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1 1 PART A . PHYSICSALL 7-I1E CRAPIIS/ D(AGRAMS GIYEN l{-RESCIIEMAT'IC AND NOT DRAWN TO SCALE.'lte JensitY of a material in the shape of acube is determincd by measuring threesides of the cube and its mass. [f therelative erors in measuring the mass andlength are respectively and 1%, therEximum error in determining the densityis:(1) "(2) (3) (4) "All the graphs below are intended tolepresent the same motion. One of themdoes it incorreetly. Pick it (1) (2)position(3)timevelocity(4)timeonir A - (fl[U F{at r(rm r{aiqllirii riidzL d " it y]u'it { r{-t r,r6t?.1 \6rei-[t !r-t(r rrMi .u61 s?qr{ o,tA 6. oa ir<r sur u' rr{ u\tt lftoit r4$d 1% d{, a q-t qr\.{r:ri rrol aUttrt 1Du:.?2{.t0)(2)} (3){"1(4)SPACE FOR ROUGH woRK / rt srli{ rr,l'H(1) (2) (3) (4\ 6%.))))]]}}}}}}}}}}}

2 {l qqr nv q<lu {s mr< .LRi ro1 sl 6A*il nd "L ili ,,1121 i1i r"X sl 8. t 2timel-[n o masscs mr = 5 kt] and m" = 10 kg,.oruected by an incxt('nsible stuinll over africtionless puller', arc noving as shoh'nin the figure. Thc coefiicient of friction ofhorizontal surface is The minimumiveight m that should be put on top of ntto stop the motion is :m13mr =5 kg r,t'i m,:10 t<g "t *G,rrrirdl \i d?il -r lErt{ Aq1 r'iilqit qitil. ,-rBG,{iEericaL :t r-tuti, ,rR ri E. [ 12q\qttq 1q D. r4t rtt'1t 1tZ m? .t L11 ,rs( a' Eq mlir1 TTrmrg0)(2)rll(4) kg(1)(2)(3)(4) kg4A particle is moving in a circular pafh ofradius a under the action of an athactiveLpotential U= --. lts total energy is :2t'Qt sSL, a Ror,rt<r " .q .tu{I[&RqLr U --I= o,r<tur,Lfrr li 6.)]]}}}}}

3 6i6rtq{'1., (l)4a2k(2\ ,7(3) Zero3k(1)k0)4a2k(3)rl.{3k(4)(2)2u22a2A/P age 3 SPACE FoR ROUGH WORK / rt 3r{{ rqr,r5In a collinear collision, a particle with aninitial , o strikes a stati()narv particleof the sa:ne rnass. If the final total kineticenergy is 50% greater than thc oliginalkinetic encrS\,, tht magnitudt'of therelative velocity bet\^,een the two particlcs,after collision, is :{ Ir !{(2)(3)(.1)Seven identical circular planar disks, eachof mass M and radius R are weldedsymmetrically as shown- The moment ofinertia of the arrangemenl ahout the arisnormal to the plane and passing throughthe point P is :(r)19N{R2.;is d310G uie{sPrgi (r i)llinear collision) rti,,., .iecit ur[q: ,r\ rvr ctto,r 6/Eq [+q? sr?r iui ore,|sr{ d. "i .,i[iia 1naln Gt",i, xti[ru ,r[.]]]]]}}}}}}}}}

4 R Gt''.i riai s0". q[ :I .,r{rsprqr ar6, ,li :eii q"i fift ai.$ ,rlirLqrtiL(r)(2) Jz u. X&rMi, ,J2(3)(1)r{qla{i r[.r{ rtut?, *j M 6rrr qrrcrdl r,tin Qoar{l uc au< <{ot:R ttrr<tdlq (Gr lliil\[i,,{i {(-(,r (q]ztcr) ri(.r t}. +t', ciqu:i Ag R rriril uur rrdl.,rs[.,rlqqi[i 6/sc{-{lr{B1tatIoo2t,oatt6(1)(2)::l\lR"l9 NlR 222255(2)MR2(3)4vn'(4)1!lrrrn,22(3)4rrrnt(4)1812MR2 SPACE FOR ROUGH WORK / rt 3r.{i i{r-I2A/Page 4 Irrom a uniform circul;rr tlisc of radius RR-,nLl rrrtr>! tr \ , , ,,i - ,.rroverl rs shoh'n in th. figure. The'l-,Ilr,.nl ' l ,'f lhc rpmarning Ji\Lirbout an axis perpendicular to the planeoI thL, disc and passing through centre ofLlisc is :(1) 4 MR2(r)!Z un'qqla{i rr[.,1r rr-r+ut R A6111 4-i 9 M EsrPLr,qit x{ r "rit ', [ f !.))))]]]]]]}}}}}}}}}}}}}}

5 '{tti .,rtict o..r(-,,.r-rr hq((1 :i oRtt ] {l \r i E41 4q1-i ,-r-r(q{qx1 ii:e o/sl.,{il ql:.{L'u(3) 10 MR2(1) 4 MR2t,\ 19 vn'940:: l\4R'9(3) 10 MR,A particle is moving with a urdform speedin a circular orbit of radius R in a centralforce inversely proportional to the nthpower of R. lf the period of rotation of theparticle is T, then :(1) Tc R3/2 for any n.(4)\IRo)s rgr urt< "ls.{ ur{ n Aoi{u <{ruLr roiG.{r r ,rq.[ qq ] i R il ns tur-u "ln rxqreHiqa B, -{1.{ur trq,G:l t}. ol rcr-ilqtrrLR- .tsrdlq T d-i{ a __ .379l9It8(2)(3)(4)T: R'Tr R(n+1)/2T t Rn/2 SPACE FOI{ ROUGH WORK / ?t rtr{t tr-ld,rqr n rD T* Rs/:TdRr'T d R(n+ 1)/2T e Rn/2(1)(2)(3)(4)A/Page 5t2!lt2RF^?nq9A sotid sphere of radius r made oi a softmaterialof bull modulus K is surrounLledby a liquid in a.)))}}}}}}}}}}}}}}

6 Ylindrical container. Amassless piston of area a fk)ats on thesurface of the liquid, covering entirc crosssection of cylindrical container. \ rhen amass m is placed on the surface of thepiston to compress the liquid, the fractionaldecrement in the radius of the sphere,/drlt'lK iz{r 1iis,&ii ., . la'.. ,, O.,t-i r-L-l )irJi,r..r,4t5rilq ,{r11{i 4 {tdi (tir tr?t,1c ir.., iro-Su ".r"et e,rii[ [iv-t {t-it n rLl[ ni J. &+z:-t-j ei,it,-r-rcrELit{ \r1-li }j$.i r,1.:r}e qiL"ti 8. oaii m,izr1 eui 6tz+it+ttz1G\a utx{dti Eqlqai.)r'iqrr{'l Ao,{rr{[ ard r{iGt3 qz rs]I )!{i(t)Ka(2)3-g(3)_r"c3IG(4)ro. Q {e .,L ,{r{tG"tJ qr[e[ qr).t 2zC qri V,iz( * i& r). 11 ta1".il Q+.nsL .,t1or{ i1 re z v uBr 6. ai (a) iuti ,iR1 ${ (b) .riclir Gt.,rai uni ii3i(1) (a) 18e K (b) kI(z) (a) t95 K (b) kJ(r)Ka(2)3^g(3)mgiKa(1)10.]]]]]}}}}}}}} }}}}}}}

7 Two moles of an ideal monoatomic gasoccupies a volume V at 27'C. The gasexpands adiabatically to a volume 2 (a) the final temperature of thegas and (b) change in its intemal energt.(1) (a) r8e K (b) kJ(2) (a) 1e5 K @) kl(3) (a) 18e K (b) kl(a) (a) 1es K @) (3) (") l8e K (b) kI(a) (a) 1es K (b) kJA/PaEe 6 SPACE FOR ROUGH WORK / 1i$.ij +ltt't'1112 The mass Llf a hvdrogen molecule 2; k8. If 1023 hydrogenmolecules strike, per second, a fixed wallof area 2 cm? at an angle of 45'to thenormal, and rebound elastically with aspeed of 103 m/s, then the pressure on thewall is nearly :(1) x 103 N/m2(2) N/m2(3) x 102 N/m2(4) x 102 N/m2A silver atom in a solid oscillates in simpleharmonic motion in some direction with afrequency of 1012/sec.

8 What is the forceconstant of the bonds connecting one atomwith the other ? (Mole wt of silver = 16 andAvagadro number = x 10ts gm mole - l)(1) N/m(2) N/m(3) N/m(4) N/m11. trdlt6/-t .,r8.! 6ur x 10 27 kg 6. 6i tonUt4iLv< "rL.'10'irile, xR it'1, ? cm2 itriqq,rqil vllt le,ltr 6'ri n-u riur-r l>" rr irqr,r{\t( ettl{ d {:t {&R+!u\, it<t rO3 m/s itcs\ at{ \tut !i (rebound) d, rii [t'-ucr 6vi1 Eqrl9t arrafr qr1.(1)(2)(3)( x 103 x 103 x 102 102 N/m212. qi61 q-rqi qitl{i \rqrqj i,rts [ltrrqlto12lsec..{l e,tt"1(i { nrq .{ted rrQ ( )d t). {: .tugi u{lnt .tatq1 tu{ oisru ,,iq("t1-s) aD<r rur uarol+i \e{ }z{ crl ? ( qgarn = 108 "tr= x 108 gm mole - r)(1) N/m(2) N/m(3) N/m(a) N/m13. A granite rod of 60 cm length is ctampedl3at its middle point and is set intoIongitudinal vibrations.))]]}}}}}}}}}}}}}

9 The density ofgranite is 103 kg/m3 and its Young smodulus is xT)to Pa. Wlat will bethe fundamental frequencv of thelongitudinal vibrations ?(1) 5 kHz(2\ kHz(3) 10 kHz(4) kHzA/Page 7 SPACE FOR ROUGH WORK / ?i Ed{ iru,r6o cm eiqd ltna {3 ,hdz. +{O{ A{iqr{lqq r{irrsrql nyRrr tr1 <[i i"rn(longitudinal) e' }+qrNo srqrqi r{A 8.,)tdz-il q-rtL \103 )i{.i,riislcra pa r). r,u rti, ,tE t .,tt1R )zc{l tt1 ?(1) 5 kHz(2) kHz(3) 10 krL(4) kHz14. Three concentric metal shells A, B and CoI respective ratlii a, b and c {a < b < c)have surface charge densitjes + o, -tr and+ o respectivelv. The potential of shell Bis::{qt rBc;tir 5''r?ii A, ts 1,1-i C il 4$iEo/u,'t't a, b 4'1 c (a < t < c; il 1u {t'.l-it{ - o. - L, -"n I'd tJ. B-!'.lrr I[+tr{ ,1,1(1)(2)(3)(4)A/Page aa2 -b2+ctItood(l)iIta_- h_aa- +cb,-2 -2+abl^2 b2b +cb2-c2-+abb2 c2- +aItiLIl(2)(3)(4) lI.]]}}}}}}}}}}}}}}

10 *"ll15. A parallel plate capacitor of capacitance90 pF is connected to a battery of emf20 V. If a dielecnic material oI dielectricconstant K: I is inserted between the3plates, the magnitude of the inducedcharge will be r15. 90 pF .)e1j iiuu: q?r.{(1r qs urri(r laziqnti zo v ernf qtrqdl 4arl u{ qlsqrqiqra D. }. 5 ;. A urjdafizr utqftl q qlrlsddcltlt di vla'Hll qzii srrt<.tjrqrr{i :i{A r}. il&rr "11*otn1 r<qh.(1) n C(2) n C(3) n C(4) n C(1) n C(2) n c(3) n C(a) n CSPACE FOR ROUGH WORK / ?t sr{j +qrne-'Y 14>,Yq,.rlzJ16In an circuit, thc instantaneous current are given bl'e=100sin30ti=20sin I30t I, 4)In one cycle of , the average Powerconsumed by the circuit and the wattlesscurent are, resPechvelv :(1) s0, 101000(2t -'E .1050(3) t; ,0(4) 50, 017.)}}}