\9- qr< I IE]

qqr{frqd DE['ta : q{IIT-o8 .1 (i)a( ct ffi{firnSl + 1020"+ 0 = 52.30'+ 3vszg + !g::!y = yr26 Calculator t{ complex mode ( :Il€ g DEG angle mode seti:ctT I frr+, '(rozo" - 5230") +3- , ' = 'press s6[t, qsF{ q$E Resultqfqr<+4:s'€-Ii 66 eFtl 'i' {?GE complex number, (F @ qffirq-{ itt&lv complex number {[{ modulus € argument fr6g {6v, vector frQ qfq;66g answer. 'OPTN' : "shift + CMPLX" Press {-Gt options q rINg, ..r20,' option bl select<'Ft I Bg<: rzo EIq(dI ffirlr< Answer €r{CQ = 2.9655L - 21 .8" r0 (r[tr{, r = 2.0655 q[q qEfrq-{ vs 9{ fi{ q<( -23.8" q{n x qrm Rcu-< ftr+ Zg.B" @ va ,sT fr'{r, fiit qfffit { qtcri ffid F-crQarlT I Shortcut q< process bt 1+tr+< W e+[ Lengthy F-zFIFr r qt hanAy EIT eifq q< OGtr shorter process qk 6{t r MCQ N qBl <lffi frC< t glil vector (l (Set c.IrSf6tt Math, Static Elechicity-F (t Process Apply $-:IF ellit(-{ r a fiEEr+<{&{a: 01. BIC{et p = mv 92. p=g!=1(-r) dt dt' =-, 3 <cE<qlE: O:. <FEr slg, i = FAt = Ap = E-{rirgri< 1k<\t{ O v{6q61<t {(<s{-ftEut € c(q(: 04. s{r{c'l3r cGa.cl {3: qF:rtfrs: m1u1 +m2u2 =m1v1 +mzv2 ffi-+: (i) mrul* * m2u2, = m1v1x + m2v2x (ii) mru1, * m2u2y = m1v1y + m2vzy 05. st{Fr <I (TrSi CsGt, MV = -mv 3 w(1te-+r<: c Q&qf"ro q(fi:ulffi e q{r<uttE-{E qi1fts elgqr I es{ffrsQ&g"mcrsr(, u1 +v1 =vz +u2 3 ur - uz = yz - yt ("speed of separation = speed of approach,') mr -m7 2m, 2rlj, vl =+ ur +-u, : v, = ---::::r_ u, +_'_" ___. u" - m1+m2 _ m1+m2 - - m1+m2 . m1+m2 . 3 qQGqf"FF {(q(:Qt s{r{tt {$fts afrs I 3 Troi 06. nro6< E(T{t (lS1, F. = y, d* dt 07. E-"lrrr 4ffi <co&< eq< E{q sk <Er = Fr - ms = v" * - mc. 08. t c{{ 'tGI <r<EFn 6{rt, v = vo + v.tn} - st, m=m0-#t vo = Tr{rF{qfrr<'t, v. = fi;{e 616ry6fiT{t c<"t (i(<rF{{rqrs), r = qfr<tRsJIT$, mo = r{lElfrrrqs-n, m = t q:IS eliEa I IE

qqt{frG|d 5E,EI : q<JI{_o8 10. 11. (dfrs'r&<6srE. 09. qvsEr SFri', 1 = lmrz = MK'z; K =E@{&< TFTI( q? ,lr=1"*1, qqrgaFl qs Bq{hT, I=lcor,a*Mh2; u.o" = v{5qrgffi qrEI qrc4rswErd qFFF, M = rr{K w, tr = v<rfgrfift qs cI(-$ wrgiIFT ws< {iV] 12. {frnfu, K. E = 1ro2 13. (a) dftsu{r<f, i= ix F = ix mi = m(ixD O) c68-<t s{r<{, 1= lo = mw 14. dftit s-{c<r'E cK{Ftt {E: I1r.,:1 = I2ro2 (I, mv1r1 = mv2r2 f{lfusi6 4{sqIs6ql 15. 6rgT+ T{, F. = I{ = *rz. l 6. <tsk {rf (R. 6sf"t { qlrdtQ-d qfu 6rrq, t, n e = * ; tan 0 = f, dr-+< wo r 17. (a)i6,t=ixi (b)t = Frsin0 18. t6,t= Ia 19. S'jlEI, P = ro O e&teotto, rr" = }, rrr = } tQ<.nort u, ada< ; {Fft{arrert p1n6<;<r} ffi,1 ffi+: (i) eR qt{5[< ---+ (ii) Eqn <FrtFr --+ (iii) ms pfrn Eeiir E{ --+ (iv) R vrqir E K E? --+(v) {Fr <frc{ Ans 6< <8Tr{I fE"."-otlqav-q (o = o) -i- ti-f f .-{ f--+p -f--r -f*=rn3; ft= IdsFot-loR!i]!i{ Fcoso - f" = ma Fsin0.+R= mg IN] *i,tlfiftsr{ firSffFT\5t{ I{"ltC{Fr{ fficrttars Ilmq-E qENr{tit'llv (,-t ll-- I=MRz t = lypz 2 r = ?ypz 3 I = ?vpz 5 I :1v12 12 I=1t',I(az+b2) qsF =1.* glr '\ lfur€esrmRS""ttra,r. fi

I I t' I lo i-mr Io o o qqMfrsnoxrrg l- cur.-orT rcsra (" = o) F-f.-mgsin0=ma R = mgcos0 f c"r*04;-1 qs-sra 1tr ftq.,$$ Fcoscr-f.-mgsin0=ma R+Fsino=mgcoso mg mgcosu Fr+t q y<q: o f grc.t E<ftfift Fr+rt< +c<l +rfu-< sffiq F"t, s' = e + r [Y<q ft qfts*t <q ffir {lrq rs qtqfus g<"tft{mg e f c{t't s{ rl o rgm"t ffi frrd< xr{, +fdq-< qB'<'{'s Y{.f, g' = g-f F{qrT qdtq g ir f €4Q ftrs ffie sffi q({k y<q frftr c EF rfrr{Ft q{ rl :r61fr11-<d.lEr: .gJ,f J (Frstm) -frcm"t . g.l,f 1 (FrqtE(eltft)-, c{t't {QGqrr+arar(< mq: 11 <g Etrd s< c:nq qdle, m1 = m2 ErE vo1 = vz ({( vo, = v, qs I qdF, qi{r(< "r< <e 1F c<"t Rfia-* +r< I 1i1<gEFd w c{l+ (m, = mz) e<i eFF frfr{{sB uifrfu (vr, = 0) qcE v, = 0 q<( vz = vo1 I q{rq, crqr{< 'K )T {{t cctr{ {ts q<( q{ Tg x fttir 6rt frm Frrc- qr6s r (iii)T€{Rdvdqfil{(m1 + mz) e<(sFcaqrr€Fn&fu 1uo, = 0)Erqvr = ffi"o, (i( v, = .-?gr. vn_ qcttq , ciSIN-< 4.54 >r <gfrrO "tftfu n-<f S1.g {t I - m1+m2 -r (iv) >q{€EqbTs glft (m, >> mz) e<( EFF q{T€F {&fu 1uo, : 0) <ce 6Y[qT u1 = v6, €i\ v6, = 2ve, q{ts, x$(ud "td stfr <str{ 6'i ar qflR<Fs qllrs ft-q Er$l {€E stft <g< qtlfro.t cru| E6 qT r (v) &qT <gE \n-sis vtft 1m, >> mr) €(( ssF 1ftfu (uo, = 0) Ecq v, = -vs, ((( vz = 0 6flt {l{tr t (m, - mz = -m2) q<( (m1 + m2 - m2) {64, {$ftEd qir stft <sE Rd on+m q<s, Er$ {€E Ek EPlfi-<t c<rtfrlasfrr6EFqu< r qQ@I"ro{<s,(: 'i&}iG<Tr- (f,n,vfi,+)^rul,)- (it-, +mr)vr) = tfn'rffi-"ir<<"tG{fu \\\ qffi;mqgrrqtrffi"tqDEL.. e

a 01. 04. 03. 6Ir{I s6tR <llfi( FA-{ i?<Flf s{I< t F,rdfts E-<lT't i,E{9. Tq Fq<( ffi-q F6 tEr{ i \e isalTqm 6ru< coF&{ wFr? [D8,22; Din.B, 221 (a)ixF,ixF (b)ixF,ixF lAns: al (c)Fxi,FxP (d)ixp,Fxi qsQ Ed € <lFiI(RFiE qsF asmR ut+fu .{<( qsE fr( (< co-r frc-s q&arr-Im at++otft qrm Tl-C"tr5F ES'lfrT <lFflr(< q{"F* JDR'22I (a)V2,1 O)l:1 (c)7tnQ, @)\E,,lZ ad1ffi ; (3) ; re'i&< {rmftft qfl,]g _Ka,.._ Krine R =l_=t,,li y', frit-EfrfrTl< w<6 cstct {s? I DB'22 | l,\ns: dl (a) 0" (b) 45" (c) e0. (d) 180. <-rFn( csi< e <r"r< cs?< eqTT qap- [RB'22; CB'lTllAns: cl (b)qgskqTs (d) cfifus vfi<'t (a) aifr.lfu (c) mF{fu (a) Fl9 (c) ua 06. 0s. 6slr{fti<B,Knk<nari<e _ IRB'221 (i) q:rc<Iri Er{ (ii) c-{Yircl Dr{ 07. (iii) ifrqfu-d lk<\i{ er iT ftuccotqFc6'sz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii EI{F: (b); F,"1 = 0 {6{, ma = Fn"t. = 0 = a = 0 q{R {rn<'t qr<; cflr{I VT.f efrr< clr qR {qr<'t Er4 Efu{ft< 1R.{6 Er< {f I 6s[{t s"fi r fr frTCr fi $ft 'g {irq sfq sr<e IRB'22; CB'21; BB,l TllAns: di (a) mtB+ O) €mffi{ (c) c{q{ (d) c{Jr{ csfm c$"s ilftF Glc,I(-dT {(sr( {Kft-s afl IRB'22llAns: cl (b)Qe1tu (d) rdfisEdr{ t oa. sl=66 $a 1ft1ffi',rqs:r\g-l - IRB'22]lAns: cl 1a) Ed x lvl O)tr6x dftsrdq 1c1ffi x rfift+mt (d)i6 x cdfr-rynt 09. Fr6<€os- IRB,22llAns: dl (i) Nm (ii) d1,ne-cm (iii) ft-poundal firu-*conFcEsz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii It$1il ffi-{dfid qlrng frga "RIEETL.. qqr{frGrfl bEI ota : uF$I{-o8 MCQ: fr'iE <qaqq5{{ c<f6 q$ \e Wffi frro-d Eft'rsB rc q<(,t;r<ff EID Erfd E-s.< cte : 2 gm, 6 gm e 4 gm v-6d-:r &{D Tt|f$ {all-6[:I A, s \3 6 CSIfiI Tfi qrs-{ {k't"r5F 5 C{rsrs 20 <K F.rd {r{r {6$6tte(EK dfto vsmE <qnqrq LA, LB s Lc I qs caItrF sqierffr E<y naF@a:I 5 cm,4cm€3cmt 19. ffie15a3 a agsfl< ?<Fm mut +-sz lDin.B'22; RB'221 (b) 6.283 ms-1 (d) 125.60 ms-1 (a) 1.256 ms-1 (c) 9.283 ms-1 ll. <ErPcqt 14. Dm< .dft<F6{rf TE? lCtg.B'221[Ans: cl 12. 13. (a) 2 rpm (b) 15 rpm (c) 30 rpm (d) 60 rpm {:trT{q: (a):v = r, =.(+) = o.os x (A:a)ms-1 = 1.256 ms-1 cfifro s-<r<'r< ffirq frCE< m'tqE c6-sz lDin.B'22; RB'221 (a) La > Ls > I-c (b)LA > Lc > LB (c) Ls > LA > Lc (d)LB > Lc > LA {'flrfl{: 1c;; Lo : L, :1,. = marf;r,.r I mBr30 : mcrfirrr = marfr , msrfr : m.pf =2x52:6x42:Qy32 =50:96:36=25248tlB ... Ls ) L.q ) Lc qsB {EqlTsmK uf+&< mr+n-+ <npr<qt"rcr q-us-l<q1T$q6-{- lCtg.B'22ilAns: al (u)!M,, O); Mr, @y)vr2 (d)i Mr, <lgf< <1ro "ii&< FKt"m tc6m mut frr'< or<- (i) <fuTT <1q1fu E"i-{ lCtg.B'221 (ii)'tTG--{sLTdb'R (iii) Trt(fr( rfic"fdU"jT frco.rr<ltqBc8sz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii w1rt6: (b);vm"x = Jfitan 6 frru.r Sft"r+ qrtra "r<<6 @ ar:fr E-c< rts : qsBul+]-<q,s.rg-R st{$ z ksm2 rDffifrfr630

qEIdfrGlA lEI'[3[ : OFfiI{-o8 16. 15. (c) kgms-1 17. <FK qsE[E - (d) kgmzs-1 ICB'22; SB'22; RB'l7l ISB'22; BB'19llAns: cl G)qggi]irslTs (d) cf-u{ftT{ ISB'22llAns: bl (b) [M-'zLT-1] (d) [MLzT-1] IBB'22][Ans: d] (b) t = rla (d)t=la IBB,221 (c) 10 m (d) 12 m EIoIF{ 6fiF'ss-{c{'tsE? lcts.B,zzl @; tu) n (c) 2n (d) 4n 2rN 2nx30 T:[I{I{: (c): (l) = , = do ='IT raos ' .'. L = Ito = 2xn=2r'kgmzs-L dfros<r<c'r< qqrcolqFz lCtg.B'2?; CB'21; BB'211[Ans: d] (a) kgm2s-2 (b) kgms-'z (i) <EI € <Fi-r1frTfdffid eqk-I (i0Eflrr('l<rlk{6{ (ii0E<r{c'ld iR{6rfiqrd ficr-d@HFcEs? (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii T: {l;I: (a); <FFI rrlE = Ft = m(v - u) 18. ffi<qq<qmffz (a)ficl<67 (c)144<+ il<fnffqt6$FF? (a) [M2L2T-1] (c) [ML-'zT] cq-6fP (a)t=1 (c) t = I2a freqz (a)5m (b)8m 19. 20. (a) ML2t2 (b) ML'zT-'z @) M2LT2 (d) Mr3Tz 4 N fi qTF <6d O"K 1 sec $Ift frxt e<rE ss166e1ffi3s? ISB'221 (a) 2 kgms-1 (b) 4 kgms-1 (c) 8 kgms-1 (d) 16 kgms-1 wt{f{: (b);v{r{rkqffi = m(v - u) = 1'1 = (4 x 1)kgms-1 = 4kgms-1 21 6dftsE{C{crI{{liilqfrs-nct 6s'FE? IBB'22; RB'21; Ctg.B'21; Din.B'211[Ans: d] 22. i6 (?),q_ssk slTs (r) q<( dfts g{rk (a) {c{r firmgft{5q*qgs;qtrs "r+<6 EiE enrd B-sr Er's : ts m tq c+fi r[cS< EIE cF 200 gm w-[nr €sE qIT foT< strd{rBrs,fry lo cm ffi lBem r [g : 9.8 ms-'z] z:. pfr <re +u busm qaFr R's<.iftt q<'Iffi IMil 1t (a) e qffi:RqgtrqBgr*tuqt.. e qqt{H: (c); frsfllG = mgh; 'iffi = me(15 -h) {rl{, 2mg (15 - h) = mgh + 3o - 2h = h +3h=30.'.h=10m z+. nc q("tfu.c-ce m w-m< <eF Bo TFIk {5RI q< E"mvrq<qfrfu$<q<s? [BB,22][Ans:c] (a) 0 (b) mg (c) mg cos 0 (d) mg sin 0 25. csqfo{ffiir< rfim GI{ fi fu'fiftE? UB'22llAns: dl (a):Rrq(aq (b)s&\ dmr{ (c).tffi fiBfu <e (O E<a frBfi{<-{ 26. FEBfld't&rVqr*q<Eqt<m< cs@ - IJB'22llAns: dl (DfitvR"fiGEl]{t (ii)<c11-s<eFc+gf (ii0 {qf'&qr {Ffr o rsl$Ifi FI frru-<c+HDcErz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii 27. 0.1 kg vr<!r 4+F "fleR qem o.s m s$ qsB {e-ld qssrs 6{c( lsTsB 'rlr sG frfr6 90 <k {dllcl {e-RbF$sCc<? (a) 0.471 N (c) 4.44 N IJB',22l (b) 0.21 N (d) 41.7e N \\\ Tfl${: (c)i r = mozr = o.r, (3II39)', o s = 4.44 N 28. C$f6tt qS >IIC'ICS {€rF e{C <FK qFr q<( qrsE{ EIII?l(FecFlsEi[sft<rE? UB'22llAns: bl (a)qVsR.ll:rs O)f6 (c)ue{&<{rql( (OfdFFFs<r{'f zq. dFs T{rs ssvfctf sFtfillrllP UB'22llAns: cl (a) r (b) .) (c) 8 (d) b 30. frrE T{cI qFIs v{ 6F rt&LT "tVl ftliT y{ctICB'221[Ans: b] (b) g cos 0 (o) g sin 0 (d) g tan 0

31. q$E GTiE qG< Tit, frFD € GffFrsrT <frEr cdft+ c<r"f< q{"ns osz [Din.B,22l 32. {III{F[: (a); Who'r : Wmin i W... 11 7 Thour Tmin Tsec 12X6OY6O 60Y60 '60 =1r12:720 firBt qrr< q-{I mn-+ T{ wft ? tDin.B'221 [Ans : bl (a) 1: 12 :720 (c)12:l:720 (a) aqf6'( aq (c){{qfiEfr-{{q (b)2:12:720 (d)720:12:1 (b)E:{4fiEfrr<{ (d)EGsdTr{q 33. qsF {Tr{{ efrd sd € F t <fr freq +-<t cs ElqcE 'iB1fu $E ecl Er{? (a) 2 e.t (b) 4 Ecf (c) 8 e.t (d) 16 e.t rT{lfi:(c);Eur=1, (2m) x (2v)2 =!x2mx4v2 = g ximv2 = I x Eki 34. atEFFk EtSfud'ldT qGqr\,-E< 4q-{<rtft *firsn (b) 5 ms-'z (d) 100 ms-'z {k"ir$ E-@rlG< <rFil( coffi? 1oin.n,zz|1.a.ns: c; {^)), OlrEf G).F. (d).,F. 35. "lRA-d ftq qrffi 14n< vri qtft lffic<a ffiftE646s2 (a) 7 .27 x 10s rads-1 (b) 0.2681 rads-1 (c) 1.818 x 10-a rads-1 (d) Z.ZZ x 10-s rads-1 {:rI{Fr: (tl);. = ? = t#A = 7.27 x 70-s rads-l 36. ftt-ir ql6tR'{r 'th s {tff{frs Rfurf< qll qf?r rsk;[ <"t? (a) :rqFP( <q (c)IrfifrEfrr<E Efrtc-cr qsqrit "rfi€t EtD ge;6 g* *. 0. l kgsr-sr q$ER{Tgds?ld lN<E ls &{t<i[T _ 37. {SEdydclsE? (a) 0.1 ms-2 (c) 10 ms-2 {Ct{Ff: (c); x = I = a..-z = 10ms-2 38. eq@ {q qfilRs Cr{ 'tB+{ {€Er ffiqG + Er{? (a) Crl-r:t {lr<t (c) T{Y<rGl DGT[< IMil 44. \\\ qBqdmetqrrReilfiE!fi... qql{frsrf, iNqa : slrfi{-o8 3e. cstc{t{(tiTBeR<lfrTirfdqk w<E_ (DR<<-cEdailr{' 40. l rps =? (a) I 126 r-r (c) 2n rad s-1 4 I . 5 kg \r-r<< q<ifi {g 5 ms [MB'22][Ans: dl (i1$BmTscrmm< (iii) I4rqT T€ cftdn-r 6('t {rF qrFr frrE-dcrHEcAfl (a) i o)ii 11 IDin.B'221 [MB'221[Ans: bl (b)st&slfirs€ (OFEfiEfrr<'{ IMB'22 | lMB,22l [Ans: bl (b)qTrirrstEqr{ (d){5FrqFIs6rT (c) i, ii (d) i, iii [MB'221[Ans: cl (b) r rad s-1 (d) 4n rad s-1 -1 c{Ffurs s m <rFTlc{< [MB'221[Ans: a] ,F v:5msl (a)E-€< O)qfr"t (c) T( (d) qfu{ q<ql{ F}G< IDB'2lJ[Ans:cl Ts 'i(af trqt-{rrit Wrqr c+qft T6"rd fr-r crtcrl IDin.B'221 ftroer<- 42. 7 kg v-cn_:r enB <-S e+E fr< {€< ftq eB{"rs {$r( frS qrqlr cwrd{ *r <tr qTi ftir qfr C<r*T qF-D-g{tg R'tfrrsD-{F arrs.r R.s{€rw <o\9 i lMB.22l (a) 2.2 ks b) a.z kg (c) 8.2 kg (d) t4.z ks T:ntflit: (b)i vlr = (ffi)"r, * (fk)r, +1,,, = (^"ff)", -:=# -28-4m2=7lmz+27='mz ', m, = 21 = 4.21rf $qre <€? 6sGI, {g$ TE s {{t-<frcstt0Er{- (i) 0 = 180. <E, T{r <-q cdturqr{ (ii) 0 = 0. ErE, $rrq q(foSqrd (iii) 0 = e0'<E,$q1-ET66Eqc{ firu-dr$mctrr? (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii. swfTEFr6s-nqF-srirEB? [DB'2lllAns:cl (a) kgm (b) kgm-1 (c) kgm2 (d) kgm-, U6{

45. G@<rEnqF-$ r ECE 6sEBc6-s? x qqMfr'sH bErr-JI : ol{flEl-o8 [DB'2U F[E"< Eftlrs-d qlFflt's "f<-<6 ElF ecfd E-sr Et,s : qTF <rgld <tr$< <r.ffi 50m I <lsk gq 5m €<i <tR-*l elg &eLT{ qrs qc{sf 0.2 5m SE l so. <fOtr< erlv <it<frr c{Ft TE? IRB'211 51. (a) 1.86" O) 2.86' (c) 3.86" (d) s.86" ,t:{t{Fr: (b); e = sin-' (}) = sin-1T = 2.86. <lsrd (rRft( fi-6{ Frd-[RB'2 1 ; ctg.B'2 I I [Ans: cl (i)'i1&--rsR-dBfi (i0 :i1FT {q\r-k <rffi ft O"ri (iii) 'tt&i ffifi6"i< fioqmrBc6-{z (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii TsIfiti DIsfu "tc6< sfurWT ir-{dft -'t{rfi ctc"ICBF rffi < sF.\,-F e]:rs fr oT 6$FF? [cts.B,2 1 | \\\ (a)t=rxF (c)t=i.Fsin0 tFn{f{: O); t = ixF+ =dxF (b)t=dxF (d)t=drsin0 lil = (rsin 0) x F firun Eftqm-d qTreTr<: "rfiq @ qffd E-sd Er\3 : (b) LM-1dx (d) Mx-1dx 52. a Fmtrs 6rrue<s{ M q<(hdT L r 46. ReFd dx q(rR sd 6sF{E? IDB'21; JB'171 (a) ML-1dx (c) MLx {:tI{Fr: (a); f ax 47. AB I{q qcffi qlc'lrs qeF{ E-E\3-k q-lir6$-{ 54. 55. 56. (a)t=1Mr2 (")r=Y (b) I = Mrz (d)r=Y cclqF: (a); I = Ic * Md2 = 114.2 1y1.12 = ly1z mtr{l qsF {€rf qnTf erE R{ q{Em <m <q .4< S"R 6qi F{E {q frTl st-<? [sB,2ll [Ans: bl (a) I (b) 2 (c.t 3 q{sGEfr'ICsFtr? ial f t'x'zax L (c) ; /21x3 dx ," Tfl{Fr: (b); I = J'"dm qFgA]lsr{? (a\ 0.27" (b) 0.28'C (c) 0.29' qF.q{ qltcs-{ qTilQ s00m <rFfc(i {sFFk 'f[al 5ms-1 6{c:i T{ca d6q Effi Effid qIc{ sE 6s'Icct (a) MLT-1 (b) tulr-, (c) ML2T-1 (d) ML2T-, eTFffi\9lr qF[<q 10ks q<\ ffil6 qs qlc'fcs E"lG{ <,tffi 2m r 'llellF(s 3 rad s-2 dft{t W.I 1Bo<rurornn-<t6 qr$'t6-{rsEc<? tsB,2ll (a) 40 Nm (b) 20 Nm (c) 30 Nm (d) 120 Nm sil{Ff: (d); I = mk2 = L0x22 = I = 40 kgm2 t=la=40x3=120Nm 57. 611-a661-q5ffi<t 'l|rw 'F6Tqfu(< 'ffi qrF-{ qfcerr{F qgEI< qlTrfd cslq (s,Ftr q6s2 [SB'211 [Ans: cl \at2Mrz (b)Mr2 tq\ (d)Y @) f f ,x'zdx ... r'a "l *. . (d) ; J_"lt ox x2 [DB'21; JB'171 lRB',21l (d) 0.30. ffi<es-s6fi{E? (a) N-1 m (b) t,tm-z (c) Nm g{FT'F{qT6{FIF? (d) 4 [SB'211 [Ans: cl (d) Nm-1 [SB'211 [Ans: a] [SB'21] [Ans: bl LL +r=f,(Ydx) . *z =Y!;"xzdx Tirl{rd: (c); 0 = tan-r ([) ="r-,(***9) = o.r, 49. M \e-Gir e t ?q'c(Id Ts {{{ q'ce< {llfrT fr({ e1q{slft qrs< {ll'irrF qgekl [RB'21] [Ans: al @Y (d)MI'? ffi(qBErst< sFts'Ts? ..Mt2 .--ML2 {a) - '' 12 ., ? 58. Qfu q.-E\3-R EflEd"r 6fi{E? (a) cqlgil afi&bFqI 161 lftas6etmrsqrqlEFdl 1c)<9 ffiom e"rBfm 1a1,c{o ceno efr cqtE r$l \\\ qffiT*eqmftorfiFqr...

59. <ls]-<<i-rsEl4frrE- [SB'21] [Ans: dl (f {Fr<l{1 r-eI'E vfr-+u< frfiqq' E{ (iD rs-ETftm 'rt€rt{r (iiD {lqr€4 qll{lt aq5'IBK c.<', E< ftrs RFr afirs fio<mnDc6{z (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii 60. <I(ft( mFt {R{fq s-il C{ ml{trd fic"ilrF? [BB'211 [Ans: al 61. (a) q{pfrrfiT$< {t("r(,s (b) Bffi frrfd {k"Irs (c) {ru< c+-u {re <tQrr< fr6.6-6 qr'I(s (d) TCsd Fre-< ftr+-< wrcomF fr"s|< F1t1-< trfr Er{I frEi6-{- [BB,2tl [Ans: cl (a) ){{4 (b) qrTr (c) er{E (d) 8{{4 {rq< $(E3r qs:F € filq< cs'tcil dFi< q$?F qra? [JB'21; BB'17] [Ans: c] (a) <Et (b) Flq (c) E<r{'t (O tr6 qstr 1td \+tfu crsrq sr<Qs EFF qlsts sr< qt Fud{cltr ('iEl ,4(sGI {(<fts qr{- [JB'21] [Ans: al (0 E{r{{ (ii) 'ifrIfu (iii) qlc{ft-r 6{'t frcr<c+Etrc$-sz (a) i O) ii (c) i, ii (d) i, ii, iii ?Er<fiil{, cllRrl{ ffi dfrr fiIc{< cEffiil qs{{6 rskFt<ffidsF1cl? UB,2t; MB,21l[Ans: c] om{frsra oeam 67. zkg sr<-ir .4sF T€iT qffi u ECE q< s{trfrf ss? [JB'Zll [Ans: a] t J- (a) 2 kgms-1 (c] J Kgms - (b) 2.53 kgms-1 (d) 4 kgms-1 (b) v < prg [Ans: a] (d) v > (prg); <re-nqTrffi{ftS-{61_ [CB,2r][Ans:d] (iri=ixF (ii)i=l(- (iii)i=* fiIr<c{FFc6r? (a) i, ii O) i, iii (c) ii, iii (d) i, ii, iii Y ft.e es {€E o 6s cE sr< xy qrs< Dgfrrs T{r 'lICl I Etqr{- [CB'21] [Ans: dl (i)r=dxF (ii)i=ixF (iii)?=frFsine firFd c+t-+0c6s? (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii qsfr 'lIG-{ 6m"r(T d-o orgrr< $6 qrqi lcs'ztl (a) v < (prg); (c)v>ug r+gfft <re'{c6-sdFNqT rc]-{F? [Din.B'21] (a) mvzr (b) mr,r2r [Ans: b] fi'ct-d Bft"fiTrqtrqtm "rmff ltF cr:RB-sd Etls : 10N {q zks \e-r<< fu qg< E"K fu s-ci q<( 4s "Ei <Fr-< frtrI T{ <{ crl{ I (q{rq $("t {d Er"r$f {flqGrqr) <ffi{ftFfi(sEC{ c'rcE<str- [JB'211 [Ans: bl oo. Eft"no-< qal{ 4s q< q$ frr5-?r cstr{I q{E c6-sz [JB'21] [Ans: d] J t, t Vt (c) (a)cEqfuT$T (c) E{EfiE&r<-{ (a) {s{ Y<Ict 5rE (c) c{tf E|rISIS S{ (a) O)EB'cfrrs<q (O{{{fiEFTT{ o) {s:I 6<rrt Dr4 (d) 6{'ft{',Er (c) mal2r2 q$E El?Fk s{ q<( <I-{t( {a[@[c z.skg q<( 2m I ElolB(s 10 rads-z ffifi-6 yr"f IE r<tu Emtqftrffi- [Din.B'211 [Ans: d] (a) 10 Nm (b) 25 Nm (c) 50 Nm (d) 100 Nm {:Itt{FI: (d); r= [c=mr2c =2.Sx22x10Nm=100Nm frcrdEf;Hm-dqtirtr$ "r<<ff $S amaB-c*ns : A € B EF qlH {el@rq 25m s 36m <IFfc{< <1r+( TlsE Ersl-sE< <tliftr cof"f 2.5"r G-s{ <l€Et 4Q 5m) A qr{d iikT< <lsl{ @\e-c< "n{ W"Wt qt?r<< "n{csfu<<z [Din.B'2r] [Ans: bl (a) 0.109m (b) 0.218m (c) 2.498m (d) 4.995m c{t{FI: (b); sin2.5" = } + h = 0.218m (d)H 65. L (b) ulI, t L (d) "l t IMil \\\ {fr<6rl{qvlrrftErflIr'rr...

qqMfruH oE era : qqIlll-o8 74. <tmd <Ist EEro csm 'IIG< cr,fl6 l&<c'ld 82. 24ool 'tfutfufrfi? q$E ElsI qG fifot ooz <t-< q{9l1\c- lDin.B'2l| lAns: al (a) 5: 6 (b) 16; 15 (c) 25:48 (d) 36:65 t4:rrqT: (a); **, = /" = l2s =1 tJt' \i36 6 dz"l Frq, p <rr< Estr< s$Eco qFE T{q{@ Erq s4-as ft56 c{'fi E[qr frrF< 6,p6f {c{d fr-s[h g< r ut+ttr<vgsr<sl{sFs? IDB'r9l 75. 76. 77. m]rfi {€{Bffi FF{q.IdiSF R{ alfsr{- tMB'21 | (D 6<'t (ii) Yd.t (iiD {&lfu' [Ans: bl firu-< rsl-{Fc6<r? (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii qTtr DIFF q--ssF slTs 5kgm2 r DlsIFr$' 10sI {&{fute 5<r.s $E dft+ c<"R Ecrrqq qc<z IMB',2l I (a) 20 rads-1 (b) 89.44 rads-1 (c) 1.41.42 rads-l (d) 200 rads-1 q{tffi: (d); E = 11o2 2 + 10s = 1x 5 x r,r2 = ro = 200rads-1 2 78. '<rq< qE' q< qsiF ft? [MB'21| lAns: cl (a) N-kg (b) N-m (c) N-sec (d) N-sec-1 79. qsE <tq&F frR flR{Tt {R Fr-{ r <mfft Ts"tcil Eat iorq {<I6t ccqr Ttrr dns l& +o qo <tqG<ffiqtc<r<qmiT? Tsl{fn: (c); E1 = 11.2 [o.m, , = i] - z4oo =:xr x (TI-Z)'z = r = 1.21ks m2 83. t-C6n L4os- [DB,l9l lAns: bl (i) Nm (ii) kgm,s-, (iii) ls-1 fou<coffic6-sz (a) i (b) i, ii (c) i, iii (d) ii, iii 84. EErnFr E(-T{{cdfi$W{t ts c$(6rE- IRB' l 9l (i) c(qrft 1r{< s "i.<-{ cfli E{r<{ q+t efl-oc< 1ii') trrft "5{< re "ttr< cflb ttffi e+t {1-6-C< (iii) c(scft 'K{{tcT 6qEfrRffiF{r< frru-dron6q6o? (a) i, ii (b) ii, iii (c) i, iii (d) i, ii, iii q:rfqlT: (d); Qfuqt"r+q(v(<rg;{r{{ s rfG:ifu SgqQ qq<fug etl-rs I .. v,F = jryv,i * -3Pvr1lm, = mr.1 ; -' m1+m2 2m, vr p = ?ml Yzi :, V ff = v2i :. vzF = v t. firu{ fiqG Esr s-d q<\ "l<.<ft errl< Bs'{ Ets: ut = 15 ms-l u2 = 5 ms-1 ml :l0kg m2:20k9 8s. c\sc{{sFr{cEIfifie q{fifrE (<'tssE(<?IRB' l9l 1a1!ms-r rur Jms-, rc) f ms-r (drf,ms-r 5Ffi{Ft: (a); fifts <e qQ&Sfr-s {iq( m, u.+m"r u") s .'. V = ::.I:-Ll-:lll--jll = : ms-l mr +m2 3 86 qrcdn-s 6c{ qtT6<E Crtcil !p rs{ 'tB,tfu \3 Flq Ersrq? (a) mg (c) mg cos 0 (a) 0.605 kg m2 (c) 1.21 kg m2 (b) 0.828 kg m'z (d) 76.14kgmz lCts.B'l9l lDin.B'21I lAns: bl (b) mg sin 0 (d) mg tan e IMB'2ll lAns: bl til Jr/e Ot,lsJr (c)\E (d) rg 80. &{E r{{tr{d <E qr6 frTro fu s6{ cETFr{ET (a) 60': 60": 240" IMB'21| IAns: cl (b) 90':90': 180' (c) 120":120":120' (d) 150': 150.:60" 81. crFtr qs-,sT{ qT:Fl5 {(.stg )Frfg3rfq qT ${"ftql2 IDB'r9l (b)l=16*MK'z (d)t=rc+Mh2 @ c<n um< s-u$o crlm< w{ens ss? (a)1,=l*+1, (c)l=15+MK S--ssl-{s|{m{w{lls- (a) cfiFrcc<rf<c{ttil&s (b) cdfts c{c'l-< <rrf< c{E"fies (c)?fiFnc<r'Rq{E"il&s (O?<Flo ffi'F{c'f<crE"tl&F Ep = 11.2 + & x ,, =ISl ml : l0kg T{t{l{: (d); I=Ic*Mhz {k<6r{( qsn r R6" eFt6i{L..

qqMEsld oE[ 'ra : qqgg-o8 87. <54qqfr< qlcel c$lq <rfttrd {llF[rs{Fr q:I|{? 94. {< qq {:IGK qil, {< <9 I1r{-< <EI E{C EFI \s-ItrF (a) cfiftss<ffin< {k<6 O)?<Res<r<rm tR-<\i{ (c)w-uukqlsFF (d) ErF >r:fiqr{: O); Ft = mv - mu = ?<ft+qGll< ik+6q 88. f{FFF u<r<ut (p) e iffi< it<y arv'w-r6 651-qE? 1q"[n m = Ed] [Ctg.B'l9][Ans: c] ru)p=T (u)p=ztm (c) p=Jzkm rorn=nB 89. c$'I6{I fr{((s 5N ldr Ekt 6r{ 10cm EqtRE ffit qr{,fu(g{ossqr<? tctg.B'191 firu-dEfr"ffi rv q<r "r<-<S qrrr<E-wqN: 6 kg vr<-i mlr{I {€rs y-T6 qF 10 m BE\9-f{ E6cl ss:,R qrs \trNfr$ <<l+d 5m qiI6{I eFIIr ICtg.B'19] lCtg.B'l9l {cdI- (a) rri,lfu {dI (c)EG.qTE (a)lr:lr=1:1 (c)t;lr=\tl IBB'191 [Ans: dl [g = 9.8 ms-2] ss. qffi<r{{fi-6TcirctTE? (a) -10 m (c) 10 m O)14{€ (d) \lE <ET (b) -s m (d)sm {{l{Fr: (a); cffi T{ fr[D< ftrs ffier qR {6r$' U"K frro ro ln Gbrr+ <rcqr qt qffi Tffi{ frrs {d6l -10 m 1 kg € 4 kg .!,-r<i EF qe q+t 'iffi {rnql{: fr[T E-{A r (c); o=l=rr:= 50Nm-1 90. {€K vd s?FF Etr{, kFro s-<r<rt (p) qqFr qffi (Ex) c+{fieF<r{- t;'l ) (a) | I ', ----+ P (a) 0.5 Nm-1 (c) 50 Nm-1 (a)tfufiE&r{{ (c) r{P( aE O) Z tlm-r (d) 250 Nm-1 96. JBB'1el uB'r9l (d)1,16 q[[d ?iFFF v{r{crl< qt{E qr{- (a)4:1 (b),,12:L @)1:2 Er.lt (b)ll\ Er.l / ") 11,/ (d) ----+P a.qr{t{: (c);+ =!- p? =fi= 2p,= p, ' 'Zmt Zm2 4 "'PttPz=1tZ ffcu-d Eft,rsB'iv e<( "l<-{q EF qcR E-s< nfs : AB qsB xY qcrEr >ntqrr q4q+{ r E(eR fr1b Hlzm e<( mEw z kcr :L_, ^,_J-_ _, ,l,l fro:e fro:tt Fq-s q< qgq< q:1-q 11 ,{<( FE-rf q< qvgl-?r qITs 12 EF, c$t-{Eq6$? IJB'lel --+p Erlr IN _--+p 91. Wl${: (a); Ek = !: + Ek o. p2 <tsRTrf(ft( cst tfr6s[.<- [sB,r9] [Ans: dl (i) 'fl&-{ 6{cr6 €"f< (ii) d66{ <I-fl({a s"F (iii)vffiqY<1quo* firx6rffi{6'{? (a) i, ii O) i, iii (c) ii, iii (d) i, ii, iii 1Rftmc+nnt<e<iew z0 N qmltm sE? tsB'191 (a) 100 N (b) 39.2 N (c) 20 N (d) 4 N {:It{l{: (d); g-o"n =f g""..r,;M = e"** q11,wmoo,,=M.g-oo, = ;1k"-.., = 3}l'! = 3 e5 = 4 N frro-< <qeril< {c$ c+FE >r+org,{m {Er [SB'19] [Ans: b] (b)T{EfiEiiir<q (OE&\Erfr'{T{ wL2 {ql{it tc): !r = \- = 12 =1= + , ' 't2 YL: 3 1 Fq-?r e E-qotfu Trlcft,fu qF- _ 1 .-.2 1 (a.) = (b)= (c) vJ - ,t tz 'NI{Fr:(a); "=+=#=+ TFFI ST'g;I q$iF. [CB'19; Din.B'19; RB'171[Ans:dl (a) N (b) Nm (c) Nm-1 (d) kg ms-l (b)11:12=l:l (d)lr:lz = 1:4 98. 93. 1 IJB'l9l ,; (d' J; IMil 99. qfu6r.r* esnfr Rur qquqr...

100. cltrs'Fr< Grt€ Elsl{{fo<{(l{ffmFtsE? (a) o" [CB'191 [Ans: cl O) e0' (c) 180" (d) 360" firEd Eft1sF "|9 qr( "l<-{q EeR Esd Et€ : ffirqt orcd qffi,,r- y<.t js <<r vm( inr e{R.+, g lFtft< qffio yfi q<(R "lFft{ ilql(r 101 "lftA-{ qrs 588 N sqr+< esB <c et drs fir{ ('lrET€E<se €q-{Emr{? [Din.B'191 \\\ qn{frglf, oE'tg I o[$EI-o8 105. 0.25kg v(<-it ltTEfrFr+i<E 40ms-1 c<r"l qEk r qsq{ c?lrqHtg <eEr$' o.z ccr$rc qfoT fi-{r c.kElTlv r6f ans ng<.T$E? IRB'171 (d) -soN (a) 20N O) 10N (c) -20N :f{I{t{' (d); Ft = -mv 3 p = -tt = -o2s'40 t 0.2 = -561.1 (a) 60.0 N (c) 470.4 N (b) 117.6 N (d) s28.0 N Efr"rro-* qtc-qtm'F-<ff ltF qrfd B-qd ntls : A l]-x 1,1Dur+tu<w*= u l't-l/ ttBY 1 06. frd Effi xy q6qr {I6e16q 6q;qG"{ Tjl{I+ {cI(Fr: (c); qFIfiT €q{ =-g-*i=-c(1-i) =mexl=s88xi=a7o.aN fio< Eft"r+F qv q<( "|r{ff eferd E-sd Etls: 1500 kg v-(<ir qT6 ffi 400 N T+l T{{6' mlqI <f€6 5 ms-2 irq{cGl Drt r (a), (b); (c) r ICtg.B'171 (d);.r 102'tl'GT t&{ a-p's q{6 T{- (a) 0.4 kN (b) 7.1 kN (c) 7.5 kN {III{F[: (d);F-f=ma .'. F = (1500 x 5) + 400 = 7.9kN IDin.B'19] (d) 7.e kN 6N €qr{i[ qTF ,Fltfi: (a);t = l-Mr, = MK, + K=; 107. AB qrFd q-clr5F 5lsfud q-.sE]-{ sl:l-f $s c6{? ICtg.B'r7l (a) i Mr, @) j r'1., (c) Mr2 (O ; Mr, W<Fr: @+t-u<c€;r,= r"o- +Mr2 = 1Mr2 + Mrz = !Mr2 frro-d G@-d qTrqnF' q-a<6 qrs{ EE-d E't e c 6N 103. @)sr,fu tDB,l7l (d) E]!rcct = lmR2 + I o< R2 2 {€!t Vd=m 108. AC \o-m ql:tF qT{ TSd B"K fr.{l,ftE € ss? [Ctg.B'17] [Ans: bl (a) mg (b) mg cosO (c) mgsine (d) gI fi ro-dEfr ,Im-dqlmtrirr<-<ff SFerr*E-c<rls: i$r,f{ tf mr=5kg mz=6kg e--* -@ 5ms ' A s B ftlE'{ 'r<-11-T{ fr'|AE ftro eTt cfif Td?K ECE ci{{ !fi{r cwrd< "lir sm fiq fiq {freoftqR fiqAsfrmE-q(q| 6N {€rf 6N {q ltil FqlT{tft bm <q r T€trd qt"flE €q{- [A[ B',181 (a) 0.8 N (b) 3 N (c) e N (d) 11.2 N ,i:Il{Fr: (b); W = 6 - 6 cos60' = 3N 104. fim \,-c-< 6slr{I Dffi< <lt{I( qr,fo q<t qrq cfg'rffft qffi< qlr'ioF q-s\r-rd EFFF $EQGI cr{? (a) qs-EqdR1 =f =#=(*)'=o'=lt=Tl 4ms-' cc{r(i *-@ 5ms-' @* (c) fre"t q${rq: (a); lK t $,) IMN \\\ qffimqsrc{BgrqqE-{r...

qql{frcfld bEI qE : o[$E-o8 toq. crsr({ t{ e {gd a{ ss? (a) 2.50ms-1 (c) 5.83ms-1 {ql{Ft: (a); 5 x 4 - 6 x 5 = -5 x 5 + 6 x v -V=l.5ms - l lo. E"l.C<ls{w6{<ffi@ ISB't7l 1i) v<r<et w(<ftu q(-< (iD'|fr"ifu crnftuql 1r1rw{Ev@q"ro << frrr*mnBq6-oz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii iT{t{Fr: (b); {({r(n "1d vk"tfr-o a{ = o ms-1 qw6fu flL< qft'|fur 6<rf = (5 + 2.S) = 7.5 -r-r .1 {({'(FqRBqtrF I r l l. c$FrE rr{ir lIreT qliqI {ftffiq2 [JB'17][Ans: bl (a) MI;1T-'z (c) MLT-'z ftEd Eft"lrer qtrqfm'r<-<fr qrf{ esc EtB : "qFtr E[?-fr--d s< lkg I qfr 10 ms-1 6firf EFI qsF c"Ic{rfi ql?tl{ qtqFr= s-{E I qrs c'IGrsF{ q-?ft E{ zcm" l l 14. <5-\9-sFctqrE&tr flr{s&d{(qrc{&q ? tcB,l7l lsB'171 (b) 4.17ms-1 (d) 12.50ms-1 (b) MLT-1 (d) MI;lLT-' c.{tr{Fr:(a); '= (Y), =t= " - 2x2:72-2 s=4x10-3s u+v 10+0 1ls. dfrsvfi<it qrfl- [Din.B'l7l lAns: a] 1a) vffi eB-< s ?<fto qr{[rR FA-{ Eqr{dcrrFI o) q-seRsFrs € ?<Fl-s c{c'r< eqr{{ {{F (c) ?<Fl+qr<'t s dftswm('F ffi eclrrrwFr (O ?<Fl?F 6{ € <,tfi( FBm{ q"tr+< a$r 116. ffiftq E{r{crR {R<6rdK qld-lDin.B'171[Ans: c] (a)4x10-3sec (c) 1x 10-3 sec (a){rffi{Tl1 (c)ir6<cql{ (b)2x10-3sec (d) 0.25 x 10-3 sec O) cfrfi-sV<rcldcfi{ (d) w-s\9-kq:rc{;-dI${ 112. 2g vc-< qsB {€rf 1.0 cm 4$F I\r-E clql't3] T<l-fi qaEr <-gF-<qsst<qn-ssE Z tcB'l7l (a) 0.0000 2kgm'z (b) 0.02kgm2 ' (c) 0.2kgm'z (d) 10.0 kgm2 {:II{F[: (a); [ = mr2 : 2 x 10-skgm2 I13. s{r{(tksElcmfi4-I c<'Ftr ? lcB,lTl (b) M Lr-, (d) MoL,T-2 ,r:Il{Ff: (c); s{r{cl-?r slTS = s{r{ t x EiY I 17. q$F EFFk v{ 6kg (n( 6slc{I vr clc'frs D-qnt&< (a) M L2T-2 (c) M L'z T-1 (b) 1.8 Nm (d) 18 Nm a MCe: fr&q 6ry15s-q1n<Qtr{q-{qqft< q{ s wl{t{ + TCt{Ft: (c); v<toV'nft 4fqF ft1.[s 'fisEfi 1sf{l< A+B e ffi cfirs< E-qE&< <llrfi( r mr2 *=E-t= , - mK"=-l-.'.K=vzl 02. {r{< StE 1R-{6r;r< Er<rsa<r{? lAns. bl c+]-{E c&rz q?IIH ){ T€T qtfr \s cFr 6{rt u1 \e (a) u<r<ef (b) <at (c) g<ct (d) 6<5t E6 r, w-uolT oFro I, dF-s y<{ q-qa TCt;, q:'f6 qCEI- [Ans. dl v1 q<( lT Tgd qfi s 6.Ft 6{rt u2 s v2. 05. ITFI \9-r<B EE <{K Tc$ QG{'rs c\T( E.E FIF{ ,f:n{ir: (a); {,tFr vrdir 5F +o< xv Q&sf"m qcq{srqm{RfiT{{rir q{<P-( <e 6014 o"t|d frfiqtsd Fr{ a|dqd E{z 03. 01. {Ft?r E].EI {ft€dcl r$EE? (a) [MLT-'z] (c) [ML2T-1] (a) r = I2a -I(c)r: - c)K=+ (c)x=f 04.'fisqt {srfl-< ul+&< u-c't&< <l-{t( ccrt- (b) [MLr-1] (d) [ML,r-,] @)t=r4a (d)t=lc (b)K=* (d) K = ,.iz (a) u1 = v2 (c) u1 = u2 (b) ut = vr (d) u, = v, (a)41ffii (c) mlF+ <IFrI( 30 cm r DtotECe 3rads-2 y<q fE +-<rs TEfifidE6EI{HS.T(9ET<? (a) L.62 Nm (c) 16.2 Nm rNlql{: (a); t= Ic=mr2a = (6 x 0.3'z x 3)Nm = 1.62Nm (b) mfi (d) Fls6;{ IMil 06. \\\ "lffiirEsrrrtr@{etu{t..

qfl{frgld oEI 'tA : EFST{_oB oz. v&sWfts <q 6sE{t F.tl-?r "flTqR's frFrmd Frq 17. 3|6 6srkqffi{lnrs-qr{q[6flA<rG 6rt"f <<- ef{-+-<e'{z [Ans. bl (a) dt-{ (b) cali-{ (c) certiq (O dlffi{ 08. m sd s r <rrmft lsFFk Els&< c{rslr{I <iPc{< {r'lrF q-se-k slTcF< TF rsFIE? [Ans. dl 09. coFffi 6r-s{ft {rq:T<lFlrlEt? .. m.r2 (a) mv'r (b) - (c) mv'r" (d) - {:rKFr: O); m s[i?r {{l r {l[{k{< lett arwG v frcr u-qrc crFra qfuT-€ <rer ${ Y s{ r (dfts 6{ctf E?Fl.t s-{FI EBrf€ a64g qfiq q{ mo2r. 10. qsB oFtq'tFI clrf e& ffics,s n {i{FF {rd Ffu qsr setr $qit< E{ mkg q<( q< 6<'t v ms-1 (G{ c{Fl+aItcffi S"r< e1e <EI (N ,cor+) Etrdl' lAns, al (a)0=tan-1 Q (c) o = sin-1 (r) (d) e = tan-1 (e1) (a)al&*lfu (c) cdfts E{c<'t (a) ma - mg (c) m(g - a) lAns. b.dl (b)o=tan-rf{) \rgl (b)E{r<{ (Om'r1fu (b) ma (d) m(s + a) (aS 3lmrz (b) ,n.' (c) ] mr'z (Q J mr'z I 8. qQfu{"|6cRqB(qsfuo e-{- lAns. bl 19. qsF fr+E a V{cGt fro +mrq r m sa<-< qFsi{ <]fu' Fio&< mmmo +u rd {crM q{r<? [Ans. cl (a) mnv (b) T (c) mn (O + 5 kg \e-r<-< qFF {g 10 ms-1 6fitl DEIq l <eErs zo frr$rs ?tFll'{lg- Em Ss T{ {C{Fl CI(g qr<? (a) s N (b) 400N (c) 2.5 N (d) 25 N :r{t{Fr: (c); ^ = "#:-'= o.5ms-2 F = ma = 5kg x 0.5ms-2 = 2.5 N. Grod qslsfi{ qsw{ {ifu-{ qGst<ftrut 20. u. $T {&3rrlE-{g qsfr(sn$"K1a) c+EFE<tfu+r< O) qsBFEWT{frxt+r< (c) qstrdq{v{"tftrt+ra (OE"irs{rrft{Eqr]t (a) L = Ito t")t,=? 12. dftsvfi<'t € rfifrs RcrFqcqr{el6 6sF{E? (b)L=* (d) L o( 0) (b) 0.025 kgm2 (d) cskf,rEtm qffis qs<lT Frcd-{ g'<ct, a = ? [Ans. c] (a)a=g (b)a<e (c)a>g (d)a<g 22. 70 kg sqrfir qFsi{ fi<t's $qqf$Ift crGrE ficD< frl.F mrqT r ul-< E"rc< <tqr <t<t- [Ans. cl (a) 7s3 N (b) 720 N (c) 686 N (d) 700 N 23. ss {lr+< q$F {E l0kg v-mt q4E <g{ S"R 4 sec Eml e<m c{cl-i 4m 40 ms-l qr<? (a) 200 N (b) 50 N (c) lso N (d) 100 N {rrFfl;r: (d); F = 19# = 100 N. 24. 30kg v-c-ir qsF fu <g< m{ 2 fiRr? IR sL< 36 kmlh s Bfrio r*< q{r {Str{ B"F ov qE Ec{Ff s<rcs Er<? (a) 2 N (b) 2.5 N (c) 300 N (d) 5 N {ql{Ft: (b); F = ma = 30 x r,--1L = 2.511. 25. qsF Fr+t 2.s ms-2 g<c"l frro ffitq r Frq&< w<l dvmr q+$ffiw e0 kcccq Bfi o ew wtw T6;T. (a) 252 N (b) 630 N (c) 887 N (d) I 134 N TjlFtFr: (b); \eq{ = m(g - a) = 90(9.8 - 2.8) = 630 N. lAns. bl 21. [Ans. al t 3. <-,riT( 6sA< € ETc <.dK (gE-< ecFrs 45q- lAns. dl (a)q.sEkqTf 0) rdfi-ss-<l35t (c)E@'l&<{rMt{ (Of6 r+. corqE 6dfts s{r{C'l<r {(<5F"t Tq? [Ans. al (a) L = o) P = S-{s g:FF (c) r = s<FF (d) F = S<FF 15. rst61 qEF qft"trs qTF dE fifu {sd Eq:tfrr <ltct{ 0.s - r qsk q o.s kg qr{ q< Wqir q-Frr si5? (a) 0.050 kgm2 (c) 0.125 kgm2 [Ans. cl 16. ?<FFVdct € cdn-+Wcq<ca-6 [Ans. d] (r)r=; (b)"=: (c)a=r2a(d)a=ro IEil qfur5rd ssm ftD.{ "telEd...

26. {l6M crlem qsF <fto tzoomTmin c+c{ esB grl"FR 'irar T<rq I w]"Fk "iraEr <IFII( 200 m qr4 <iaB<cfrFr+nE+oz (a) 0.01 rads-1 (c) 0.1 rad s-1 (b) 0.001 rads-l (d) 0.002 rad s-1 {trl{Ft: (c); v = tor +to =; = # = 0.1 rads-1. 27. qsF rc< Effi s r,,r ({ qffissz (a) 50 kgms-'z (c) 25 kgms-1 lo s fr-fi FGI I s{r{(rkr (b) 50 kgms-1 (d) 25 kgms-2 28. {qHFr: O); E{lTCrld qfr{6{ =Fxt=5x10 = 5U Kgms -. 5 kg s< \e O.ZS m <Tq"rc(< eFft frfr<rEl 50 rads-r dfto c<c"t "tvtrs ail-scqEt{ rlffissqc<? (a) 0.078 J (c) 0.73 J (b) 390.63 J (d) 585.94 J rrfi{Ff : (d); Ex = !^r' + )1.' = lmazr2 +)mkz02 = 1m(r2 + kz)to2 = i*G, +|r,)az =!72^rzrz = s8s.e4, 2e. v = @&, r = <i-fi, g = qGofqV<qcrqFrr< 6sI{<fftEqffi{? (a)I1 (b) I3 (c)v2rs qr til4-[rr (ii) n e/ < \c [Ans. dl td):- :0. <eE $pqs Pr'c-rq< +rq< v< 20 g r 1f{ qs Er- (< T(9 I m I qs {k'lrs qEq-{ q:rs <)e / IAns. cl (a) 0.03 kgm-2 (b) 0.0s kgm-2 (c) 0.02 kgm-2 (d) 0.04 ksn-, 31. {ffi< sEP {r ffi1563- B [Ans. c] (iiD fro<mtlFc6-sz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii frrt-d tftlrq{ qrEIro "i-<-<ff ED er:fd E-w qt e, 6 kg EG3r q$F {TF cq-ro l0 s E[-Td qTE 1r{E 300 ms-1 c{c't 6<lI {c{ crFt, d(dF c?t EsrEt aas 4ffiaa 6op5a3 ftro vmt ftq r 32. T{r$-< qlft'E{F l4E? [Ans. dl (a) 0.4 kg ms-1 O) 0.8 kg ms-1 (c) 0.18 kg ms-1 (d) 0 kg ms-1 IMil qqr{ftnd iN ptE : o[{lr{-o8 33. (TSF$EKC'IC{Wi lqrrr{? lAns. al frlrd tftqrs{ qrER-r "r<-<ff EE qer< egd Ets, fft ct-+ uha-< Erg 3.84 x 1os km q(i DJh 1Rfto 1s+t-< rr"f[?t 27.3 fr5a qs-{R Eqfut Tr{ I 34. Elm<(frfi-oF&- (a) 2.85 rad s-1 (b) 2.66 x 10-6 rad s-1 (c) 2.66 x 10s rad s-1 (d) 2.S5 x 10-6 rad s-1 :{{t{Fr: (b); ^ = T = ;;*"",* = 2.663 x 10-6rads-1 35. DlmT?<Fl{ c't- (a) 2.044 km s-1 (c) 1.022 km s-1 {:rt${: (c); (a) -0.5 ms-1 (c) 5 ms-1 (b) 0.5 ms-t (d) 50 ms-1 (b) 1.55 km s-1 (d) 5 x 103 km s-1 v = rrlr = (2.66 x . = 1.022kms-1 36. 6dft$ 6q o- (i) ro = 2nn firu-d 6$tlDr6r? (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii 37. cfiq-s'fG{qqaffis{ft-$<ct [Ans.d] tirtano=* (iitL=I(,) (iii)r= Ia frrDTc$rqFc8sr (a) i, ii O) i, iii (c) ii, iii (d) i, ii, iii 10-6x3.84x105)kms-r lAns. dl v _.... zfi (u)&l=- (lll) o=- lAns. bl (c) ii, iii (d) i, ii, iii (b) cfrfto E{r<rl (d)'tffi 38. cs-E.{ftfi- (D qrtrsfft{{{ (ii) qF T€< ife"fcck frr$ fu F.{ (iii)qn{l{Y Fru-<cqffic8rz (a) i, ii (b) i, iii ol. frco-d mF{F qrffi qsF etst t Frd? [Ans. d] (a) Nm (b) Nm-t (c) kgms-1 (d) kgms-, 02. lyFr cslFil<K,{kE9ld e{G frE<lfr-s({t{ic{ E".Fftr< 6,F <lFlfrT c+frqt "iR{6Tq{{p [,{ns. cl (a)<FIiIElu (c) ?iFFFS{CE f

03. 20 ms-1 c{crt Esfi{ 1000 kg v-r<< qsB EIs 1500 kg v(ffi .{TE Q( EI$rs {|€l frcr qscftel :Igrqm c{ 6{crtF4F aFsr{Ef c6Etq{t{l{: (c); m1ul + m2u2 = (m1 + m2)v + 20000 + 1500 x 0 = 2500v.'. v = 8ms-1 04. qsF <r 4 ks Er-T{ Q< Ts{ b"t< ft'st Til{ TgE o c{trFf,s 30 ms-1 c<l qlsqTt Tr{< qFt TE? (a) 12.5 ms-1 (c) 8 ms-1 (a) 30 N (c) l8 N (a) [ML'z] (c) [M'zLT-1] (a)K=I M rox=fi (a)(rxt,rxp) (c) (t' x r,p x r) <-qFfiftz (a).lffi<q (c)ffifitftrco. (b) 10 ms-1 (d) 7.5 ms-1 (b) 20 N (d) 6rl'r{lBtffi o) [ML,r-,] (d) [ML2T-31 (b)K=T (oK=.F 1b) (i x P,i x i; (OGxF,Fxd) [Ans. dl (b)$$roftf(E (d)El&srfrrs<-{ :TqI{Fr: 15); F = ma = mi = } = f = zoN. 0s. w-g\9-krsFltrF< :r1,4t 6sFtE? [Ans. al 06. 6s11{I !r {€< E45l&i <r',ITl( .{F6? [Ans. cl 07. 08. qrB EFFR q'gsR qt:rs 2 kgm2 I Effi frfrri 30 <rd Tirq I q1 dfts s{6{'l ss? (a) n (b) 2n (c) 3n (d) ar qfiqFI:(b);L=1.=l.T=2tT ^ 2Trx30 _" 50 f4l rc1ru E, qu-eTrEFrc I q<( dfts 6't to ,{<{(l-{S{-dcsFE? [Ans. dl (a)E=lrr.r 61 n=Io2 (c)r=]l<o (d)E=1tto, 09. M .e-r<-< qsB{€ &( 6{art x-qrmw]-grrlr{ nBft{ I qefrn<wtr*r (a)T+' qqdfrsE(r<rf- [Ans. a] (c) (<zY {l{ (b) g< alrrs (d) sc{ {l{ {fr q<qll cs?-{ ? s{r<C{ F e<( eq@ fi F E{, Er{ 6dfts s-{r 't i \e E6 i ,qr aft fltl lAns. bl 10. 11. cd1h e tcar€r+<qrElqlo{tq-<ml con 65fr+ qqt{R-GH lEI 'ro : oF{II{-o8 12. 2ms-2 V-fiq E"Ica E5-s erF ffi erE 6{r qigl(lt< Tr{ E({ft <4 1 1 80 N e6 6lrpfi1 g( E(<- :fifiqFr: (b); 1180 = m(g + a) =m=#*=1ooke. 13. qr8 cft-qaqr .asE \n-"Nfi-s !-{"t Erd o) wadn-$ 6{ci {&m uerqr q< sd M q<( <rfl( rr<ry{Fdmtb{fr{fu fi4rqdr [Ans. bl (a) ]Mro'? (b) Mrzr,l2 (c) Mr2o (d) |Mrto'z 14. q$si{ 1wFi"ft t w-g-gT< sFro fur q<5F t-{t qcr< ur<ftr+ 29 ra65-t ffiffi 6{c{ {<rq I Ifr cc qStq +r< dF-o e,i 1ffi sr< lo rads-l {-{, Eir{qVTqVEIRqEITSSE[<? (a) s0 kg (c) 60 kg (a) 2r (u) ; (b) 100 ke (OmimBtm (c) 3r (d) i w1ff{: tat:L=lLl=t, ' ='ol, =21,. ' II ' 10 ' 15. m \e-r<-ir est T€ r <fft(< lsfon "n< wwfus EE.(qr IgFFI{ 'ifr< 1{ls$r4 T, T€tr{ E K m-u{ftqcq<xrq+sz lAns. al 4fizmt - +n2mr2 anmr2 (a)- {b) - lc)- (d)rtmr' 'TzT'f2 16. 4 kg € 6 kg \r-r<< EF <S {aIl@C{ l0 ms-r q{( 5 -.-t 6ff qse ftrs ']frfi-{ | el{"'R {f{I 1I€$< q< Tg Etr {.s q<'t{ sdIcs alfsFI, {@ T{i-?I 6<tt Ss? [Ans. b] (a) 10 ms-1 (b) 7 ms-1 (c) 6 ms-1 (d) 4 ms-1 17. 1000 kg Er-T{,qTE&T1-ql{lqE< c<"t ot-qt tq twnq +-{e | <lgll,,r-?r s+f <q 18ooN, iRrytwtqwE<Bfieq-sFEqqsc<- (a)0N (b) 11800N (c) 1800N (d)9800N qqt{Fr: (a); cq 6<''f Q< oR Wq W r XF=ma=0N. 18. qNfi-s cc<fts Q<tTSm 800N €qr{< qsB lQr+ qans sEtc$ 2ooN qpfro <re'K erarw+ r fr<r<qr* v{+ {qc'kr n14- (a) 0.2s (b) 0.125 (c) 0.50 (d) 4.00 T{i{Ft: (a); p, = $ = "-399 = o.zs. 19. qsF FB?b r5ms-r 6<crf B"rr< E}qr ootgry-r+< '4ow qR{ Frcrb q-{-Er{ F<rc Grc&< E"r< q< gqs{H s6-{ Er<- (a) s88N (b) 900N (c) 750N (d) 800N qqtqFr;11);effrT{F rgw{ = 60 x 9.8 = 588N. rEm b\ \\\ lffiqrqvn*FwtuEt.. <I

20. sstr frsE r ms-, g*cct fro llftqr Fr+=6T {c$ qf9-6{ q$w{ qfu-< s< 65kg {rq ffi cs rdi w{e<$-<r{{- lAns. bl (a) 3s0 N (b) 572 N (c) 2s0 N (d) 637 N 3 kg w-(n< q$E T€< S"m toN <zr qcrFt l:.?rm T€F 3 -s-2 g{rcl EFI(g allrf I <gF< B"r< +s s'fuf ffifrTts<[q? (a) 16N (b) 13 N (c) 6N (d) 1N Jr{t{Fr:(d); fr = F-mg = 10- 3 x 3 = 1 N. rTg{c.I EE{]{ qsB rilB 6ri ffivtfir-+c'i<: e"t 21. 22. (c) 3 (d) e rFllrtfd: (d)i ){ 6sGI. sr =* . u = 0... ......(D ,,2 tT6E6E, s2 =f :.v = 0.........(iD (ii + i) sGr {E.2 'sr = +-t-:Y')-nul =e -ui ui ui "' sz = 9Sr. 23. 16kg \e-rn-< qsfr E< <g< Bq< 4s <ltft sN € Sng <qf E-s {€< 6{a1-a qfr-ar1 q6qqt {cq t&F ell{'fF "Il<< F\9- sct E(6F {mlw qr<? _1 (a) - 'I (a) 0.5 ms-r (c) 4.0 ms-1 (b) 2.0 ms-r (d) 8.0 ms-r (b) 4000 ms-1 (d) 4 cms-1 (b): ,rcpFr: 15); 4y = II! = !I1 = 2 *r-r. <ft S tg \9-Kn q$E ,{To cqt[o 20 c .e-r$r qsfr afr 1000 ms-r c{c{ ffi E{ E(< T{.rs-d'rilqr<rl ss? (a) 4 ms-1 (c) 40 ms 1 wIltFI: (a); v = +a = 9i3:1!!9 = 4 ms-1. 25. 10kg \r-rffi q$F <€-d E9l;r 2F {fci3r fi qrsFt s<ll<t FIEI <eE< 9<+ {T 60ms-2 I M sc<a qsF {g{ E"K 5 F {tr{d <Er ErrFt FiTl< {rE {fr {€tr{ 9<ct 50 ms-2 q-{, B-r< s< M {E? (a) 3.3 kg (b) a.8 ks (c) 21 kg (d) 30 kg qcFflir: (d); * = ffi - m, = !I1!M = 3e P*. 26. Fq q4q q6s< rtc'rs nfr <-e< qs-.q{ q++ {al]-4T:r r q<( 2r I {fr EkEd $ tffi wr+ e*, sftq-d dFI$' v{r{c'fd \tr{'tlE os? {a) l:2 (brr/7: I 1c;t:V7 (d)2: I r-{r{o: (c)i +,= *..1= E- E= ; rEm \\\ ra.friqr*frwr"r""r.:Jqtil{ffr'gtd tErtEI : orfitT-og 29. 27. GEletel G{r{ 6iro crf[s, frrnFr <kT< qftr< frrs< nltlfto qrf B[ Fdt ss r 6{rFr <ffi{ 6{I'tf{ fifno- ,{fr !r-{f C6{ atl-rs? [Ans. al (a)6{-ETft€ O)Tfu{{ (c)aqf6'(aq (OEt&--srfrmrf 28 trEtrd< fl&<ftft<1c< 6aa1ry mi = kF; q?rEn. (i) kECq qsfi4qqefiF"s &;{s lAns. dl (iD k-q< {F <lFterEt{ q$r{rd s'Er fr6< or< (iiD k-q< {r{ sr qhfuE r fro<c+tqDc6-rz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii {lst{ <1rs qq'.<5E EElr{R {{{ \smd iG csf"t qa<- [Ans. al ti) 0 = tan-l { {ii} 0 = tan-1l{j- rgc (iiit 0 = sin-rl firu-d 6{FrFc6r? (a) i, ii (b) ii, iii (c) i, iii (d) i, ii, iii @<e<mvtl(Ertqn-<- [Ans. d] (i) E[\9-rF-d E{c<rt{ 4fr<\6{ s6 (ii) mlBsdr<r'k 6$1r{t {k+iqsdnT (iii) erFd EFIr<r{ €'Er llE fi fr'{t sct firu<c+HFq6'sz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii ol. cdftss-{c<{frrffic{r{? [Ans. c] 30. 02. f{FFr F t, cdfto c<'t € $g-{ <rFk{< TC$ qryr6 rfFtr? (a) co = vr (c) v = tl2r [Ans. dl (a)vfi<tt (c)s{r{(t<st{s (b){q (d)F5 (b) o =; (d)v=or frlrrdmYfr"$p (a) s9-{ (c) dftr cq'i lAns. bl (b)qV\r-Rsh-{ (O rdfi-rsdm't (d) i 03. fnFt<r e1fus 6qrq srrd c pft-rt, {4{ dfr{ 6s@ 04. qstr {{{ ElsFd qrffi {-calr{F q_vlglr sFrs r Erq s< <flffin ffC'frs qw-?f qlfs qr<? lAns. rl (a) 2t O) I (c) i

05. m1 \e-m[ q<( v1 6{crl{ q$F +.rt qTt sr<< qd q16qS a"666 {ffi ft-qr <mtr Q&qPro <C4, {lid-< "Rr fr&{ F"tlir Grl Ec<- [Ans. b] (a)2v1 (b) "r (c) -tr (d) 0 l0 N <Er csf{ {€3t E"K A{s qFI sm/s'z g<.t @ qrt 1ms-, y<6I & qrt{€rgtgfrF<rsqm s{S <Ft-< nrd Er<- (a) lN (b)2N (c) sN (d)soN ,tfi{Ft:(b);F=ma ;. 3=1= Fz =9?xF, =]x 10 = 2 N. 2 x 103 kg sr<< ,{TF EG so In vffic(-{ qr6 {srFl,( 'lIeI 12 ms-r {{w&-N q(Cq Y<rq< fr-s (a) c+lEil frro [Ans. d] (b) c$rE< <Er<<frcs (c)T(.6<-1th{<Frd (d) 6S-g € er{rsiTfto a<r+< 08. ,{$F eilEqt d{{ lsrom vt$ qsF qFs .c-r4 n&cs ffi(qr <fi or-c< cHG Pfrr {l-(el 30'q{ Er<q$trdqffiTy<ctE(<- lAns. al (a) eT-t (b) g3-' (") g4-' (d) 293-1 q:ltEFr: (a); g sin 30 = g2-1 09. <ft 6sl{ {{tElir El-<rf€'ilft 6fill3r{1ffis{@{ q{ eErd {€E< dft+ s<r{cuf< fr+ c{ <itF-i[ Er< 07. 10. I N :1a1 - frC6-d- [Ans. cl (a) lkgxC O)lkgxlm (c) I kgx I ms-2 (d) l kgms-r ol. Iffis 6s,lc{I fti?F.tR <ltff @A-d e ?<fto v{r{Ct{ Fa{ q.l$-{r$ fi <rE? [Ans: bl etqE- (a) <IFII( (c) "lRft (a) rs (c) uPuF EFro O)*r,.h (d)q44qs O) 6dftss{6{'f (d)E65tG<<ilcT( [Ans. al [Ans: al (d)dlB{ oz. s&-q ETft{ fi 6a1-a aq-a e11a.qfrq frfiqrsd rrE prde-<qsz (a) mtr{ (b) 6I{ (c) cEFq IElil N\ \\\ qffifi{EsIcrftm'ttu6lr... qnrffrCmaErr€ rqqfi{-o8 ll. fu$s sftfrF$(q- [Ans. d] (D nF&nce<8"mfr<r+r< (i0'K-"tF{frqa-s{ft (iii) qrrrd C<FFrew firu-dcTHEcE$? (a) i (b) ii (c) iii (d) i, ii, in {?Fr <[5ftT etl$ w{q]T roR fifrg 6mt ffi q{ EnT s< - [Ans' bl (D E-<l-{'t1fr,m (ii) Efl-<{qd arrs (iiD 'lGrlRF1frffi firE-d6FrE{6-r? (a) i (b) ii. iii (c) i. iii (d) i. ii, iit t:. qqgft"t <ec{q 6eIT {g-rctlqEq fum <l-<rE sF efta$q q6s en6 q qa- lAns. bl (0'iffi (ii)rtfrstfu (iiDv<r<t foEd6oFEc6<r? (a) i (b) i. ii (c) ii. iii (d) i. ii. iir 14. qs$ 1ffi (g E1{ DEfl-< 't-[atv;r qsfr E{ {6{ {ketqi{(sr<r q<FFr{tqF"lIr<- [Ans.dl (i) E-sr r& E{ sc< (il) E-sr {gt "iGq-{ {c< (iii)'tfuft{ T€ Qn e<r Q< <u ot&ft+ qc< frru-{crHBc6o? (a) i (b) ii, iii (c) i, iii (d) i, ii, iii fr6vs ffic6qs q16-q16 "rffi @ arf<E-s< ms : a kg s-dfrFB qsF <€< B"ld 40 N <EI 10 sec {r< futtor<r 1s. {sBdsfffttdqR<\fi- [Ans. cl (a) 40 kg.r/s (b) 50 kg.rn/s (c) 400 kg.m/s (d) 4 kg.r/s 16. {fr'{S{ v< 8 kg <T Elr{rE {{rT v<r{Ci< {k{6 Er{- (a) 800 kgms-r (c) 200 kgms-r lAns. bl (b) 400 kgms-t (d) 320 kgms-r 03. 59 \e-r<< qstr {€rs ,- an ry]<I etrs dr{ 44 rads-1 .{ TffFI TWd A{S\5? (a) 13.69N (b) 19.36N (c) 16.93N (d) 36.9IN {:[I{FI: (b); mr,:2r = T frru-q Eft"trec qtrqlrs "r<-<S qF *er< E-c< q1s : 1o4kg qffi{q qsF ir+6< w 1.5 x 1o4kg r TrEd< ctc"lcs 2000ms-1 FGIE qt4lfi 200kgs-1 qr< <rrq i <rsnB {M E"K firo fifu6 <Er r

04. nrsFd{]!FI'- (a)5x103N (b)4x 10sN (c)5 x 10-3N (d) 4 x 10-sN {Ct{Fr: O); * = 200kgs-1 ; v=2000ms-1 $fi, F = (ff)" = zoo,zoo0N = 4x10sN 05. <r+Btr{ydct6Ffq6{- (, 'Bkclr qk{fr-$ c1't c<Ft Ecq (ii) 'I,l{ fr'fTr{{EIn C<ft Er4 (iii) <r$d-{ mlDs< c<ftqrq firlT6rhB{6s? FO? @)i <r)# 09. qg-sEr EFrs06. 07. 08. (a) ii (b) i, iii (c) i, ii (d) iii C$Ir{IftK Wtrftt 40kgms-1 <6iF 6<RtfS lAns:bl (i) {g< sd 1kg {rq 4R 6{al40ms-1 (ii) Tt<s< a0kg (rq 4i 6{rt 10ms-1 (iiD {S{ s{ 6.3keR6{ €n 6{ai 6.36ms-1 fuo-d6qlrBq#6? (a) i, ii (b) i, iii (c) ii, iii (d) i,ii, iii 6rk{t_qsB qr$R qr"lrs $T<E <.s< 1{T nG-{ flft{6rs <I{T cFsTlT EltM 6sFrE? '[Ans: cl (a) mtBv< &) qms{ (c)w-sEkqFrs (Odftrvfl<'t q$F L ffii< ${ ErsK {irfrtfrcr q<(?rdrd q?-"]m ffi qrF {rc"irrF FgF{ EsFl&.T {fET( [Ans: cl [Ans: bl (c)+ at F-r vr ! s [Ans: bl 10. (i){s{sLTnE iTfrGsl.< (i0 T6{ cdfts 6{c5BrB"f<fr\,'<+r< (iii)T4rqrs-dBfifr6F,r< frcFd c<rF Fqfr<r? (a) i, ii O) i, iii (c) ii, iii (d) i, ii, iii 60tc{I $rc*(s't< {sqfr.f ffirLTEGE{ dfr.f <rq-<Eqqfr? [Ans: a] (a) aIffi{ (b) (Ftf{ (c) cdtF{ (d) trfi Fo-< Bff"rco< qnen-o "r+<ff EiE qffd Es-d Ets : CD q\rt eft-d E{trTrt {5q AB qq1.l-?r g;{crrk - (a) rTF &) ftaq (c) uErocf (d) mr{ E6l {ct{Fr: (c); p o<v;. I!2=*=i...pcn=4pae E4 ;3 Ez I: I l. ------) cq-{ IEil ,lft<6+* qsns Rga {arFd.._ qqI{RG,ld.EI 'rO : UFTII{-O8 rz.. B16<qtilsr{L ur,Y\ nttrl <Lol- [Ans: cl (a) MLT-2 O) ML2T-1 @\ MLzT-z (d) MLrT-3 13. 20ms-1 6<r{ {&+{ 6str{t q$E <-e< {ffi{ qH rsoI qc'{{gFds{r< l sE? 14. wtqFr: (b); E1 = 1-,rz --u=?=31199=19L*-r-r @t{I Fqr{ S"m qTq ffi Ff W CF s"tTEd dfip s-<r<"i- [Ans: cl (a)<lr9 (b)s[{ (c)T$ftsql-rs (d) {vrs\e 'ifr< sTrs€ qtr{ qsB usk vd lokg e<( Equlfr< gtqt( o.smr ufflE<q_sof<el{$$sZ (a) 18kgms-1 (c) 28kg65-r (a) 25 kgm2 (c) 0.25 kgm2 (a) )i = srffi (c) XF = gi{s (b) 19kgms-t (d) 29kgms-1 (b) 2.5 kgm'z (d) 50 kgm'? G)XF=s+o (d) Xi = e<T 15. W{Fr: (b); MK, = 10 x (0.S), = 2.5 ksm2 16. dftss<r{rkc(<s.tTE<q_ [Ans: al 19. 17. m \r-( s r <mtft lSfof< frq Cc€-c qCr< q1rn6q; TTAI'f&{G$E? (a) mr<,r2 @) ]mrr,:, (c) mr2t_r @) )mr2.i: Eft{Ff: (d); E1 = 11.2 =!7^rz x a2 =!^rz^z 18. ftro-{6sl6ilflFfscr{rtEtq&s? llns:"; (a) Flq s F6 tb) <cq< er{s e qEiEK qT{o (c; cfrfin wr<t e t<Fr+s-fi<q (d) clE?m s clEEld:rqrl ffimcq- (D Tft s<.rqrtrTGT (iD "s*q,rT NJAnt' ul (lll)r=Fxf frcr-<coffic8<lz (a) i, ii (b) i, iii (c) ii, iii (d) i, ii, iii 20. q--sEln qS.F G,F[E? [Ans: al (a) kg (b) m (c) ms-1 (d) kgms-r 21. zkg v6<<t {gtrF Sms-, g<Cct e1E.ftq S-?ICEi TE <"I Sr{FI s3rrs qr<? [otbq{"t<e r, = SX1 (a) loN O) 5N (c) tsN (d) 20N . T{lqFt: (c); Fn"t. = F"xt. - Fk + (2 x 5) = F"*t. - 5 ... F"*t. = i:r\ \\\

qqI{RGId !E[rt-o : q{JrT-o8 22. fr(F{csFrFpE? lAns: dl t"li= aF o)i= -aV(c)i= Fat 1a;i= aVt fuo-* Bft"tc<r* qn-qlrs "f<-<ff qF +ef< Eu< nt s : aft {ftfi{In tm ?RdJ .q<i ztg ra-m< q4F }rs e d{:r E[e< q<lR-T s Zqr{r< qter erqcr nT'ffift q(s-n ficqrs q<( "m{ftr=,i q€ qrcK sls fr[T e<( ffir< a?-o-L< ffiaffi qrffi qlrrrs w-srold EFrs q<( D-q"lB'd <itryt( fr{r <'<-E r z:. aft q{:r (srq q'eft-{ qwli Aro +s fr41 +r-<Qqz (c) 50N (d) 70N 4{I{Fr: (c); 30N q<rrffcrtt c s<pr{F a qrq,<rq<clt{{q q{lTfr. --i!- = a = 40 + 30 - 40 ' sin(o-go") sinqoo sins -coso sinq - lanq = -1. o = 126.8" ... Q = --= = 50N fu: R'z =Pz -Qz +P2=R2:LQ2=402t302 <qcm{r<r+66fi"tTEz [Ans: dl (a) 101.3" (b) Lr2.2" (c\ 123.6" (d) 126.8" {cl{Fr: (d); .os-'(f) = 126.8" 24. (a) 0.167 kgm'z (c) 1 kgm'z (a) Frd, > Frd, {T (c) Frd, = Pr4, qq' (a) c$-ETft <rq:r q{r (c) *1.FftT Trq-d q{r (b) 0.67 kgm'z (d) 2 kgm'z (b) F1d1 < F2d2 q{ (d) F1d2 > F2d1 q{ 1u;c+vfuft<cr<w (d)qk<-q<wi 29. TS{EF<TFSE? (a) 10N (b) 20N 31. cdftsY<r*r{IEI (a) [r] (c) [MLr-'z] 37. .'. P = 50N [Ans: dl (b) [MLr-l] (d) [r-'z] wt{l{: (a); | = #P = ifr>' = 0.167 kgm2 1{4 qs slrs cca Ec"i&< {ffi ( qetl ffi@d- (a) i e"f (b) 2 e6t (c) 12 sct (d) 36 e6t {qt{Fr: (b); T$ qs Eftq E6q, x, = }; 14r s+ 2s. m € 2m vm< @ 'ibq-a T€n "Iffi eTt SCE ElI[d ?<Fl$ E{ C{C"k q-tqlE SE? (a) L:4 (b) 1:JZ (c) 1:1 (d) 4:1 T{t{r{: (b); 1, = +,+ - p,: p2 = 7:,f2 2m 2x2m 26. Frq qsB(€ o ffit qcm rt<ftro {scs t|r< r {€EF s&< sFl{ FilT o catrf d1 Ercg F1 T{ ,s<( {G-.{ atR fuftrs o nlrs d2 Escy F2 <"r 4({t't ffit E{ I {€tr s&r <ft]-d fr{As frce g<i< [Ans: bl 27. T{1-qI54 Ddtr, rtt&< EIof E16o 41rif &i6+ "irg @{? [Ans: b] <EI € <Fiit fr-{FFIFK eq'O-CrS ff Tr{? [Ans: dl (a)rls?Fr @)F6 (c)Tle (d){cqdsls 4kg e 6kg w-rffi !6 {€RcnEFrq 10ms-1 q<i5ms-1 6{H,4st frrs E{1< qr-:r qrs q"f<ro <Eft frqr {iFk fi q-srE{cqmE{rETo c<'t sts<<? (a) 7ms-1 (b) 5ms-1 (c) 6ms-1 (d) 4ms-1 {:II{l{: (a); 4 x 10 + 6 x 5 = 10v, v = 7ms-1 6.$m1 ag< Krl< frrfi Er? <<r<B g{ <6t trcM rF-irl Er4 qi c{crF- [Ans: b] (i) {l(l< mnnr "ik<6{ Es Tt (ii) frrs-d {kt6 E{ qt (iiD fircd 1k<6r s{ frru-d csnFq6r? (a) i, ii O) i, iii (c) ii, iii (d) i, ii, iii {sqt asl,ol< slsGn 6s'-s.flft qr qrffi {r't(s Eq'lG <11-{.l(ErET- [Ans: b] @K=h o)K=; (c)x=f (oK=E {rm( csB-< i = zi + 3j + z[ e <e FE-{ F =zi+zj+ zQqrE,ffit =r (a)2i+zk @)2i-2i @)zi-2i (d) zi- 28 li i kl {5IT{FI: (d); t=ixF=lz z zl=2i-zi lzzzl cs.lc{t ({i<I B* eas. T{ &<r alF rE E< € yfiq<r t 6f tv [Ans: al (i) w r\5 6{ft sr{ YdGI EE +{ Rr{ (iD s< <E +{ qr{ Yd6t so <Ft qm (iii) .!r-rtr{ }r:rF y"cf Et-< firu-d 6{t{Fi{6-s? (a) i, ii 32. 34. F2 JO. 23. qqrdfts 6{rt 1fi-<o c+tr+ <e< $+ <itn( fte"t qre cdfto s{6Eut T\5eq qr<? (:a) 2 (b) 4 (c) 6 (d) 8 wlqFf: (b); Lc(l+L qr2 +\=22 =4 frcr< Eftqrq< qnqn-o "r<-<6 EF qrf< E-rr* nt s : @<rmoR< m 4oN r fi ltB{ {c{r aF <-qE< {Fr 30N €<i qE 4fr <rqd dt <rprTl &-{t Tr< I c) ii, iii (d) i, ii, iii {?FI Eil \\\ qfur+*esr6{ftsrlrrEtt...

38. qFF dfro r<cut f{T{s <-€< qwEr sFro 'tffi<- (a)fre"t G)&N"l (c) {fl{ ',{:[{Fr: (a); E=!ldz;a = 1 {r{, +l=2E :q. ertr q&-d ffirsrr5d +Ft< cfift+ orytte +s <<e lAns: bl (a) 0.017 rads-1 (c) 60 rads-1 q6fq{ro<flq{- (a) rS (c)q-sts-kSFrs 43. q-s\9-ld El{-rs-d cFrE emrqlfiru-d Eft"lrq.d qlrElr+ "r<-<ff @ ore-* B-c< ms : 10gm \r-r<T est Pfq"tt <<r+ 166m ffi1-6 qffi {sI{ qs El6s &{ 10ms-1 6ret qTE ES{ aslst{ mr{flTi1S(qr [C = 10ms-2 {ir] 40. {{fufr{(s{eftEl{$s? (a) 7N (b) 10.9N (c) 10.1N (d) 100N wqt<Iq: (c); fifrrfr{c"b6 , (t'* r) =o.or (S+10)=10.1N 41. JTFfiEG-{cg{oFEFFS? (a) 100N (b) 10.1N (c) 100 q{t{Fr: (rt);wr6ofrTcs, = m = o.o1 (#- 10)= e.eN +2. $+<v r€-{ <lt{f( cfn q<( ?<Fro s-<i<r"i< 47. c6ffis666q6 45. E<Etft Grc6 E\etrFrFr qsw{ <JG' frcens fr(5r 6$1r{1 6S(E I:IrEGT C<Ft vtft rr{ $ir6{, iI?Fr Frcd<q<"t, at [Ans: c] (d)a<g o-, o., (o Er<s6t E=l 2 (b) 0.105 rads-1 (d) 3.14 rads-1 [Ans: d] 61retfr<vtrf( (d) cdftrv<l-{'t [Ans: bl (a)Qftq1'rs' (c) €stlft+ &)qRfrSPrs (d)Rft6c'(T( [Ans: a] .1N (d) 9.9N [;-gJ a--{\ . \ ("'v ''" ,l td) 9u ,.5 48. 44. 6$Ir{I<{Kwr<1 20% Ifrqr{'lB.l&retfr "i]R? (a) 360/o (b) 40o/o (c) 44o/o (d) 800/0 (D cffire* q$R-{-< c]ffis q-ss-rd EIT$ {* (ii) {r:r E[s< q]-g Rq ftra $man vm< wtttr qssmemoYL' '3 (iii) fu-6 fr F-stGK q_ssF EI{s ; M r, frru-< cEnBq6oz (a) i, ii (b) ii, iii (c) ii (d) i, iii rrqrrrFr: (c); Ep x p2 = !!z = H - * = (i#)' = 7.44 ;. Ex, = 1.44 x Er, .. "iffi1k "rm++"2"r =)^r"1+ imrv3 <q>RrdEfrrE.d Efteirs-d \fll-{trs q-a<S qrtd BE.{ EI,s : 6fkqt qTF {s{r<{B 5u (<['l Dai:tFt m s6d-<t eFE <g qse 4gfiTiIT u c{C{ DaNFI 5m w-Cn-<t q,i-< qsF <grs <]-sT ft-e (<( {l€k "rd <€ EE e$F ft.s Tq q<qlT rcrs atFF-{ | {sw{qFrcltE<6'I$s? (u)-lu G)*u (c)u {:rt{Fr: (b); 1 x 5u + 5 x 1u = v(5 + 1);f u = v ,{t {isr{< qIc{ q<( {[<- [Ans: dl (a) elffi e<(s{c{'t EsRt Q{ eltrs (b)s-dm f Ifr qtr,{<('tffiR{am.T (c) 'ifrI& q<(s{r{EE.Entel{ "flT (d) 'l&.lfuem 4|{ q<( src<'i Q< a[r$' iTlq sLT{ EF{€T+c<rQfuq"ro xrv({cE frr5< cslqtr {w? l,s?fl64 ){ (g-d qtfr € eF Gtrrt u1 € v1 q<( lT <{K qlft \9 el{ 6<5[ u2 \9 v2 l] (a) u1 =v2 (b)ur=vr (c)u, = u2 (d) u, = y, {:lT{l{: (a): vz = lil uz + jA u., t Vz = rrr - m+m _ m+m Q&qt"rocildi ffi@{irfrEefirs- IAns: cl (Dv-fi<'l (ii){Ifrs.tfu (iiD'ifrl& firrdc{t{En6r? (b) i, ii (c) i, iii (d) i, ii, iii IEil (a) i qffii{qsrcrFffiqqD-{r...

a 01. <ffid{Esl-r$arE? IDB'22,21; JB, Din.B'22; CB'19; JB'l7l EEE cerdT T€< s'kr eqs <Er \e {Fr-?r fuTloro-:l eclsdl ErEI {Fi31 ElE I Q&-qrr+nrv(<tr+<mz IDB'22; Din.B'22, 191 CR'l9l Nq?i <trFt <I c({c(..oo61 ?Irfu {ffi< {(qd< tn< {ffi{wE< m1-{ ET, cq}r< 03. {afroQfuqt"roqqq(<ffir cdfi-o s-<r<et otro <re? IDB'22, l7 i CB'21 ; BB'l9l ffi cotr+ fiffi wma qk"ns T{T<E crtnl Tgs"tl-{ <lIn'T( cs?-{ e ?<Frs E{trrcik csa-< sqF-{rf (da$ s{FPt {Frr $mn <e< $r qffi< ct'l.rs ${ q-usr e cdFro c<c'R e"FF4rs & qcf< ct"tc$ T{mffi ag< dFfs v{r<'t <ra r 04. Flsl-"r<]'t{fr(fi? IRB'22; CB'21| ftft <-olni mE< <t c<e5fl& EdT< wr e$E Fu.1t <ffi{ 4(3tl-q;t I arylft <q< qr-n< riG q-ssK Fkl.t $m{{E1dltsRK{sFHf qlrs I qt w-srr-n- Etfis sirm <EF-'fCat <ltcfir <M &ET Rro tE <F[ q* {f(s mqft <o 1E <r r er$t <tsl{ <i\ft r {rq r 0s. F6ff? lcts.B'22, 17l SB'22,21,19, 17, l6; CB'22,17; MB'22,21:. RB'21; Din.B'21, All B'l8l EEE * rnt* 1fu<u <c< Bt 6{ F-{rs {d furf.ft-e A Rn< \{<q4 eE-< re q{q {5q-< @A< - ceEl T:I]E sc1-qa5q ffi a6a I c+trqt frffi wc+< ul<p6a gfi GT(g {5FT €I;I <g(g Y<Gi ItrCE ElS Er{< lBB',22l p@ mtr+ ry <e< c{d s< {fr ,{$F fiffi k1cs m€yle F<T ${ rIF sGr qsF Fffi wcm IIc"irrF & m€W <o+t< qWm e]{-s, & fiffi qrs-{ fic1r$ wq !r T{tsr q--ssEi sTtr{{ wl{ Er, eRtE & fiffi qt cen-o mSW Tg?FcEt E? 5gr+ u-e"i&<<irn(<ce r qTs-rs&6<1,<r{{st{s<r{ | 06, sl-<FFrgi ft? Tgtsl<r<wi<r{l 07. E@'iBr <iIfi( ff? ls B'22 | ffi coliFl <tr q&F +{< sl< fullfte $irrlo("t{ffi{ER & rs< cr fr'gfrm{Fw$ & rNtffi qfurl<qsrc*ftor"telr'{r... (I rFiIdfr{ECI bEIcr& ce: fr'tE<E<T{R{ mi6 {A*'Ru-F1r+ q* € l1{IEo"{ + 08. qvsllqt{sFfr$<r{? llrB'221 @fi c+6 1p <o csrrlT €sF R< wct< ut<ftro sr<ffie EC'g_ en$r{ et qffi< qr{rm <str{ q-Esk qfsrsficsqa'qc\9_ e&EsqFT{q<<{ s erhs Ecurr$< \e-K< eoirP-ffid cT&,T {<flT r os. cru{ft{E+l6s<ro? JCtg.B'21| @ft cr <n< ft${ c$clT <s wtwfu€ {s"iral DEIi:s afirs q<( G T{ {{rys T6{ {G"rCeK {6{ Ewl-r< cssrfi frce q{tq mE,l,e{c"l frrt +r<, sIroccuTft<q{c{r ro. qrfiz fifi cr <tfo++t<"tR< <ere qfrftq a aftftq <g< "|oT q{{R qR<\6{ s-<rce Dfn \ofrs nEI <FI I tt. ffifr+<r;r<qrE-IE-Ns r IJB'2r I p@ c< rct {E s.{ c$]r{t (q calrs Ee,"H ss { <-it( q-{Fi T(dK s i:F{ <(E<t {I{Iffi eFFl.l{ s& q66ffifrEaq{c{1 ssr{[t<tt<+"t{EEfr{r lJB'21; Din.B'21| EEE u*q crpclt <r<Etii E"r< ene <tfoo re ari q{, E"F {<{fi-d mlB s{r{ l C(<fru afirs I T,1(fr( cslrt T,fiF <rq? lcB'2ll ftfi +rot< EE qtpfr-o \e-rq-< q-cq c rsFI ?sR sr< DTrs <r(ft( 6rt tTrqr t+. rqEGTft <r+<{(Elqt€ I plllwawtsrs:1sFFt-< "rcq qm6ffiE T6< B"K qtrr+-g <rr< cqlq s R"iA-sTt qclR rs-€ calrs <]?wd ftro qsB qfi-o <q frrt sr< r qrc crERTft<Er{6{r 15. E-?ft? tDB'lel p@ co'rr+ T€r Et qrrs l<l< frt?-s$T cs 13. lBB',2r I lcB'2r I rqsr fr$ Tr< {{i 1E or< vtrr< rr <ce r 16. ffiT4+? ISB',l91 p@ cor+ <e< B"r< ffiq te{ {ct-< ERt € fiE<Er 17. q.{(<sq*r{{qFl-rf <r{? IJB'19I EEil c< <e crtnf Tc< B'r< fum s{cdr El-rs clTTr{l "ral !kr{ eIaft-s q+qlT qFI{ ,h <-{ +\6F g\9-$Iq W Es TI qrs EPr(<$G|ftdf {4 {F I

qEr{frs6rd DEqa 02. svElft? [@ vgst <e mrr+ {s< qr Qf',ftE <r't&+{ q<Sl< qfr<\in-{ <T<t cnsrl-< et?rclvl I a cQ: Re]v <qnr{rqfr 6ff "tftst( q$r<-qr$ E{ s qnlT Es-{ # ot. +*q{tE6e=qtTfr'-6{qtqls "fl\3{k{sFHtT.t<fi1rts-{ t IDB'221 [@ c+mt ofu +<r $ft\i EIT ftq {tE <rfu< B+< e$F s&fr$ € Ec?trn F.ur T<q {ttrd LE--',-t s{ eexl{ ffiftn1 4qq ql{ s'{ e <ffid fu'{lstE aFt qs r qA fi{ {IFIS qls frr{ q$o 'j1.€*| TsFr-fl F:r I oz. dft+ v<rcr'td ft-r fur{ "fFsTtTl{- aiFlrt Tir I p@ $+ vr {I("rm csl6{f {Sd qwfd ir-l{s q<i dfts 6{c"k eqvqro cdfrs s{r{{ <ra r qMvtfr, dfros<<ut, i= ixF; qrtfq i € p cr vrrw<fu i e<fir<rqr< & vrq<ERn-:11-;r<rq-q q"lff{fiT{ Ekf dfi-s v<r<cuf< fi-o "ttert sF r 03. E-{qEr qs-dr qtr{t{t 6rcrt e$rg <t{t qs 6{5;I? IRB'221 [@ c+rr+ n-<vr +s {srq ctFfi qr< vt frv'< +r< +gs ffi< B"r< r ffi 1o <u vn-<r ffi , i = r x F r fiffi conq<E emrl< 6rar, r scf1{a qs cetr+ <r-q< Emt"tfr.T<pgrc mft<<, Er6< ffiqrqEo c<FI << r eq-{'ffi qR{Ft firg q<qr< asq q-r+r qI, c{Rf EIrs <trfi qr, {tr F{ <"r Ecltc'l E-{qt c{FrI {f{ | 04. {f{<\5 9]Rft t{ <o w< w{ c'lIE qT 6{'t Tsq {Br 6{F-{? q]lrrt <rq r lctg.B'221 EEE $ carm T{ cirq qR-s 't& <tgN eltrs frg <tffis "ttr ++co r|r-+ 1ffil<r qr Tk"t "lFFil< cdfi-s \r--{r<tt T<-{W est efiro I stQ f<V +gco afsr{ 6{rt s.fi\9= etFF.r{ r Sfd.t dft+ s-*r<"t, 1, = 11y1 4p y = ! s{0,, " " i r sft qig <fgcu .n+rn F t s:rc\9- aIFFR I 0s TfsF drs {i?ir-{ qn-dtfuq cssrd{ frrs 6qrq rts FF c{ rs-{? <irlrt +-< I lctg.B,z2l [@ <tom <iko :ittc-+n Wr<rfr ceuffi <re< fir"t ttcu eiro { <|* oR s,ru-<.fft frq<< ft.T arE qtcr{ DlEIls I qre sqT qT B'fl(.t (mg sin 0) &EL<< ftT stq 65s 6q-g,RTft €rs E tfiE T.(r r IDB'221 IBB'221 07. 6 ffifrE qq ffi rq 1E +m w arfto<.{qt nt s r p@ q6't +q 1E< wl qtft dfrr r{ qrtl ElB-'c-rfifls <t r Itr qtRs e"n qcq{ qI{.c"lit FErcci qrs q{c<-ir e"t< m qr<r("t <t fr-odq fi qrgFt sr< q-ro qMrr rq <mr lttFcigr-< ro-$s ev-F \e d'ao efs-R Cfr@ql RsT131 etr utfu,srfif,s T{ 41-c{ qfiGsrqqf+.(<rq-dAg Et&Eifif,S T6{d "rW€ qfu "r'fu ft-w e<iq <rs-dfu-fi<q{.6$.Iffi {I{rG-?r€ 4Rrq{ E{ {I r qq[lrrlB HTf s-dlFrotErs[ftn eqfid"lffiTE{{tcfi?<it?lrlF-{ t lJ},zzl Eil mr<H fi+'6 <tq elwrfl F'r< .o-<H FiecB g<"t ern+ a; +rq lftft< vffiv y<q q< {l.cet (ottril Ek IE RlcIr eq-{i qffiq g<+ o< c+rr+ tR'+c'lqrdllslFr<t ffi, Fr+t-e €q{ w - m(g+ a) Fr<f qqrfirt E6[rE a = oot{raw= m(g+ 0) = mgCfts, \Bqfl{ rftil 1R.<6{ TE {t I ilvr<<itrftr ed ERffi{Et<rtr8t<rr lcB,zzl EEE iffl "irat EIG r-qk cr{ q1g'K frrtq-q r€< sfrIt qgsl "fiGBro qrar fts E;r6 crqrs "flr<r q qvqeGqs--<Iuq-+'tt&Ero esF m'urft<rtr<lB+-<rsqsr eq-ll uit&FFl-qerlscrs"rrfrsfibr{ 'it&<ts<qfr$fu$r<r e Ft<rqi<r-sk<ir$?&Err{ Ers carrs <8r<< EIqfrRtt6FT<tsq{ts <riF( q< ef(Tlq-{ l{{ | a CQ: >reFIwlq{{s {$e{{{IEET or. sls fift2 EEil {<q-rq{rT{q{r ?l<<g{tr{d 6{<Er 6$t({I <g< B"r< er{q qg s16F slg <EI qFI r rE

qql{frsB-rf,lEqa 09.,Iftft frq'qrsr {tc,trrF qrlw&cs qlg+ls <q€ {r(? rtfitrt **-:r,l'rlrt F-?r I lcB'221 EEil 1FI? fre qcw ft'1ffi w6fuE qm6{-<E Erqs {6fu EF{trt rlrr {r{r Dl{frrs {arft< eafrr"i< FF{er b"r{slsr< q\errs t( cqm fRa-< WV aft1 qa6 efcr 1I r frE ftft-< dfr'o v<m"t qsR er6r I Eti N dfi-+sar<ata;q+<tqre-{qft-idn-s6'yqmq<<r{<<rorXtu"tffic{r eqrw{<DT<"rtfi']ft?< U;G:rql;retfrs;ITr 10. ft'{t € e&fr-fia{ "R-lqr+ q{fiE+rd{t-<fl{fisrr EEil A'g rg qfrfu< {l;r ,tirFr e ft-+ fr"t?s qsTt {€€ q<t qr{r qqnrs fifu{ 65s n11 6qqfl, fiE}5ag gQtqF'q{ctc<, ftm s eGfrrrr<cr{t&a&a{€<Bffistqrrlr rEm 6$trlt<€irb"r-<tfib<qfdrE{ {<'<Efi&rqsqtr l l. 6FFfl{<Er q[nlcrtq-{qtFE {Er{ - <rR]t$T I p@ mrnr n<vt< El< E{q <q &s llrl< cfrfts V<"t IP $<ru "nc<-efr fr*,1sr< <ar csFtlt Ec{Ft s'{t <G(q ql-rr mlrfl ftrs EcnFt f{I <{(q EFr E"R r q-{qF F<qtr B"K {{F{R eT@ TE cT,Bit dFf$ yilt IE scr qI, cF]< cqt qrl rlrlit <Er <fr r<st< <Rr+d ERs r+siFr {Icel ETll-lGI elcFi s-fi Et, Efqre rr6{lE rfrPrs Y<"t IE $t-< {16rI W<t( E-{q]< q 14{ EfrnT ftri $5g qT@ {cai-< {Fr, {4{ qs ct6 <caiir q.mFI fra< pg vt< +u crl-act t"t EI-TFI F{t q[Trq E-]:r E i< r 12. lrlcErsltrqr ffi@ dfr+v{r<ufjl qst{<Illltfit r lDB',2r I IRB'2ll p!fi q&< Dtft]-< +tb +{ c+fO< c+m Ert qr\rq1s- Tg <r+q< $<furc'-<woB {alle1 sl<cf q{I qr'c-ro s:r <6r ar-qm eLTMi-{F6 'Its{I {ls, q"l]-r{F]glffidftft< ERFf cn{t{fsr i = i x i = ltl = rFsin0 = drr s{R, r <t a ss 6ft qc<, Esi 6FI F6 "r|€il $r< r ql;l sst +{cq F:r <6r qc{k't er.qqfrT f6 "tt€rt {-r< I umf< nb-<{zs 1fi tBc-s e T-{s{ E 6 Emq-{, vl c'rF rlt61qfsffi< T{ (r <I d cqD F qciiF <ar (F) s({Ff c<rsE*rftgffitqfsEqrqs:r F Emk't Flfure- E-f 'fieatn*r\9-tiE"f Rlo-{ {@ rtd Tr{qfd IR{Iq;rc I 15. <lfrdB Rfrr{$t+?filr' c$-{z [Ctg.B'21] EEEf,<rmo qeftfi <q s s+r T{ T{, E1t <GF St +?r< r <tfos qtrrq <rfi-{ o*u ,* u1u, sB a t-$+ eas<rr<fr"ifts:5Qw efrfr*<-t'tE$rrl'nr ,{RlglB <tfrscfi{6<sleT|itT(.t \e sc{ {mqtrs(q<rcr< gdp {c< 6{r{t Rb(E cRFt r6d r qld {FtITd ftr$ s&fr$ T{ $:t Esrl{ qft[s ars qko <q EITFI s<rcs E{ I ott<tfusSt+?qRTr t o. cow ptFtaft qft-{T crr Et cls stq irtr ffs c{-fl <llyttt :F< I - EEE Qs qq q<rq sgu< emo +m frg dFio s+c<{ qq<s"rftE aF{]T (dftr m"t (o) ifr otlrir vcq ws I{awrvtr<tvfi, q-Ee-1-<sFrs, 1 = J dm r, r Ets de F{c{ w +tr{{ 14r vrm ffi w<qn +r<, +rq q-ssR SFIS fi{r frE L = Io = constant effm I I rF:tIF o(= 2nf) 6e {T qdlq q44 AGr<rt s O-ff lDin.B'221 IMB'221 IMB'221 EEil ilrE.ikqr r+rq<lTrqR-{<1fo-Tdqflr-fr< 1fu{ q{{\e-t-r<q(\9- {-rs G, st-<qwErst{s ie Cdfr+ mct< qffi<srfrg c<rq<Ecr celrf 6flFIT{v-alIF6e{s,r-df s{+, qtur< cfrFfov<r<ut g< enr+ sdtq, q< q-w-f< el.+s re ffiftE 6464s E"1'qa q+cry q$t afrs r t r. $+rx c+tr+ lltir qvEEr sF-s FFt qrq ft Eil <rl-iBt T-{ I - - EEtr qq-ffq crtGrTT€< qgw{ slTr c<FrE6q{9tr{ dftos-<r<"r, g4q "tFt& c<FI{c<rm eE${s{ T€rs ellTlrs <r y{ctf{q-{ sI[E 6Fr 1fu"r <ffi{ ercfl-q;r qr{ | t +. "'n&-< aor< Tlb-{t ntFt{ ffi rE ft t EtEs{@ {d <r{{l -{ {fr { lqrs,,-Tl"tlt qd I ICtg.B'21] lru <]e r:Erq Fs s q{Gtfi*nE,

qql{R6la oE rra : s[<IIII-o8 1 7. tffi Ere Tfu{ 6IE|{ cslslffid {lft fro "rca' qt m{t qrf$1 l''q r lCts.B'2ll [fismste $t<atl crnr< mrtn< *ft< B"r< ffiE rcqft s c+sfi{ft <q mrl <r <IcT,( {<r+< Ek T{ W {cr {liT, +m <tft foo "Ie rr].r rtr t-q?Er{ {{m{F s-{q|{ cDtcffi fiffi{, q& Euu-m s&ofu +c c<ryeft e<( 1{ffid +re 6svm {E€ IE q, q aqer{ ,r+,er< fr{t sr< <rFrl( {<r+{ Ek <dr t{r qcr {r{ r *rqlta L<ffi< csltrtr{a11a65Qaq6 q66, @r++ "rq m+r ts. <rq<<rqdfrs,qF?F'FE?{' qsF qfr qT-a- <Tt"l'rt TT r [@dfr'o en-+qrsG qFF"rt€lT<l{ruIrc<cqffi qo+r<rq<ecsfrEt-{ (N) r qfq$ffi,{EF=ma u513 qFS = \e-tr<< qqS x Y{C.I{ q<i$ lsB,2rl .'. (FK qcF €TF Efr qF:F r l 9. qls eblrnI <l el{GE v-{qF T{cq crFr ffiro 6dPrs F t 6<Ft qr<? <lllrt s-?r I [@ cfrfto v<r<tf< qq<Fctfu qttffi<, Mr12o, = Mrla, + a;l = s1r1z dFi+ c<{crF efir€r 2a ffifi 6e15E qfq ffi€TR qr{ tr{rt fiQrT \F 6f{? IJB'2ll {s ebffi qr{fT r +.:r allrs q<( EqrRs q{qT r mFt q[r+ r cfifts s<c<crt< {Ks"]-ftEsI wffi ebn-+ q<ql* c,.) c<Fi q* q<< EctRE w{{F - 5q qn 1 qe{F, qE eBk{I q+Ets rfrft+ m{ Gft sr r 20. cq'fiffi{{krt {iil crm<qfuRsfirsfrr<qlm 6q{? [@fiEnr+<orpryrr<, qtsrsffiqqFsR"tftssfrfrTratmr F1 = -F2 r e-{rq<rcftet fi6tc{Fr(E fi Tt6ffi B1< tF$ € cqr q<( e-{Fr <FK E"r< qfr &rt fi ffi'{ r e Efr fu Tl <cffi Ts{ affi fr qaE frrs qt6q 1 21. $ags6as;o14T<ie {Rs6fte-{ ffi "t@'qFqt a:-{? <frl <rd I p!!l t-q" sre wu {+<s "ftF sG <Iq&< "ttfr "izV <tr + c+-sfrTt <} qerrFu <rq-?r +Erc{ r Erq <e 6rrg{ ft-m oM sr<r \s{rs-E'<q <lird<r ft66 6rq rr< I ,{t q{c<ou <ce< Fkr"t<ts&rqfi"tcv{T{r <rS-dW&n ffi<Erfrrtr lcB'2ll T6t Fd ) t{g<s{ q<( Y{cck e6lsE.rs fi TFr I ) I <f{t( Fb-{ q<(<rdK 6sA< qq}-irs }6 <r{ I I r aro-< <eo fiEi-l 1t t.; 'r r Br<6< q+-o ftEtq-ftbr< N-) e r <ur EI c<l+ll' lIT ?<Fr+ c<oiro FE mrsi qR+6qq<l<t*r 'er E6 EKt c<w {t{ $ig {qcq ffifi-q 6a{ qffi a-41 c-gR 1 q{q, ss q-E(si {€Frs rldl(.tt {-r< r qrF qkeftF r<E-flE?F qI{EI ri-s-dTliif{ rdllElo a{rl z:. '21: DR' I4r t<E&-+ +tr<rmfr-q{ dfr{ F tccf+ 6{-{? [Din.B'2r; DB'l6l ffi $mn <e< crlfiI F"ir< ?<Flo 6{'t qsF qrs Q p"6 619< S"r< fi-.6rih cffi€ ffiffi 6q5t e1 qco E<r € SI wEt 2 mv -7- qa-rq 6frf+s {fi"k E"r< fi-ffhqr stt{a ur wrtr?<qlt'ce "ftq< r+efrW We< efst cfllot T6qs EEE cfr-o c.rr.T ete ch€$r "1r{, fr+t s <rfu-< q<r+cuf< qqB g< atrco I <fu aqa frq 6a6q Er{F ch-{, s$r s]T cqs{l{ fr-rs' E{F[t< cnft cW {l{r stt q<r<ci;r qqB S-{ <FtF d'sl <lGa s"{r:rc'l3r:T{l{ v{r{('t Ptqrq{r<rI-{r lcB,2l I lcB'2r l 2 r IIIV I -TlDin.B'2ll

q!il{frEEl OEI're 25. Tr{d{ "t&fu< v{r{crkrr(<F.tft& c{r{rr{? IMB'2rl [EEl <mB <<l s,tr-r< frcre tfis er e-rF c'rqq frcs arrc fi'fe srr uBM fi{qH{ Fr{ "Rftc< "ifu< fuAs ft5q 565'6-q g"K q+E <r 1E <r r qQ s&frrt <c6K TrE <r+b Sqrr< ftr+ urq r fiEiFK y6r {qr$t<, qi fr$ <E q<( EfrfuTf T{ {:rFt ET r Fre, At q{(T ?RIm{ s<r-<rlT qfuq = <rort< E r< e{@ <rffi {E {:rFr q{ r qs|r< T66'&n qE s<r<r"r< cc<s"Iftegf frrl Ean r 26. fr{t € q&frTI cst {6d6t<ffsrc<+t-e+r<z IMB'211 !Iwrt fr$ e e&frT1 c,ffi lE &a rO< E"r< +fq t-c< r eoq T6{ E"F sM F{F "tlr< ll I ^.+ -I, EF<€ ., 4{( m2 r m, <OFlfr m2 €<Bfl<Fr <EI qc{PI6G(, \e-r< mz T€F mr ,n nn rr. c< B"r< F, {q s6spt 6Gr r qrmrE F, = -F, g<l lerl = lFrl r oA 1fr&f rf<S.m \_/ \_/ fr-$tmr Fr+ 27. 6$t[;rt qr$'d {tre[rF q+F <g* u-q{E< vlct( o. s m T{cs ft c+<tta-'r IDB'1el fi!fi mtr+t jl <e< crq v{ fi erF Fffi fr w mfi w <t ${ <tcg Fr<qTF Fffi srffi Tttqrs & cq€Ee {6$qk q-s\r-Er elTs, & Fffi qcffi qlc"r(s rr.d !p 16{ q-sEk ElTrs< wl{ E{, Ef{(4 & fiffi qt rrne r€Qps <eo{r e{ 51gto u-olG< om( <rE r ueot&< <ml( 0.9 m q< q{ <gE{ wq w qs cefrs 0.9 m Ec< eTFR'-{Tss.-iTlsin4 cw.\e-l-?rslTs "it\e${r<q<sF{er$sq-sir-ksFlls<T{1-{Ec< I z s. @ <e *rcd< o1-q qr-{rat qli"<r c'trq {(q(E @qpr+ qr< ft ? <ilrtrt q< r ICtg.B'191 EEil ltr <en w$ Qi\5qrls q${ !trE, rwd< a{ s 'ir{ TgsG< {qlsFr qmfr-s c<'l fl{ all-rs r s,]-{l-?r, Etr <g<qc$c$(!fin mrEccsr{< t{<wqft-+ c< J \tr'Frq\e{twsl-flBsr <frqfrre wracft "l3r q$'cl-cql qtr+ sm, .,*r< EIrq-< qtclfus 6't {r< {*r v{R r'$r(< "Ir{< q61ffi 6q qt$ q<i rrsr(< "rmd qk"lfr-r c<E tl, vR wqm+ 6rrj< "ifr-<\i{ !A<r qftnfr-r 6{rf s?r cI al.s'Et qttc'{ qBrs col6q cqs{E Qtrq"r+<<"nr 29. v{rs q]vt\sir <-dTl ?{{ 6s-{? <frlrt rFlI I fi!fi mrr+r w <s< s<E <-qI qrgl< rRrT"l r qt s{m q]sr s{ <r{ | 59361 6Aa 1e'ffi, F = ma + 6 = ! I qq64, m {tr{] {€iit Elsl s{ r qMi 6< Tsr c-{ctt3t }met 1fr'qnf r 6 =-ft,m, =fr<w [sB,19] I l{:qEr$ttc{<w{&-r\r-l 30. qvst<s<r{T {rff '||\3Tt{titft? qfFlfF{tsir I lBB',19l EE csrr{l {€ G srq-r{ qrs Et<l ff q{{-r{ {ql{ afliFR er<"r'c-tt qrqr q--sslr qR T4 qr{I <I ftK ,4t eKqElrs <t(I cqT, {€i qft'lfus q<,{l-< qffiqltt3trsR<EilI1-T, q'Vq Ers <rdrd $<ql 'it\snt:rl-{ I 3 1. lftfu fiq qrFd Efffr.t ${ctts celr{ aL" "lRft tr6 c -q< {r;rd ftfr"l qfr<6{ Er{ <rleBt is3r r IrB' lel [!fi 6mnvwr+<E"r<1ft crtr{ c"rre 1Frft at g e<*r+< qffi Sr< r qt{T{s g' = g - to2Rcos2l r qdn1{qffiSc{ c"[-{ gq<fi{ or2Rcos2l {fu"f Ifr "tlr< r 32. 6stnt {€ir €ef{ ftfl,ft-dr ffi s-fi t{ q{? <rl$t Fir I lcB,19l EEEffi{ffi{FwC{{cF<Atq{rfrftrcriEcl€ellcsr t = Ior q{Itrr, osR|| 6dftsV{or = 0 CCEE6 0T{{r qqfgf€ i = i x FrE]t<rt(<<rE<<qffiE<esffiwq{r ::. $+<s l-g< dfi-o E-{rirt 6tm-t(6w qs-<il$t {{ I IDin.B'19] p!fi c$triT R1 <T qq6 6qs p6 1fua1-q cr1rlI TGtl-< <$fl( ei-< e<( s-{r<crk GE< e"r$qrs & ftC <I qcq'-d {k'rr$ Fct1fi6 6dftr v{r< t <rE I sfr. 6rIfi T"tR {,t{t( @E-< i q<( E{r<ri F qq Er< cfifta s<r<rt, i = I x p .'. L = rp sin 0 r qiT6t, 0=0"q[s L=0 Egr qdtq, v<r<af fi <jI4I( @iLT{ ffi qs, GT{: {f,+rfts'rfr, Er< m ctrq dfts s<r< twss r E \\\ ,iffi+*quimBgr'laXr{... e

qEl{Rcrf, !6t eEI : o[ifi{-o8 34. s:$"r{o (FEwt1 sctftaT <{- <firlrt Tir I r{r-r 1ol qllu el,l\s1P'l-ll6l lq- lrl1rl<P{ I [Au. Br18] [@ <'fttT[q.<mreqFfrT<osslqtsF+r<csrstFfi"Ft{6nqH<&R--{cefrL<,{rETEstq.I$EsnIr q,fuaaqfdf FMffi € Wtsfr-T{S"idfr-r?Tr-<l1., ,lG"rcakE"Kfi6qr<r !r("tT{s\fodq "jr+qt?s-{f sllt Tt r eli y+t T{ qt(<s6f+{ <Er I :s. <-eft,9-tr{ ffiq {f+rq e<lG {g qrq.&(g {Fftq ql{.r{ Et rrm]l r'< r - Egl <61 6{CrF {ICat Tsrr{l-Cq a;$ +<rQ <-g qlFfus qIFFF ql-r{ I rfiFil CTCSt"t E|q q-{r connr con"t <q frnt siirn 6fi'F frs <<1<r{ <rr< esB Bflt\t {rfi< r ei E"rfit T6{ wtr "tffi +r< c+qr< r qstr T€ cqFBlE T*r+ qrq ffi qrm -E qa r c<rs{ft fi Rcrld {5rr$rt frxt em r +rq FG qffis q*ql I 36. rrsrd +qs q$ m,Hfi-r+ +s crE"t EE <l{t E{ Et stir.ttq <rFllt $?r I IDB'171 IDB'l7l 3',1 . 39. 40. <tot< d+no qtt dr+< mm< frc3' Eq<tqlqTr c<Fril {sFFtirirclD-qIE Effi T{n c+is< ftro mrult <e Ec<lq.r qrr {T(ft( q<qT rIE< aGft$a5asqrB$"tt<t eq<rq< cql"tF fi{I Rcos0 = mg€Rsino =It;. 12ng =i-r=tan-r(,*t'; (lsR <1rs< <ffif( s c<'t Rc{< sT n {,T(ftr rot,t Fft<q <-<t ss r Pmg 'qvgl{sFrs sokCror"aEcuftffi? lRB,tTl [@uu-O<oro s0 ksm2<tN1<1T-T€Ers,iqrmut<firor."6.-z ffiftog{cct{dlro{F sgNm1fut F6 Ecslqq r q"tlgfa{ TqI <l-{ c, <gF< b"r< s o Nm tr6 EFH €{f Sm, sl 1 rads -z rfrft+ g-<r.t a<r< r 'wlFI v-r+< Et <-g< @{"f<t {W( ECE EI-?rt 6{'t fr frT{ q6g -TFffl q< r EEEI ., u m, v-m< @1o liqc{, cc{r{i Td 6{el u1, u2 q<( T({r(T o1.6d 6<ui v1, v2 qrEql'{rutfr, " = (fr#) ,, * (;h) uz q<(v2 = (f},) u, + (l=h) u, h, = rz = mqrq, * = (---:) r, * (;*) u2 + v1 = u2 s v2 = (,,*.1!-)r, * (__.,ry) u, = vz = ur p<B, wn sr-<< qF r€< @"rF c(q{ Erq Et<l 6{'t frfrffi F-{a I frq crsr EBfi-ro qfllll{ 6olr{r <lfur vgur< ere-+ w{+ tcn 6dft.s't& ft€.t q_qd q\"rd fr{ r EEE<tfuT 6sm F6 efirl'i Tr {rq frrttr-d dft+ w<r<'t qqffi a[6o I mIr+t Fntzl< gr--src-ld srrs, r, dfto mq, o q6a, pffi6-a cfrftr s-<i-{'t, L = ro I {6dR q-ssEr etTs qc(s' s-trffi rdfi-+ m"f freq qsr qnkrqt TqFFft wu 14r+< w av EFm c+rqq r,qrs q-se-Er qFrs sF I1r e cdft+ 6{ut 1ft 'ns r esFsfftRdTg e qE-$t qft-ftqTg-dQ&q1,f+c(sr(Ef6d 646rk qfr<6{<ltit tp-dr tJB,rTl !I EEE ,, e m2 sLK{ QEqt"FF qiqr( EI6q-{ cc{rd< 1r{ F{ ur, ,, €i( 'fF 6fft v., v, qc{, qw+ qF, ,, = (H#) ,, + (-:rL) ,, q<R v2 = ;h ul + ffi ,, qft <eF m, vr<-< ig <fesl T€F m, stT{ {6{, u1 = Q I Was, EIft TgFQn atFFF q<(q--{st{€E qFt C<rffr"tAEftm5Br[\9 es.sirr< I rM

01. 02. 03. 04. qqlzlfrsur{ nElra + t . 141 tE< mm q-E\r-k sFra {{K .e-c<ir qrEq]- <frB1 s-< | lcB'r7l @ vrmr vrfi, mrr+ <g< ut&r gqII mci< qffic+ <l<I mrr< er$qt <q q-ssl r ?<Flo ei&< ffirE q-s51-< qR'fi't q[q s{ I qFrk, crlr{ esF qrs-< wr"rc+ {ms o+F <e< {a {fu o1ffi55 qtql ch€TK E${t E[qw-s\9Ke1:rsr!6f {E qs qp6f ffi, t = Int qt{ftq<"i cl6s€ 6{FI[ <I-{ q.s\'F EFrs ffr ft< mrq wgsr< lR{I"r+r a cQ: r€r{rq{rl+{ro {$ e lTqtE-s< <rsl{<il\ft(ficsAT{? p!!l +" 6{r<cr{ 'fi&-{ DtsNrqt<Rr<< firs Qtr+ (TCE tl{r v("1{q <ror< c$vT&s{fr$ sr< !T 'fiB-< Qbr+ qem eKqgr$ <tfl cq-* r utl&E {< FE c<rtl u-crs uccs <j-o fire errrqftT qErg (cErl {l{€ {< c<Ft <rr ft-g q(q <rq< ffi esB fiffi ffTF c<ft qc,c- "fl13 qtr slt'fi& {< rn{&ru d-o fire sfi {{ eLqTqfrT qfuru <q clr{{Rs-?rN {rd {Ir {"rd'nGE <tsT crlr-+ Qtr+ <mr qt Qim {t€$ qvIcs <tsk a?m< "llt csEl-T< "ff,t cqno {Frctf ft$i[E{r qrs<lgfi<iTift!.<cqrqF<+m<rsr<scq<Rs?EfrfurT <cq<,a$E E{ct eITMft{ 6sE]&Tft Tq c-trfi ls <r<'ttfu--< Qtr+ !].erl dft 611 q6s 1 FEEcl-dq& filr+ {roo ftt<nst ft z [@ Agtc-+< {E1a 1ls sr{&< <en qar {crtqrr c< ,rf{ Tlf{ s< "Fi +'{ m+q- trErdr, cslh, frWr ffi<mrcfi€tr+<qB1aerrmlmrTu s<(10-3'ks) frFt? ++q F6l1-< 6<?t c<Ft c{, q{F, qF qrffiR mcur<+EtotEq<Fmrt&ft{w<"{rq<IE{rrfr['tqtr<ctFr<r€q-€{{gir(sGfiEtw<n&lqarsM]ffir e{< 6srq qfrflfuir-f Eg{R]l-qlrql<Er, {€< 9<"1 fi{ {< s'{ (< 10-106.-21 E{ ErF fiEtr{< tl&{4 {c{k'l g'l'Frl FEr 'll\etrI {I{ {Ir q(srE T{ Y{c6t< <rrf< wtlttFo q<r fiEtr{< tlt\9Tq ca{q{lq {{ Yfi"R q-{AefiGs csr@ Er<|qI r rsl-r{l T€ R{ F]'JTc{lrr- <T :i:rr{c't EFr:r|{ qm FEtC1< {e{q emfw q.{r w{q]T frEtr+< {q E[-3]"f s-: Tm Fil I €cq.rE \flt{$ta{T qrcqfr-qrg-f< {e <r{-< o<I Er r ffi c=|{tTFI-tF {{|{mT CtrqmvElEtr$Ptqrq r+s 6{''{z EEE! nUtc-fi n-eT {ql{flr<, Y-<6r F{ qrq E{s {4 s:I qr< r mcuf< tffi W-< <E, qE qk+6,n rc c<ft mt 6€lI Er<, 9<c6l-< :l];t \e\,- s{ << r s'E ffi Crl_{lT TltE {-ilK {:]-aI cll.Fm,]g ClEElrs FiW{ 6r{ 6{.I, <l(s c<rt< Fffi qR-+ir+< qn ffi :rsm Ercq, Fr{ y-<6f q<( q&fu $ {{ +T q-fid E{ r FWr+< i&* rc e qn ao-< wu t""t-6 ff? [@ AW,m flft< qr Tq <s slr+r q1R, F = ma r €:l{, afos rq' {fr 1lI q sRro, a = o r q{ts, {gF{ y<.t W I q\r-<Ir, <]fus 6sl-c{I T{ e{s 4I {(q E< <e R< efl-5rq, eftftq rc 6r wlire +<-et< F{r<, €Elt ui&< rqTEr 05. 6fifi-$E{r< t<onuftI<tz E!!l $+<-o mn-* {6r"iF <lFit( F?< ie hFro s-<r<car< eE< q"r{r6ns cdfrs s{r<{ Trr r qn +fr, ? = I{a roru< qrtt csTcil T€<tcf]-?t <lct,( ei-< e<< 5 = <e{ kFm s<r<ri qsq<, q(EIT{tr{ <€F< cdFrf s<1"'1, i = I x 6 = rp sin 0 ff eB .{str 658< <lFl I qq-6{ n e.FFr{<r frs { dFfs v{r{r'R frs Fr(ft] sr< | qvgrd q:r+ c(@fs qt qr E"wqlF ff z - EEE c+tr-+ "nsa qnss "ms{.e-rd'q<@ qfr "r+*r< et srm< qk"Ics "r]Efr< q-ssl< elrosl-T{ c{E & "flr.- w<fu fi urr< m ft-5ru vfrs et wr ck"lcs "IlEtr{ q-q'c-k eFfr€< qnFr Er< r :rF +R, mtr-*r qqsa 1gs< B"f< q<Qg 1tr "f+-"f< nt ut ox q<( oy <-?n-{< s-gsk e1:rs sc[@N I, s Iu {R & 'flr\r- s<@ Et qrm eq ft-Als qRE 4t oz <<Fr< "lIF<r q-sq-?r qlts t, rc{ffiGl, Ix * I, = I2 \\ I , I iffiffiqEr6{ft6{"l{I5-qr...

qqTtrfrErd bEI 'I3I : U[{fl{-o8 07.,qe frC{ efr RVr{ qe AEr{d fi r+ ql?I cq-{ cq{z EE u-,a- fr'* efr c<rVt-< td CIf+ ig efr €sm< s-<r<ui Wr ft-g efr cqVm "r< efr< qmfi{ frro ftqEf s<mut Bq9l{ ql r q$t, E{trrcrFr {(T{F.f {ElX$ft, CflB s-<i3rt *Fr c(E s6{ {trs{ pRq ftrf s<r<"t Eq"r*.<u Qr< r ev-+ <ao efr< E{5qrtld {:1;1 Eirrirrt PErq TF r a CQ: frnE <q{c{rq{ ffi6 1ft${ emT'l s $ss-a qqqqq1 q.S s T.Til Eg-d --+ E 01. 1000 ks.e-m{ q{D<Fr 7s000 J 'iF{&frr$5-ff{{{$ 100 m {rffi(RftB q$EliF-dqqq-{<qtrilsrd €rq 1 0 m q<( <fgR qlgqraK q'ffi6 E!6Et{ {ffil{ O.Z m r IDB,z2l ('t) <F{F{E-{r{ tffiq-<r 19'tfuT't rtsfrlT <tctr fr.iT"lcEffi q&-qr l'-flu "fl{r{ ftz ffi&Eonnftr$s"t F-d r ch\e<I qLq, uiffi, rr = 75000 J (T(w{, m = 1000 kg qq<t qtft, E1 = ,*4 + p2 = ZErm p=r4l7Sbooirooo .'. s{r{ l, p = 12247.5 kg ms-1 (Ans.) frq-t: E1 = 1*uz = 75ooo = u =./2, 75ooo xl= 2x75ooox#=e.z4zms-r qFl-<r, p = mv = L2.247 x 1000 = 72247 kgms-l S m'u*wrq, <l91<r 4{, d: l0 m <fqT ElgEI-T{ t{I{S Busl, h = O.Z m €rl{, sinO = } = t = sin-, 0 = rin-'# = 1.146" 0 = 1.146" <lI(ft( 41i r = 100m(IF ( frFt? <fuo-< qry fr1.t1qq{ <M "fln {C9 {6{15. 6{et v1 {6{, tanU = E = vl = Jrgtan0:J100 x 9.8 x tan (1.146.) = 4.43ms-1 q<k, Eft"I5qd ffid C<uf v *)mv'=75000=Et=v= 75000 x 2 x 1 = Jzsooo x 2 x -L = 72.247 ms-t (TQ v > v. vlQ m{{ +frrrfi-*"fiq TMT <iS 64s${".t iT I ,ssD vfft 'FFR sd 40 kg q<( qVsR q-Frs 4000 kgm2 r El$tF EFFIET+ 2 frfi6 a666d q{r 300 Nm 11{tqFptft E5 qm1E $-re r s& Ffrd roo (rd {fiqr (q.[Fr {trq< lRB',22l I ft{t? fln&sfi'cilcm{:rl$rc FFrrdlrjFrsq1\e I I 8 E ('D tfrlc-rDFslD< T4q {ffi fi{ro-< r (q) tft,ftsrqffi ftq<fiFf qlirulsl6 {FrtF {F{ er< t-Ets l ut+t6 EGfrfr6 roo <Er{rdr , = T ='""joo = 1o.472rads-1 El$l:{ q-sst{ SFts, I = 4000kgm, sToK 1ffi <<, Er = 1Ir, = 1x 4000 x (LO.47z)z = 271325.568 l rE

qr{frGld !Eqa : q{fiEl-o8 E ffiEqFrflftF6, t = 300N q<( EFffir qW]-{ SFrs, I = 4000 Nmz \il$ilWft.r=lcr+61 =l= 3oo = 3 ' I 4000 40 ffig;q aq4, 6 = *a q{"I, EFFI' AIFIET qdI 6.N CdftS C<'t O qr{ I ET{fdI, o = o0 + ctt = 0 = 10.472 -*1 * t = lt= n.+ZZ -, ='o'n'!"no + t = 139.63 sec or 2 min 19.63 sec S<l(, 300 Nm Rr6 EFFI qlFrIN 2 min 19.63 5es 4lrtr< 1 qdlq, &ft z min e EfslE aflflre "l]?n:Ft qI I 72 kmh-1 6{crt D-{:rf{ 1800 kg v-c?? e+tr <s rttG {hrq EIGTT {tsf 1000 kg v-(<3r qTF q1A flQr+ Piel ft-<F etrs Tcq'Ei tr|€t firrEt r {l?E erd 't|Q q'B oFfrE qr{ 60 m frr{ cclrlr c'trEt r <Erd {r,t nl&-r{ atFFI 03. tru'tqr Elq rlfr, E6{ttr tt{6qq"t {rl qqq qfr e$D q@qt"ro crv( r ('t) Efttrq-d'ilG Et etFtm 6{ d{tclir+tft {E frF$n-{ frE E1-< ctr frf{ Tr r iq1 a1fr<ror<rrElq 'tlfiE{fuHqffi xlcrc{{tDltF< I m1 = 1800 kg mz = 1000 kg 72\1000 vr = -i?6i- = zu ms ' vz-0 v =frfrs mut qffid, frfrE qlftr< t, v = 12.837 ms-1 frRs c.lt(<ut, vr = o ms-1 q<( E<Y, s = 60m gfq64, a = t:!1 = o'-rJ.2,a:z)' = -1.378 ms-2 .'. qrrq frfre-Ir< r+ it& nfi< qqq 1.3 78 ms -2 il&Etr qffflF <I{TqT{dft {q, F = (mr + m2) x a = (1800 + 1000) x 1.378 = 3858.4 N (Ans.) E qrsffi "F{ {eft, E1, = } mrvf = 1 x 1800 x 202 = 360000 J {$T{< qrrilil& EE qsrq EFr, $RCE c(sf{< "ilTd tiffi , Ekr = } (mr + mz) v'z = ! x 2800 >< (72.857)2 ms- 1 = 237423.4 1 geft, E1, < E1, glt qlt< ts<lB cEr r efr estr qRGqtlF cw( r ICtg.B'221 8 E qT<tqifr, m1v1 + mzv2 = (m1 + m2) v mrvl+m2v2 m1+m2 _ 1800x20+1000x0 1800+1000 .'.v=12.857ms-1 ("t) Iffier€F? "6lrl-sFrfi{TT-d r 100 gm wrfit (FF lFf<r{etrir 4 ms-l 6{H B-ffisr{ S"trd <F[s frE {cE r m $tflr(it]Flst{ "ill,l{ifltrrtEcqr ISB'221 04. fg Eftflrs <fu A, B € c frqer"f< wv' 6$t{Er9Wld bt{{<(Ers fiFtcc{? utfi&-o fug<r.r< {tw{ fr(I<ote*r rEm \\\ trg iffirl-dssirrfrw"F{D.rr... (I

qtTI{RGIfl !Eq-€ : q{ml-o8 tFt rads -1 tr E qll31qlfr, v = ore 4 = a x 7= to = 4 .{<(o=? =q-r=4='i .'. T = 1.5 7s {s<l( '6rr$Idt 1.57s B frT(q-{ril{<q Ts qm, Ts = mg + Y = 0.1 x9.8+o,in = 2.58N akq<qriEn<Er^ = Y- *s = o'i' - 0.1 x 9.8 = 0.62N IBB',22l I sfflt$-{r 8 (-Ft Rcos0 w=mg €rF, v = 20 kmh-1 = 5.56 ms-1 r=3m tem$vqerq'qGqfi eta q<qFFtEr'@vftt e"tte' q< {Fr ch\3$ qfQ I qfsr<I eFs nFtrs 'utfu qftt ectlq' <({El\gr4l,NHr{s(<&rl E qR,'t&urr{m qBfrfi 'v' qceEfiatltmarr q'ffs,;=Bmgiv2=VnE=.,=r[i!-v=Vb.1 xJ x s-8 = 1.715ms-1 =6.17kmh-1 s{ts, eE rsft€dq c?rt EBFts {fuftTl c{ro mFt r 1Wi tufte<"r r*6 tkFts ui&ffq| n?|r{ r C fi-{<q1i-i6€ r. = Y* mgcos60" = l1f + 0.1 x 9.8 x cos60" = 2.09N {s-<I( TB > Tc > TA 0s. El'cffi q+t qrEE <f€1-{ qs qEHEt 3 m <itctc(T q<E <t+ <rs[q r qsq{ qltrsar qlrdlA 20 kmh-1 6{crt RrEqltr€{Dtfrfido o*B+q rr-iEr1t 6qgE qsq{qQrir-{srrdtft c{T fr-dt"fiE d-o q&-qc F-{rg,flrd m <fi{r< drs' qsF cE-6-s-d"t csd m{tD {&'ftqt o kmh-l Brs{ qt[Rr Ffsfd drs rrRftl rirt R6r 4t q<( Er*r< s <rsr< Q& v$t e"lIq o.r €(i g = 19 -r-r, ('f) {it .<'-{ qkilQ F\5 6rfc{ caf{ flt6f{ rlfuT <t{r qe${ F'rd&E? firfT s-d I ({) q\rfi-€{cr (?1EERFrE {e-fu1-{{{[{El E q{q <q, fs = pmg = 0.1 x mB ""fa,Y=f.+Rsin0 =?=o1mg+Rsino = 5 = O.r +_-I x sin0 lmg = rcos0l rg mg =+{=0.1 *tan0 rg 3tan0=f-0.1 rg = t".,0 = lI{ - 0.1 3x9_8 - 0 = 43.6' rM

qqr{frsGrsErfs E 06. A t6s = L tr4P =Lx2x72:0.767kgmz = 0.167 kgmz S v'm<tvtfr, R B'fr<-< Frc* q+ € d{:r Ece< &6 AB = t m q<\ v< 2 t<grqtsF\5krffir< - qftelqTvlr{ r:rffirft PQ q(s-d {rms T{{ cfrfi-+ c<rrt1{r{:nn I uB'221 ('D Eft"f(qdqsFdvgulrteFr+fi{re<r e (s) Bff"ima nefr< $r vr rvfra o ceks atrq{ A R-{rs qr{qd s6{ r+q&< <rflr(a ftnq qffi+ Em? rftRF+sfr<r <if{rtq< I 8 {s s d{{ fts< {<lfu frr-s qtrEt-r=R< sfufg qrffi c|r"65 $mn nre< q-EsI< sFro, t = ! vp ... PQ qrs-< qr'ns 1{l.l{FI AB we< q-sEk sFrs, I nn me< &.(l, t = r rn ABE[g<s<,M=2kg - PQ q(s-{ {k'I(s $Fqrq aS qrq< EsuiftT (,I{t(, Kpa = # m q<l-<r, c-:F s T{{ qce< c{(aTC-{T qrF E1-gR-T ft-q qeqastr-< qB+tc q6ffi qlcflrs 1fu:flq qrs< D-@rlfrn <l-tcr(, x= i .'. A Rt frcr qfuc< q&qts qrm {tc"trs qftmn er rce< ue.iB< vmr(, xa = * rn E-sr 6srq< E@'t&< <rFrtc{<w*"ns = Irs = 6 = 4 = I K4 i 2.13 2 .'. ro = 2 11ro qdg, 1fi st o fu catco A fr-Ws {ffi\r- ccq E@'tfr< <rl:TI( fteq qcr slr< r 07. P € O EF Crfl"trF'-d v{ $fl@61 0.02s kg € 0.05 kg I p € Q CTIIEFFEIr$' 2 G 'lal$ dElr CldGt rftq {arq',n 0.909 m € 0.709 m l]Hk{<TsFFk 'rrqqtEfr'+-slr{FFd 30 <k{ilr{t<qr 1ottrrcftu o.zzs N.T{:rq {<P s {al qrs< {llfiq ft-s veqr,or< qfufs qrffi qkoffry 14-aql< 8rc3 rotl&< <Ifi (, x = # sltcs effc<t I ('f) P cqr{rfd cfrn-re-iftrtet4s? (s) p € e c'tFrFF<rTskw$con{9lFfrrV<n-<2 'flR&rstr{R.Hlottfr1&nt, , ICB',22l 8 I E] \\\ qfurl<esrrlftm"t*tssr... e

cfrfto s-<mrt, L = morr2 = 0.025 x 3.74 x (0.909)2 = 0.065 kgm2s-1 P{g<rdftsstrr<'I L = 0.065 kgm2s-1 \\\ N=30rev t=1min=60sec o = ?II = z"s 1-11s*:o = 3.14 rads-1 r = 0.909 m m = 0.025 kg qEl{frEld oEI rE[ 3 qr8l{-o8 E {oI irfu ETq c-S q{rs 'ltrd, F = 0.275 N 'nl'{F, to = 3.14 rads-1 ; mp = 0.025 kg ma = 0.05 kg; ro = 9.999 ;n , rq = 0.709 m fisTt qt-cq, EftTd "flEECsd q$TS [-trg, d = 1 m qlT<f qlfi, .ine ='l = sin0 = ZI19l + 0 = sin-1(7 x 10-r) p 61-aE 146q< mrc {oF ETGit{, To = mror2rp = 0.025 x (3.L4)2 x0.909N = 0.224N a clFro 1{r{d 6sCE {E.lT E{s E]-{, Tq = mqrozrs = 0.05 x (3.14)2 x 0 .709 = 0.3495 N 08. qFq-{ <rG 300 dEr srtr{ esE {crs zo cm ?qr{r{ qrF <ftd q6 qrs 6icE q{pfi-{, sre TqTrd 'l[at s& frfid oo <R5*trqr clts {€Er qF-Yff{t$ tr{,irv (irq&Fqs$a$qr{#bn={r ro "- +frm c<( q&frfrF1{q{$tTt l0 <klk+r<Tsdq<FBt$r+Tfi.sftF{r IDin.B,22l (lt) qtqfr-sq{qtrqstr<dfi-+v<l-<'tfi{s<Er e (t)'tffi v-qT<ftd Bq-d eT6 EE-{T ftq"t qfir<6q+-+rs qc{? rilfiE$stm frr$rtqd I F<Te€F>Tpt 8 I cnsn vrcq, w, m = 300 gm = 0.3 kg <1;*ff(, r = 70 cm = 0.7 m dlto r<ut, o = 60 rpm = 50#" rads-1 = 6.2832 rads-1 _ .'. CdFos<r<{, 1= mr2o = 0.3 x (0.7)2 x 6.2g32 = 0.9236kgm2s-1 (Ans.) ! "iAuf"" *.am . ^' =+= ? x 300 = 200 sm = 0.2 ks {ffi ffir, / = (70 - 1o)cm = 6o cm = 0.6 m "lk<fu (dn-f c<'t, o, = (60 * 10)rpm = 70 rpm = 701?* .16.-r = 7.33 rads_l *-6r s-{ts <Fk bh, T = mozr = 0.3 x (6.2832)2 x o.i r'.t = e.zs N {ffiu w+qF <Fi< Efq, r' = m,a,2 r, = 0.2 x (7 33)2 x 0.6 N = 6.45 N .. "g( <Fi< vu Etr+< qRrf"f Qa s.zs N r qffiv q<qm <Frcs Ekffi "ifr.fl"t qrql 6.45 N I qaip, bffid q6flq .s.[q 6a[Qr lffibri< {frfi"t (8.29 - 6.4s) N = 1.84 N r 60 kmh-f iG{*F qsF &q rzs - <rrnffRFt? 6{q qlQrr rtr 6TR rr{ slg{Ers q6s <fr{E Elrd {k1 lfi*lqrEaRcir "irEqraTq{FffTiy l m q<s. cssrrT 'rF qr,fst<lRrtrd 'flEft-dEi.tRo r "rr', tr"'rt ('t) E-qqFr<fsf{<Tt\fr(6sFtfi4Tsrr u I c+r56+r*+r+tffiF+sn<<m*, _ 8 (_EETJ 09. tr trstr <IsR qrft( 6sFr 4.014. (Ans.) + 0 = 4.014' h=7x10-2m'

qqEfGutd bEI ot-o : olriJTll-o8 E ''t'<csEts, d(ft( cst"t, o = 4.0t4" <k, fr<t+r drq< qry c<uf = u' llPit(,r=328m qF]-<t sfh, ran0 =.sL= tan(4.014.) =;;*= v =.,l3Zg x9.B x tan(4.014") = 15.0187ms r <i-+ qFotq< qr{ &ft c<"t frq 60kmh-1 = 16.67 ms-1 r ftg & <nrft< mm ffi ffftw 15.0187 ms-1 6crt "i.T qc'c- "trde r 6r+< grt fr<mn 6ff1 15-0187 ms-1 q< cr-c{ cFt qsrEr ffi C{rdT< cT.t-{ cs r 10. 4m efqRfi? q+F <fsl-{ o+E qf6{d dr$-d <ltfi( roo m q<\ Tlsl{ Ess qE$r BEEI{ "fldor o. sm r <to qe-o6-{ "&< qsfi "tG oot<mn-r 6{c{ uarQq r ('t) <hqd qrq <tst< <lrftr c+F[ fi{a qs r m Efr"l<; q$|ft 't&D Us c{"t fr-r'llfi Dqrs etf{F fr-+t*{AB"sstc< fr6Xq.irrq rs-Fts EN r IDB'211 8 I sine = i = H= i... e ='i.-.(i) = z.re. E o.t=Y .ut' <o "nt, g = 7.18. = tan(7.18.) Bft"rCO< rtt&< C<rl v = 60 kmh-r = €{16{, v > v-,, ... Es c+c"t utl&Efr+"icqE{F tErr;rtt = 1;#;k- = vmax = 11.11 ms-l 60x1000m 3500s I 1. qlRsl-{ vd 40kg r m e+6 v6tft+ Bq{ qrcF-d {lr"rrs qNfissfc{ ${fl{ {'filTlq]3r etgkwe Erc zsm <rF{RFi? Wf-$t{ "EQl SG fifi6 10 <]iI Tfiq | \flfiEf Qrd ftc< rorsK ftrs q|'rcs qftrF q<( c<ry c?trs 6m q'caqoFFqrecfrqmr IRB'211 (s) qtfirgt sffiT cclro 6rt-{ frrf qr{6{ Elr 6dftr v{r{rB conm lffiq <-< ft-{t Et'fifi&-$ frrdlrrd $rffm "16[6il5;rl <rd I E stfr-q etsfrt cqrro cors< frro ql+rq E1-r dfto qr{c'i!r mffi {m qr{ Tt r frEEffid cfrfts 'ifr< lr 1o r1^o, 316. r+tr+t E6 ftst + c{rq 6alr{t FqE rfrfrs s{F t T(<fro afl-rs r t = O +S= 0 + L = S<FF+ 1.1.;,1= l2.;'2 ,{rltr{, 4tFmqmtr .q("tftq' qffi< ql."lrs {(re r c<q v("tfu qrffi qk'Irs {{R, qE AilhT{dft ff Em't { ccm qfft+q {q@fu€ {{N alFFr< I Gre, r = o, qt qkq mrg< frrs q|{(g e|r$r{s dfi-+ s*r<ut cc<fre e|r$.r{ r qdR, Ir<^1, = Izoz {6{ I ,2 q{r{, lr = +o t<g x (f m) = 6250 kgm'z or = 2nx-g.rd.-'=l rads-1 e<il2 = 40kgx (6m)2 = 144gpr z ... (,), =.1-r9r = 4.545 rads-l 'lz cdte,,e?m, <,r, >'(,), dfts 6<rt c<IgIlr{ftg L = Ir(,)r = I2oz sFF {FF-r< I ... ffifr6 ss5a6e1-s 61'541 "tffi << qt r EMm \\\ )oo qffiimeqmRgr"taffi... e

qEl{frGrd brleEI 1.3m, &vr{d 'flEq["I$qqr{d "llE 11 cmSqr ('f) Eft"rrf-{ fibl{cnq 6fiElt6{-d alt\fr ( mt tffi e< r lCtg.B'211 8 (-Ft = 3.44' E lCtg.B'2rl aftvr $rvr Fo-r s1-s5agffiq5 Fq-a. fr@ fifr€T{ qTe< q(er Ed 5 kg e<i <1-url( 10 cmt E-v-s Frqd ne qfi q6E1 41c46s l rads-l 6{crt {<Iql ('f) Fq-) qnEce< dfrssdr<'tF(r+<r ($ Bft11F-d 6sFr r-sF ett{lcs qkr <KR rq$+ <u <c<? {tft&T-v-lr< <rFBt$-d r (-ffii fi1ffi vflrsnTft .g ffi< c'rs+q wcr< qlc1rs {<e I .'. qYsF sFrs, I = \y1rz = 1x 5kg x (0.1m)2 = 0.025 kgm, .'. Cdft+ s-<f<ut, L = Ior = 0.025 kgmz x l rads-1 = 0.025 kgm2s-1 '"i's(g {t, eFFI ffirE q-s.sk etTs, I = 0.025 kgmz {{ (sGI, I, = 0.025kgm2 * Mhz = 0.025kgm2 + 5kgx (0.Sm)2 = 7.2z'kgm2 cqll {[{, 12 > 11 ... qa 6q6q rdn-r s.{c<,f , (ro), F6 0o) e<( cdfts {ffi, (1 r., ) vfi.6 q6q, .'. qn 6q5q-qsBrs aflTlF qlfr F6 Er{H s qko nfq c<cs er< r qpls, fi-q-q q< qeE amcE qks <tffi aq$l <rs << r E E 8 12.500m<lFrt(,fu,astr.ffi4trm<tmFBr<rurescw"teB-,r-a<-<rq-{C<s-{tiqqlrqrfitkrlqcrr{1qlTdEt {ksir Tlr<ff E<y 1m, fur{d 4ls qr{tt <tr+< "fls ecm Sq e<( Es('fq' 6{EEr{< nt "nrc-< w<ff 69 ({) Eft{-sT<lIsGrFrffir{dqltr{6{uEfupl.[EqB-qT$irrir{sqqc<"rtfi&+sfrqfrrdq.tir-dr h 6 cm 0.06m sin0 = i = tm = l + 0 = sin-1(0.06) .. <nqFsr r+l"t, o = 3.44' ! <*-l*, $Fft" 6stcr, 0z = 'i,-'e) = ,6-r (11119- -) = +.es+" sFfA qI{. tan0 =l+ v =,/rstan0 q{q, finl<rlcq {6fi8 6{5t, vmaxr = V50ffi; gsms:z x tan }44o = 17.162363 ms-l 4st'fcq {r{tu c<'t, v-"*, = @ = 2o.399 ms-l V-.,, ) V.r*, .. Sg('lsi ffi{qlt({ d* ws fi-<t"rq qfrer snF :{sF:r qc< I A ,H B A .--rO.*ffi <P B IE

qqPlfrsrd bErrfi3l : qrIJI{-o8 14. E O frcr< G-o-l e eoE leror< ur+F< ccs'ftrr fts< q&ffivlr< es qr csF €<( Fq-q. q E|+fu{ "ftcgd {qg[6r {firc?r lqi ft-m pe qr qefiqtcqrq&E"tls<v< m = 2kg q<(<iFfl(r = 1mr [BB'2tl B G-o-: trq-r (rl) AB qrfd {'ffiF Et+F< qWr< qhrF-d {H 6<< s-d I s*rcu6ltftqtqrqkef(s, l=!mr2 =!x2x 12 kgm2 = 1kgmz E sqofr@, Ir = 1ksm2 qrfim, I, =lmrz =!xZx72 =o.5kgm2 qlq<t qlfi, t = Iq wqfi{ct!?6 e6lctt, lrg', = 120.2 + I x a, = 0.5 x o, = a, = lqz ) dz = Zc't (q) "tIs EFrg c'flfitrt"t ffi eI{H F-{rq,$q-{ {[<l e€ qft IE *q ft r qfiE-wrt rrlrllf ETs r \9 8 m=2kg;r=1m ,. erF< {[$ e<t Ifi IE << {, frffi< 1{{ c<Ft << mrqg cdfto wq qaFfr< v4{-{ freq I G@ 500gm .e-r{{ Ae rc qefr ,aT ?,ac(I-d ftlfrArE qf,str< rlT{sfft qs PQ q< qfc"l.[F qG frfr6 30 <k T'Gr {ilq I x A (q) xY q!?rt PQ 6<Flr{t qrFd {trem Eefi-d qgeld sl{+ 6<Fl cr{a rffifuf fr5fitfift $5li]\5 Et\3 I ! ,,""*or."rr*q9wdsFrc, tyy = ! ^12 * rn (i)' = i -t, = i * 0.5kg x 12kgm2 = 0.167 ksmz PQ qs qt(q-r$ qpEtr qtTS, Ipo = Lxml? =1x 0.5 x 12 kgmz = 0.0417 kgmz .'. xYqsqlrqr$EeE<w_usmeFr+ mFf r 16. offi<1-st11sms${tr(<t{rfrEar &qtr+<roFsmE€Vtqir(cssGr{fr-{ktcF<lt[i-dffi0.4mS[r <ffid {+l{{rt 0.2 e<r e qfn vffio"yfft, g = 9.8 ms-2 r IJB'2I I ('t) dl€lir<iRfr(@FtF{rorr e $ ffi & riirsrit(fu.a1qEsvr{qr4E'r:s c{rrt ,h {r{F-dI"t(T<to C{rg<tqs<z 'flftfur{rmF< r 8 15. ('D PQ wrq-q41646q*5u dftos*r<utffiT.< r uB'2r I 8 l=L*12;L=l"1=1:mlzx .1 I =.r1 x 0.5 x 12 x n kgmzs-1 L = 0.131kgm2s-1 1=50cm+l=1m 2 , = %31 rad s-1 = n rad s-1 ;m : 5009 = Q.g [g rEtil t\ qffiq<qvnqRu-*rr?rEEL.. e

l.= \\\ h = 0.75m d=20m m = L400 kg r = 100m h = 0.75m d=20m iF<t r m=5kg;r=0.3m; . = uo#" rads-1 = 2n rads-1 S fr<r1cq+r ctsxl-?iq-{r{c{I6 c<{ v qcq, ;SFmg=v<y'Frg Elt(ft(4t efi$r{, V= 0.2;g= 9.8 ms-z;r = 115 m =v<r0zxlI3leE + v S 15.013ms -1 .. xrftw ft<t"tq' m"f, v = 15.013 ms-1 (Ans. ) 17. 1400k9 sI<<r qr:F 'tt&-zom q'16 ffintfuEtstr+sFcqrTrslTitrtrd Els &E-r{{ Els qr"iFt o. zsm Sq r<fotl<iheavtt( 100m rsfftfiEr{$r<r ams-1 c<crt ffi DFrtcu q{r<I{ +.Gr r ('t) <M{'tt&'.d B"K ffiq q&fu'{t T{Rcrr<+-< r ({) 'tl& Efqir rIftT-d q-{Kt{ Tst s-tr(g ,Ilffn ft-+ rtule +-< r E <rordrrRft(c$t"toErt, Tlrqfiqtrffi t-Ft 8 \\\ E <rskcnsft(rslqeEra, .ine = l = sin0 = ? *, = 4.59.(Ans) 115m ; d = 5m; h = 0.4m .ino = l = 0 = sin-1H = 2.15" Rcos0=ms+R= mg - 14oox98 " cose cos2,15. R = 13729.66N (Ans. ) d-+t<tslBIEfr-ffifi<j-o nexr< q-qr qr{rm 6fff v,,"* (C{, tano ='il"- = tanr2.1s") = v#"* rg ' I00x9.8 3 Vmax = 6.06 ms-1 ( 8 ms-1 .'. qfu_6 p6-q apft66s w{Kt{ <lrtas ql<rc< rI r 18.5kgvirs3ocmvFflrf<qsFrr<{FfrF60<l{T{arElotErs5secqelEftrt{q{0.45N-m}SqcrFt T-dtqrEtt tcB,2ll ("t) 5lTtET dft'$ s-rc<rtffi +-< r ({) Eftlri EaRsqq5qEmfi5<eqfiFt E ur+m-<cAn+s<r<"r, L = mr2o = 5 x 0.32 x 2nkgm2s-1 = 2.827 4 kgm2 s-1 E *m+rn, t= [q+ o =gq = ffi."a.-, = lrads-2 ] .o = Zrr,. = 0;t= 0.45 qkliI, Tqfd?f CSfq, o = 6Do _ at = t = 9e = ?I s = 6.2832s > Ss c1 .1 ffie156 g6gfiE qrcr EFfiEr$ ellTfrll :tlr< iI r 19.,{TFEtRdsl-{vd40kgq<(qwtrqFrs4000kgm2rDfstEfrfrrt120<kr{<Iqr qT{rGEffi?$.l.s ftffiq-a6a1-6q-s40oNm mF6gmtrtq<cs-{r [Din.B,2tl (tl) DffidcdfrrvirFlrtrFE? e (g 0 <Ifu Efu"" EfrFts fifE qcrs 'r*lF qffiro qr{ E..{ ft? rnfi&o-srm{ffi srr r\aFE qt* r 8 qEl{frsld 5:{ 'l-€ : ElrfiI{-o8 [cB'21] 8 IEil qfurlrevrrqftoa"HE-fi...

qE[{fr.GId DE eta : qTIIEI_o8 E I ur-+rB<Afr+v<r<'t, L=Itr = 4000 x 4n kgm2s-1 = 50265.46 kgm2s-1 I = 4000 kgmz 120x2n ar) = -rads - = zlT rads . 60 m=0.5kg v=5ms' .=9.-:30cm=0.3m 2 qlr[{Iqtfr, , 400 _, ^" _7 f =lat+at=-<'=tr.ls' 4000 (rt1qg ffi{, Elt fl = -0.1 s-z to-oo = at' - t' = # = 125.OOs t'> t qdF,, {futrEfrFrrlt{c{Dr$IB alF[F "ff{Gt4t r .145m ('t) <F{Erqdr{ lffi+<r (!) <F{trEft"ftT sEfis<lgldffi F'dt"i.q t=1.5min=90s t=90sec I = 4000 kgm'? t=400Nm (r)o = 4n rads-l ro=0 1000ks vrd-ir qsB <H 781251 ri&.,..lG frr{ <fom u-en qa-* qbtq r+sm <rffiFB qrE dr€{ cqft{ <Et { frrrd Grq cq'.lt+I {r{tq r [g = 9.8ms-2] lDin.B'211 \9 {f{Grfr? ffifuEfr68.{.l{qlsEsq'tE I 8 20. "rt C 0.3 qB-eqs-{N (-E <-l tr E 21. E E I 4( q< '{' w{fiet l4o q" 'q' sr{tr't {glT Cl-{rlir s00gm v-r{{ qrFF {trcF E{tstr{ 5ms-1 tF<t 6{crt 60cm <Itffi{ lglslir "[qlT{tr{t crqt I lg=9.8ms-21 (q) +x q$ qc5 3 0" qTtr+ e<( 90' q'{qlrT wt< Bq'flfffur{ frd{Gt Fd I (rt) <-strdB R 68ft{rtaffi{cFrfi{T${ r c$ERT$<q=Y - osxs2 N = 47-67N 0.3 30'sqq6a, T*mgcos69"=I( .T=Y-mgcos60" : g::t' - 0.5 x 9.8 x cos 60. 0.3 = 39.217 N IMB'211 8 -!gv: t 90'wQfr{, r =;- mg = (Tf -o.s xe.8)N = 36.77N IElil )o8 \\ ffi<6rl{E\rr.sRga'i!rr-dl.. C

qql{fuqd DE 'ta : q$t{-o8 22. qFD <lsk efq 16m € rihF-d nt E]rsd gsEtr td-+r 60cm q<( <Il{ 300m I drfd "tfr.t ,{sF'c<tc6 ffi-.{ qc<lo t&ft+t so kmh-l ffi r [g = 9.8 ms-2] ('t) <lsldn't(fr( 6rHffi +< r (s) Bfr"f(Tfir(Flscr4F nB'fffir{Ar-st {I{t[{ < 1 fir IMB'2ll 8 lCtg.B'191 8 IBB't9l 8 'nffBofu:mrq-< (-t E E 23. l6 {( s< 'el' w{trfl , u oa q< '{' q{s't qFq{ EFr{' Et&-{ DIst {tfl{ qr{, Et$,t tffi +-<r< q-{, cds ftiT ql'FF-Erf {{Itrrt{ {.l{ 6s,t[{t qF {<c6 s{(F Tqrf f = (ei + si - sk) u <<r 1ft w+ ECe !rq{ fu R't-< E-<y-rT i = (i + i - i<)m rm eFFt{ rFdr qffif | 'tlG< vd 2000kg, !}{IqIE <tgf{ <hF-d <rt{t( sm q<( <fsl<r {q 3mr <Isl<r cr(tF $ftI T{ 40 Nkg-1 r lDB,lgl ("t) qEcqffidr{6{E{@F6ss? e (F) Eft"rcs-d <ffi{ trsrtrd sts w,rst <Rc-<-< arc +\5 Sq q(E'fi&tr q-sr<, qffi6 c<r'i fu"icq rts frrg "1-qsq-ffifucstr< frr$rt rq r f-E R-l E .ut, eae<-e, F = (ai+ si- sk) N;T4q q$EsFy,i=(i+f-R)m E ff, t = r x F = [ i fJ = i(-s + s) - i(-s + e) + k(s - ay = (-sj- sQ) r.rm le s -sl .. 171 = fi-3y1 1-3y = 3VZ Nm r s{tq, tr6<!tl 3JZ Nm q<( FF{s"r (-:i * a8) r.rm ,{?116qq({T{, Fr. = 40 x 2000 N ; qKF, eu = * = 40 x 2000 - 2000Ivilax = v,n", = 10J2 ms-1 (fi(ft(crr"r0E5a, tane = *. = r = "r-, (g@) = 76.23" 9FII3r, sin0 = |... f, = dsin0 = 3 x sin(76.23") =2.9L4m <frlTl:0 {< TE SCE, tane - sine E{, q4lell'{;rg I q?fl-C;r, e = 76.23.R{l{tan0 + sine<I, } + 6:: <Rq eo cm ffi{ qF{e {ER qF qlrs 200 g v-rffi qsE <€ c{[{ Tsffi< {rq E& frfi6 90 <l3r {<rftq I qor<frr+ rkq oo cm ffir< q"R qr{e {e-ld ,{<; $rs 1s0 g v-r<-{ qsF {g r<ct e+tqm q& frfr6 rzo <lirT<Irqr ('l) <R6{-< Eldt T-<11-{ <etrd cfrfr"{ E<r{ r ffi +-< r 19 Efr"ne+ lF+* <fu s +Rq Wt{ qrl+ fi{ c"rc{Qq fr ? ffiBesl-r< Rr$vt q< r I 8 {( q< ''i' q{fi1 <fu1-< mmqq"<aq, T. = mo2r = 0.2 x (3n), x 0.8 = 14.21N +ktq< ffiro{oR Brl, ru = mozr = 0.15 r ('T;"0)' x 0.6 = 14.21N ... t" = 1u qdg, Aq T{E I 5 kg s 7 kg .e-ri?r cD {s l*Ilqr{ 5 ms-l q<( 6 ms-l r{[rt 'l-fl*R ffi fr-{ qrs qr{ ccyr{T ffi {{tqir qsrq fttrs <T ffffi firo uqm s+ +r< r ('i) Bft{rcd rscrsd ryrv c{ fi4tv* r ({) gft'Ir€d {€str{ ciq( @qt"m qt qQ&{"r$- mE-5 RspqqqEqE-Fp Efs r 24. E E 25. IM

E E qql{Rg|d }EI etq : sFrI{-oB m1u1 + m2u2 = (m1 + mz)v + v = -1.41667 ms-l;7 kg s(<il TS{ C{C{< fr'C+ r qffrqffi, Et = 1*rr? +)m2ul=1x5xs2+)xz x 6'z= 188.5 I .. Ek + Ek' .'. {(q{EqQ&{l-sr 26. lm q<\ 0. 707m ?q'(r{ EF TiF TE{ qre< s-<cs {eff@trr 10 kg q<( 20 kg, €ra:r E-w-{t ?aT (I{ {tEI EEstr{ qfis q<( c{JfrTufift qc+'< wprm qfr frfr6 <cll€d{ :oo <l< q<\ 360 <k ,4sF mtDr<-< cIqlr{] qrrfrn-+ 6{rrt T{cq I ffili3F <r qrr c{rE ){ r-eF 20s c{cs< {c{i cqcr ill{ I ('t) m1i<F<{{cr{<l",tR ){wfisEF f 1ftwrae<<z fE <-l [ >rnre<mre, r, =aH4= "]1"= rot .rar-1 ; ror= 0rads-1 ;t= 20s ... 0 = o0+or x 1= 19" r 20 = 100nrad = 50 rounds zz 27. q$FWcErs< IEq-1lcRlriI qrtr$rutoG fio-ql?ofrTrtqr{l : Fq-l Fq-a. (rf) Fq-)-q< PQ-q< firefrs qVEEr E[[E 64q 3;q , \e (q) DIF&T "iRfrrce<in-rfi<qqfrqrqE-.e-rs{s-9.e-l{slrrrGn<FR-{t-Etfi&'{ RrS<"tc-qrqqsrN r a q{l({, Ers< q<, m = 0.5 kg ;ffi, t = 60cm = 0.6m .'. PQ qc.t-{ {k'lc$ q-ssR sFrs, l=! ml2: {:, O.t x (0.0)'z}kgm'z= 0.06kgm'?(Ans.) <R, um&<<nW(= r I qll:t(e, 2rr = 0.6= r = 0.0955m .'. P'Q' q6ffirrG'irsut+ft<q--wmqrrs,y =+ - 0 sx(ooess)'z = 2.2797 x 10-3kgm2 .rt, E(\9 fllt, Ere< tsTvEiBr eE?F 0.06 kgm2; {E<R, Effi € q-m< vd q-:rFr qs{]-?r.k\t, rT+frm< "iRfi ws< ?r6fi < q:rl{ qr4 E-s[-T{ q-EsR q:rs &{ cR r E E uB,l9l lDin.B't9l m = (1okg) wci-rr,asB {€.d E"R eFt {{r$ ffi T{ fu +<rq St : 4( FrE cq!flr{t Sr{t r lAil B',181 9: S: a: lms 2 2N Fq-: rqq Frq rcEd B"R ffiq FE <rffi ff{ "s? Fq-r q<qfmtm Fq-q q< q6sq:[Et s-d r fiq-l 8N t 8 ("D (r) o' IEffi )og

E qqt{frsB-ra naqa Ee<ft-r<{RnTffi{Efr = (8 - 2)N = 6N 6N Ek, R = vGz + 8t+ 2 x 6,\ I x cos90. = 10N (Ans.) E -AWo,, = * = -g = lms-'z, Ym616frsqaa5aqs ft-E1 06, -6qq "&'ftctal e copt{Eor<r .'. 0 = tan-19 = 36.a7" 8 ) c( Fq Ecs e[€$ {FlqrcT t {( frErs\e q{d{ sL< 1 s1t Fq-q q6s I 2e. q1 z0 m <rFflffiFt? effi 1sfor< *#r uV{md cdr6' 3s. 6rt(ct 6sru( ftrs qdrtr{t q{St{ fr-iPilT {li?R'-q DFtr(g e[6d I 6{ 2 0 kmh- 1 C<Ctt qltrs-q EfEl&E r IAll B'181 (rD asrsI< efral 5 km qT {:rFr eFt q&-q{ T-{(E sE-{R ql} qqft,.t TiEe qr{? e $ Eft"rrs EGFrE *rb fte.t mc't v1 & fi F-dr"rrt EE+{ isirrc "tIlr<? ls,st lffi qr r 8 tr E ql:rfiqlfr, S=nxzfir ... n =l- sx1o3 - 39.79x40 Zrtr zxnx2o '. EEI 40 <r< q6 Eqfr"t s-?rN Er{ I q:rflqlfr, E<9,S=5km=5x103m <]FII(, r = 20m tano=t=v= Jrgtano l*f,taq =, {FIt{, r = 20m = v20t 95, x tan 30"- = 10.64ms-r | "- '" - " l6rFf,e=30" q?FI, 20 x 2kmh-1 = '!1' = - t1.11ms-t > 10.64ms-1 3.6 ... qt fre"f Kart & flalfrsltq qftqr{ s-{as "Il<r<Tt1 30. qrs {ts6 qfr'{ frfu-e ql(ift{q qr{to +ootg sr++ gstrtsrEt qq{ qisF ft-+b Et E-s.t EF rris vqR {c{i s5t-T|TI +r<r RfucF{ sGF elrfd Bost 3mr E-@ qftffid q<5Eirlir w 4Skg €t( &fr ,qTfrT ftr&rs urv 2ms-'z g<r.t El6mr tm €rnb cfit64 ER swt o1ftayel p-s6aa I qr5rq ffq qrffiq yfi"k {Ft 9.8ms-2 r lDB,l7l (s) E-G <i&-d €Ei-{ €rab c{Fiwd rfqtr$ ccfu q$<s-stc{ fifu +<t c't{ fu Et 'ltn&-{rEtc{ Rr*s.t srd IEfns EIs | 8 Fr+tD mrqg a = zms-, y*r{ sfu ar<, 6q@ffisR eq-q q8r\r-n-< lRqpr q{re {irtrFr l| r EK elf,s \eq{, w = mg = (45 x 9.8)N = 441N Fi+tF €:t-< qlT q|"iIE 'sql, Wup = m(g + a) = 45 x (9.8 + Z)N = S31N ffifr aIn-R T{-{ q{l\9 €q{, Wao-,, = m(c - a) = 45 x (9.8 - 2)N = 351N .'. fi r+ift q19-s6"1 e11-6'5q sq-{ q8r\r-E< fi {T s-$ <Ic< aI r E rM

qqMfru|d oE etut ! slrfi{_o8 3 t. ;rEt{ 6tHI qiF <1r+r srMt( som q<( <lstd E-v-s "fld< Swsk'nd's] o. sm, <loEr dq sm r ('t) <l-st{ eEs <lt(ft( 6$l"tFs? m Bfr"l.c€d <lol{ 108 kmh-l 6{crt,l<tr ,*6p a1fifuaur<rnutts.ar E <fue<<ltfl(, r = 50 m ; <lsF sq, d = 5m <fgt{E-sr m{<fu< {dTr, ah = o.s m {R, Ktst-< <lTG( 6stct = o .'. h, = (r-d)sinOeh, =rsin0 .'. Ah = hz -hr = dsino +0=sin-1 (4il"es=5.2+. $'ut' <u+o, <ltrftrc+m, o = s.74" !t{ SR, rcfl6' fuqq 6{'I, v.,1u qffi ffi, 12n s = * .*, r =<trs<<tFrt{ = s0 m = v3.r" = tan0.rg = tan(5.74") x 50 x 9.8 m2s-2 + Vsafe = 7.02 ms-r fuE 'fi&r c<'t, vcar = 108kmh-1 = 'lui*' ..-' = 30ms-1 i' vcar > vsafe; affi frg1a16q Eia[tr{t {g< ir I ,h qtl{ slt{srqld {r{, Smsfd {MFI {et|q'c:t 7. 00cm € L1.37 cm. ('t) )c Eltffd <lt(ft\ 6rt"f s\5? (s) GFrsltr{ 6q,llGqR'-s6Eelitfi.{ -'ttfiBsfoeqEEETdFrr<:irr O eft"im-< WiFrcfia qffit 6dF"r lE{e frect <rq ft? ffit{s $iEN, qrc r ffi (frft'o mtl, to1 = 20 rpm = Z0 x2J rads-1 [rpm = rotation per minute] = 31 ."6.-1 e[{ cfrfts (<tf, t,lz = 30 rpm =soxff rads-l =rrads-1 ffi s cE q-s-e-R qFrs {ell6c{ 11 € rz RrE, I1o1 = t2ri., s ; = fi = + = 1 :. \ : t, = J, ) 'tt'SF "fli, qfr rfrfrr 644, 6, = ?I 1265-r ("lq cdfr-s 6{ I, ro2 : ft rads-1 q<( qfr s 6.jrl w-s5ld s56qd qt4Ei, 11:12 = 3:2 ffi e ers aifr-f 6{c5t<qfls,0r1: oz=4:n=z:3 ... qfr dfrs rt&qfu , E, = ! ttrr,l \e 6riT dFfs qfr.ifu' , Ez = ! tr.;,3 .; = e) (t)' = 0 (3' =; .. rffidFi<nutffifrEqqr+r IRB'171 I 8 "it&'ffi'l(q.Erfti{r t-E"r-l )" 32. FE-f{c'lq € Ew'fsi c{-4qlqr;rdEt "$.g-dxqr<fr EaYqetr@r{ 0.8m € 1.3m r 6{qfr{<lrf{<iFil( s00m lsB'r7l d-sfrrg"tkr<? 8 (Ft E E 33. E E 12 {( q< 'tt' ,S< q{frel 12 {( s< '{' qa q{s't 60 ks .e-rfi q+qn 1grFffi E{e emRs er< frRF qo ak Tr(g "fl-r+*r ffi ,asE nSfrs qT ckat EFr cffinff{cD?tT-{&ffi{r IBB'171 f 'D 1sIffiT {$s eT {trel ms cF frfr6 eo <k 115a q .sr56 sl':FFqnT gq11 e{ | 8 IIE

qql{frErf, !E rra : q$r{-o8 34. 30gm.e-rfit q+F qf{E roms-l c{ctt cclgil frc{ erF R< qE{qlqr {lrl &T r cliffd 'iir {trftF ER 75% 6't EtdEr q<( Qr {R'ftB ems-1 (<'t qle srd q{ qT{T (eFF 3m Er< ooF rttr< fi-qFrs {iFf fi-{, Tttrd cq-slffid +{qFrsrft {dT 3N I (<lElrfir <i{tBI'l$ <rrd) | ('l) Q<qr{EE<E<fr{x+<r uB'171 E ){:{lr{F< s{, mr = 30gm = 0.03kg fl {Gim< qtfrr<oi, ur = 10 ms-1 fr q15{6ag 6{-qf<q. vr = ur x ZSo/o = + ms-r = 2.5 ms-I lt {B{rq< qfr-c<ti, uz = o ms-1 i{:{lf{fdf< r.Fltrt l, Vz = 9 ms-1 tT $c{TE< s{, m, =? g<ffi'r< qssct 13'lT4tGt, m1u1 + m2u2 = m1v1 + m2v2 + 0.03 x 10+m2 x 0 = 0.03 x 2.5+m2x9 = m, = 0.025kg= 2g96 {lFr 2se srd-< eFE {taK {er<r rm ft( q+Edrrf<{elR TstsI{ 'l[et1flrqr {F.l<t {eF qG qrqrs s <l{ lrrertnn-+<{ac({]tqsR6<tr[{ER?,n'{rfre"t+-*tqqr{s|ffifr<r4oNTE{{F{FqtGIr [Din.B'l7l 1t1 aqr c*ra "mel<E< cfrft+ s-*r<t ffi q< r (\) rr{ {9l< ?q dT fre.t om {l reevr< {E t{ €{F {Er{ Fr{-ffi &+str< rffi +< r s<,m=259=0.025kS dfi6mut,, = Y rads-1 = l0rrads-1 {f{t(, r = 1m .. CfiFf+ scr<"t = morrz = [0.025 x 10n x (1)r] kgm2s-1 = 0.785 kgm2s-1 W1-< ?hr(r freq s-<rq, <rFrI(, r = 2m v<, m = 25 gm = 0.025 kg dft+c<q,.=T rads-l = lonrads-1 .'. mUTft <e, Fc = rno2r = [0.025 x (10n)'?x 2]N = 49.35 N qT,flE DlT, T*"* = 40N T."* ( F. ..' {OtD frrs ff6{ r rT{ E{T {qqslr{ c9{ s<I65 {I{r< rl I 36. qTF \flrEFFfir Es {l<r ?q(r I = 1m € s{ M = 0. skg I A M:0.5 kg ('t) nsF-{ qwk qf{sfi{TF< r O lft qeftT 1m <tlrrr{ "ffosl EffiTs qfi&o-v1r:rffie-<r I ne6 <+ arofiiq?qrfi<qrslm qT{slft T<rql 35. E E \9 8 lDB',21l \9 {Rqs F{t Es Er{ qvElr qFrs-{ 6sl]nt "tffii << ftz 8 (-EEr-l {il"t(<!f|< ql(eI6s IMm

qqEfrgla 5E[ rrJI : olrBIT-o8 Fce<sd 0.5kC € <IFm( = T = O.S. q(srq \e-'{rs-e{ft s \o-rq-duq-{q{ qrffi {tr'l65Fq--sslit el{$ , \: lyrz = 1 x o.Skg x (0.5m)2 = *1 kg -, : 0.0625kgm, q"F{, gfr"rr$( ff{ ,sF strs ${ qs (3c{I q4taan <m, I = I. *Mrz =1kg-, * 0.5kgx (0.Sm)2 =*1 kg-r=0.1875kgm2 chrff Tl{, qffirdt q-E\,-ld ir-Fts q-rsrT qwR sl:rs' cF&{r .'. w-usk qFls 1ffiEqr{1 37. 1mL$t(0.7ozmlnr6-*@a-<rIFTqTs<sdIITq{iEFfi10kg,4R20kg,ernaEwnQ?nr{r*qlcqq?str{ qtPF cr(llrffi qrr< tcqrr q& frfrFsqqcc soo <E qrR 360 <t3r qrE fitrl-d {rdrlrqrdffT 6{r{ lFZq I Cqtrto s{ <{ crirdr ){ csF 20s {crffi {[{I cQlrq :Iln I (q) q4+<s nenm-< 66fts'.tffi-d'tfie-{yar+t+r r (-Ft ! :x nce<, t=! ml2 =1x 10y 1z =l qm, ,61 = 30912* = lOnrads-l El{CdT, Ep, = } Ir, = } x ! x (10n)2 = 4rr.235441 l{ q(s<, I =L mP =!x20x(0.707)2 = 0.833kgm2.'.. =#* Zt: T}nrads-r q?tq, Ek, = 1 ru, =1r 0.833 x (12n), = Sgt.g4l;'* =!# - r; a cQ: aMtfffi EHt't s EsstrErFEEs-s ES s +trTE-s-d+ + p uB,19l 8 $ flnF-r ftrtrsr.td {t$c{ cqqt€ cr, xy qrF qofrd sts ccll {qlfrTd fire fuq t*m rcF* qwa st{T Efq 'II{ r 27 T( ,{< 'tl' ql q{ffei 15 {( q< 'q', q< q{m't 500gm vctit <+F s€ 2m TrliTM frrs WIffa m qRGTrs r<gEl,fffq-sH r0 second I ('l) {€Ed cfin-{ s*m{fifu <r< r (s) {€tr{ GruTft <q ffi c< q<t sfr ft-+ q*t#frrys.t qd r l8 {( q< ''t' ql q{s,t r=2m;T=10s;m=0.5k9 .1 6qsTfr <ar, p = -{ : -(':'o' = m or2r = -(+)' . = o.s (flJ' . Z : 0.3sSN qt <(E< fr$T rc6 qTE"fu.o= IslTI{fl(eI E{F qltRr q<( qt qq C?M{s {€-d qGfl(ek {rri Enii5r< ov_r<< fto udrs, ae< mtGArt ftrt qm r E E 02. E E 8 (tt) EtsF{ sd zkg qcE qT q9sEr qtTsrFs? -M

qEMfrsId iEqE : u[q,r{-o8 03. q{eI.n 0.6m?Fr(rd 100 gm v-r<r{ qTFrc $T I(er qfsfrB rt:rffitft qrs-d Etc"lcF Srads-1 dfi-{r 6{crt fftq ne$< cfifts 'iffi ff{T s-ffi I qes,rd qe&rs 'tfrr{ 6cm <ilckfd {tsErt TsIsT-{ Effi bR F,rT vfd ccu ftr tr6< qtrE?-\"'E{ etl-++tft qr$-* :Tfr"fm,ql'i dftr 6{rrt qiliFrt I ('t) c-fl{tEeE-ddft+q&lGqsfi.f{T[<Q{? e ({) Eft,f.T-dEfrREcotr+crmi&1fuc<FtRl?.s.tl{slEEEqt€ r 8 I U = 100gm = 0.1kg ; I = 0.6m ; or = Srads- ...6dfrr,rffi, = ir,, = i(ir,)., =;{T " (o.o),}x 5, = 0.15J s oal{ mr-o, E&{fu = 0.1s1 I't-qrel frftg 6s(G, r = 6cm = 0.06m ;m = 100gm = 0.1 kg;o = 5 rads-1 .'. cfiftoei&,ttu = )t^, =10^*) ., =i ()" o.r x o.oo,) x 5, = 0.00225 I < 0.01s I .'.qal{ 6ErE 'tffi C<Ff I 04. 300kg ErTd qsB'tt& zoo- <ltflc6 qsF <lsld cctry 90kmh-1 c<c{ <to firer & qR-{ <l6tE sm EsVt e<\ qr &Err-d ft-{Fil qcs <ttm< ft-*trt r m B[ r t'tl tlt&-dE"rd @tT+<qfi{Tfi r (q)'fi&tft <tutr cqI6Ffrdt1fi <t$frrE frcss.f FT r 21 4( q< 'rl', ql w{fiq 12 T( q< '{' ,a1q{s,l irs-$ 100N itT T$fiq 100cm kdr{ qTE wR qiF Etrs 200s scK qTD "flplT 6izq q-{qFrcsltrt wrs. q-?rs €{E I'itqffi QT q{qr{ cqra rI{rs ql-{s {r{ 3 frffi ,|{ s& fifr6 rzo ftr {qcq r ('1"tteffiTffi<fiTffie-qr e $ <A-E "1.1U6 6o"t c{Crt qil(s "flitr{ fr? cst{ld Esr{d C"t[F rtfiBir Ifu qls I 8 f-trEr-l 7 4l-frr{? 8 'tfiBs-v-ftrr (-Ft E E 05. E eN dfrE c<rt, ror = qt:r<f qlfr, or=oo+(It..0=4n+0x180 .'. q = 0.07 rad s-2 a--! ...trS, r = [q = mr2. q = (0.2) x ]., x (0.07) = 0.0I4Nm ffi{ {1-q = 0.014 Nm ! Aet c<r"f g<ne dfto c<'t, o = 240 revmin-' = "0 I3]'"0 m = 2009 = 0.2k9;r = 100 cm = 1m ,. EI{, p = mc,)2r = 0.2 x (25.1.3)2 x 1 = 126.3N > 100N .'. freq c+ct T<ns "n-*r< qt r 120 rev min-1 - L2ox?Lrad = 4n rads-1 60s cdftsy{61= d ffi ffifrE 6aap, 11o = 0 ;t = 180s m = 2009 = 0.2 kg r=100cm=1m = 25.13 rad s-1 96. ffi-{:rrE scq6n sokgm2 qwk qtrs Rfi? q$E $e€-{ s& r fifr6 12000 <r3r rcr {<erdil r {w cFF Sr{Ert (IS 45 sec q afElc;fqrqf I ({) ptt-qQm'{ B'rd 6rir-< qtru'cq EIg cfrfro y*rq-< ctl fi{r Fd r (s) 6s srt c(g enct,r{s srQqi-qtrqt<s 2000 qk {{Cs ft-{t tfiE+slr<R.ceq{ 'I{+xc<rc-< r I rE

qqrdfrG|d lErEt : q{flT-o8 E E 07. stfr dfto mq, to, = i?999#;rg{ = 133.33n rads-1 {T{, t = 45s ; c.lq cdfto rqrt, (or = 0 ; dlft$ yTGt, a:? .. of = o0 + dt+ 0 = 133.33nrads-l +a x 45s ,.. a = -9.31 rads-z rfrftow"t,0 -00 = (9ri9j) x t= (I!-1SIj9, )x 45 = 3000nrad = 1500rev qdn,q<e 2ooo<i-<{{r{qlr 3. 04 x 106 kgv-r+{ qSE f6b Egt frtT 3.40 x 107N q1-€t Elgi T-dt{ Eqrskcfd 1S0 sec +i=r 239O ms-l cqrt 4t6 qcqt r ('i) rr$ltrd Ewnirr tssN yd{ Ts fr'q? fi) 150sec'lit r1g yr.t cT{rdqfr ydGt cetriF q &{ csTlir +liFt frrss.t q{ r 8 F = 3.40 x 107 N, M = 3.04 x 106 ks. .'. g<t, a = fi = #H#.r-, = 11.18 ms-2 u= 0;v= 2390ms-1 ;t= 1S0sec ;. v=u+at+I:I=, ... " = r.r1?;; o:15.93ms-2 stft W"t Ri?r-sT.T qErfu yr"t q<. <m&{ mB s< <Ft etr+r <roEF-S"tr< Ul6g q.f+rq rmc frftr{-d aRr.i <rs&{ mE s< +'+m auIs +r4 E({ft {ar Q< {om g+t c<ft qsr esQ {-.at RTAET.} qffi Ydclv Ftrr {Er r qw{r nV V<ct qlft g<"f c{r<n <Ft r E E A(aks) 08. 2m B(5ks) Df2ks) ' -' ABCD q{E {.{r efslsF {tW anf 2mr A,B,C € D fr-Iro rlqfqc:I 2m akg, Skg 3kg qiR 2kcv{ {"F T{f <,-a[ r qFrs w 'rT{66Td ctfis 2m vFrtc(T ,{TF ffi frFrstcT cElv <FrtGI EcErtr slir"m &Frstr<-* c(3ks) 6qgffi q6qaclcarcsqwf{stTs 6{irfi$Er6It I ('t) <r'f{ c{-E, € vrffi se1-q qgffi q6q-a {r,1m <r{qttrd qvstT EIT<F fi(T +T I (T) 6{tr{t ffirq q_seR slrc c<Ft qrrl? ttfiB+strir frrs+t q* r E A(4kg) 2m D(2kg) r = A4Z, = ZAm: oA = oB = oc = oD =I=.12^ mt = 4kg, m2 : 5k& m: = 3k& ma = Zkg ;q-seksl{iF, ,, = -, (,,)' *., (;)' * -. (i)' * -- (;)' B(skg) 2m C(lkgl = (4 x 2 + 5 x 2 + 3 x Z + Z x2)kgm2 = 28kgm2 09. I mz=30kg cNRtut< 25 {( q< 'tt' ,{< q{S,l 25 4( q< 's' q< w{fr1 \, 8 E r= 2m;M = 5kg + 3kg + Zkg + 4kg = 14kg .1q-igElFsf{s, \ =!^rz =!x74x(Z)2 = 2}kemz... E-wmro vgW ql{s T${ | vor :8ms-r voz: 10ms'r c(qr(( 'fr{ ('t) (q) {(sr(T 'lit q€sra-d fiEo ctat +s qr< ff{r F-* r Eftlrr qqgs *ro5v-{6q t €{&{E Esrt nq.iFre {tsr{ fte ffiG-+ frctq.ffi{ rEEv Ei€ r I 8 E E 2a 2rn mr:50kg rM