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1 hysics, Chemistry & Mthemtics (per-) Cde-5 AR : HYSCS -JEE-01 SECN- : Single Crrect Answer ype his sectin cntins 10 multiple chice questins. Ech questin hs fur chices,, nd (D) ut f which NLY NE is crrect: 1. A smll mss m is ttched t mssless string whse ther end is fixed t s shwn in the figure. he mss is underging circulr mtin is the x-y plne with centre t nd cnstnt ngulr speed. f the ngulr mmentum f the system, clculted but nd re dented by L nd L respectiely, then (D) L nd L L L d nt ry with time ries with time while L remins cnstnt remins cnstnt while L L nd L bth ry with time. ries with time Sl: [C] L is lng -xis while 0 L is perpendiculr t line jining mss t pint.. A bi-cnex lens is frmed with tw thin pln-cnex lenses s shwn in Sl: [B] the figure. Refrctie index n f the first lens is 1.5 nd tht f the secnd lens is 1.. Bth the cured surfces re f the sme rdius f curture R = 14 cm. Fr this bi-cnex lens, fr n bject distnce f 40 cm, the imge distnce will be 80.0 cm 40.0 cm 1.5 cm (D) 13.3 cm F bject is plced t F imge distnce = 40 cm F = 0 cm m R = 14 cm 3. he thin unifrm rd, pited t, is rtting in the hrintl plne with cnstnt ngulr speed, s shwn in the figure. At time t = 0, smll insect strts frm nd mes with cnstnt speed with respect t the rd twrds the ther end. t reches the end f the rd t t = nd stps. he ngulr speed f the system remins thrughut. he mgnitude f the trque ( ) n the system but, s functin f time is best represented by which plt? (D) t t t t Amity : hnes: /44, //3/4, /4 - -

2 hysics, Chemistry & Mthemtics (per-) Cde-5 -JEE-01 l Sl: [B] Velcity f insect w.r.t. rd = Angulr mmentum t time t where l is length f rd l dl l L rd m t 0 m dt, which is liner. 4. A mixture f mles f helium gs (tmic mss = 4 mu) nd 1 mle f rgn gs (tmic mss = 40 mu) is kept t 300 K in cntiner. he rti f the speeds (helium) (rgn) is (D) 3.16 Sl: [D] 1 M (helium) 40 (rgn) w lrge erticl nd prllel metl pltes hing seprtin f 1 cm re cnnected t DC ltge surce f ptentil difference X. A prtn is relesed t rest midwy between the tw pltes. t is fund t me t 45 t the erticl JUS fter relese. hen X is nerly V V V (D) V Sl: [C] qe = mg e mg. X X d 7 mgd e lt 6. hree ery lrge pltes f sme re re kept prllel nd clse t ech ther. hey re cnsidered s idel blck surfces nd he ery high therml cnductiity. he first nd third pltes re mintined t tempertures nd 3 respectiely. he temperture f the middle (i.e. secnd) plte under stedy stte cnditin is 65 1/ / / 4 (D) 1/ 4 97 Sl: [C] Let re f ne side f plte = A A(3) 4 A() 4 = A 1 4 1/ Amity : hnes: /44, //3/4, /4-3 -

3 hysics, Chemistry & Mthemtics (per-) Cde-5 -JEE A smll blck is cnnected t ne end f mssless spring t un-stretched length 4.9 m. he ther end f the spring (see the figure) is fixed. he system lies n hrintl frictinless surfce. he blck is stretched by 0. m nd relesed frm rest t t = 0. t then executes simple hrmnic mtin with ngulr frequency rd/s. Simultneusly t t = 0, smll pebble is prjected with speed frm pint t 3 n ngle f 45 s shwn in the figure. int is t hrintl distnce f 10 m frm. f the pebble hits the blck t t =1s, the lue f is (tke g = 10 m/s ) 50 m/s 51 m/s 5 m/s (D) 53 m/s 1 sin 45º Sl: [A] ime f flight f pebble, t 1 g m/sec. 8. Yung s duble slit experiment is crried ut by using green, red nd blue light, ne clur t time. he fringe widths recrded re G, R nd B, respectiely. hen, 10 m G B > R B G > R R B > G (D) R G > B Sl: [D] R > G > B 9. Cnsider thin sphericl shell f rdius R with its centre t the rigin, crrying unifrm psitie surfce chrge density. he ritin f the mgnitude f the electric field E ( r ) nd the electric ptentil V(r) with the distnce r frm the centre, is best represented by which grph? 45 x R r R r (D) R r R r Sl: [D] Fctul Amity : hnes: /44, //3/4, /4-4 -

4 hysics, Chemistry & Mthemtics (per-) Cde-5 -JEE-01 4MLg 10. n the determintin f Yung s mdulus Y by using Serle s methd, wire f length ld L = m nd dimeter d = 0.5 mm is used. Fr ld M =.5 kg, n extensin l = 0.5 mm in the length f the wire is bsered. Quntities d nd l re mesured using screw guge nd micrmeter, respectiely. hey he the sme pitch f 0.5 mm. he number f diisins n their circulr scle is 100. he cntributins t the mximum prbble errr f the Y mesurement due t the errrs in the mesurement f d nd l re the sme due t the errr in the mesurement f d is twice tht due t the errr in the mesurement f l. due t the errr in the mesurement f l is twice tht due t the errr in the mesurement f d. (D) due t the errr in the mesurement f d is fur times tht due t the errr in the mesurement f l. Sl: [B] Y l d errr in d cuses mre errr in Y. Y l d SECN- : Multiple Crrect Answers ype his sectin cntins 5 multiple chice questins. Ech questin hs fur chices,, nd (D) ut f which NE R MRE re crrect. 11. Cnsider the mtin f psitie pint chrge in regin where there re simultneus unifrm electric nd mgnetic fields E E ˆ j nd B B ˆ j. At time t = 0, this chrge hs elcity in the x - y plne, mking nd ngle with the x-xis. Which f the fllwing ptin (s) is(re) crrect fr time t > 0? f = 0, the chrge mes in circulr pth in the x plne f = 0, the chrge underges helicl mtin with cnstnt pitch lng the y-xis. f = 10, the chrge underges helicl mtin with its pitch incresing with time, lng the y-xis. (D) f = 90, the chrge underges liner but ccelerted mtin lng the y-xis. Sl: [C,D] Fr 0 < 90 th is helicl, but fr = 90º, there is n mgnetic frce nd under E it will me lng y-xis. 1. A cubicl regin f side hs its centre t the rigin. t enclses three fixed pint chrges, q t (0, /4, 0) 3q t (0, 0, 0) nd q t (0, /4, 0). Chse the crrect ptin (s). he net electric flux crssing the plne x = / is equl t the net electric flux crssing the plne x = /. he net electric flux crssing the plne y = / is mre thn the net electric flux crssing the plne q 3q q y y = /. x he net electric flux crssing the entire regin is q/ 0 (D) he net electric flux crssing the plne = / is equl t the net electric flux crssing the plne x = / Amity : hnes: /44, //3/4, /4-5 -

5 hysics, Chemistry & Mthemtics (per-) Cde-5 -JEE-01 Sl: [A,C,D] lne x, y nd re symmetric w.r.t. chrge distributins. 13. A persn blws int pen end f lng pipe. As result, high-pressure pulse f ir trels dwn the pipe. When this pulse reches the ther end f the pipe. high-pressure pulse strts trelling up the pipe, if the ther end f the pipe is pen lw-pressure pulse strts trelling up the pipe, if the ther end f the pipe is pen lw-pressure pulse strts trelling up the pipe, if the ther end f the pipe is clsed (D) high-pressure pulse strts trelling up the pipe, if the ther end f the pipe is clsed Sl: [B,D] pen end cts s fixed end while clsed end s free end fr purpse f reflectin f pressure f the medium. 14. A smll blck f mss f 0.1 kg lies n fixed inclined plne Q which mkes n ngle with the hrintl. A hrintl frce f 1 N cts n the blck thrugh its centre f mss s shwn in the figure. he blck remins sttinry if (tke g = 10 m/s ) Q = 45 > 45 nd frictinl frce cts n the blck twrds > 45 nd frictinl frce cts n the blck twrds Q (D) < 45 nd frictinl frce cts n the blck twrds Q Sl: [A,C] Fr, 1 cs = sin i.e., = 45º Net frce n blck is er in the bsence f frictin. Fr > 45º, blck hs tendency t me dwnwrd nd fr < 45º, it hs tendency t me upwrds. 15. Fr the resistnce netwrk shwn in the figure, chse the crrect ptin (s) he current thrugh Q is er 1 = 3A he ptentil s S is less thn the t Q (D) = A 1N Sl: [A,B,C,D] n the bsence f resistnce between nd Q & S nd V = V Q nd V S = V here is n effect n current distributin when resistnce f 1 ech re cnnected crss nd Q & S nd. R e A A 18 Amity : hnes: /44, //3/4, /4-6 -

6 hysics, Chemistry & Mthemtics (per-) Cde-5 -JEE-01 SECN- : nteger Answer ype his Sectin cntins fie questins. he nswer t ech questin is single digit integer, rnging frm 0 t 9 (bth inclusie). 16. A circulr wire lp f rdius R is plced in the x-y plne centered t the rigin. A squre lp f side ( << R) hing tw turns is plced with its centre t = 3R lng the xis f the circulr wire lp, s shwn in figure. he plne f the squre lp mkes n ngle f 45 with respect t the -xis. f the mutul inductnce between the lps is gien by p /, then the lue f p is R Sl. [7] B n squre lp = 0iR 0i 3/ ( R 3 R ) 16R 0i 0i Flux sscited with squre lp, cs45º 16R 8 R 0 M i 8 R Cmpring / = 7/ p = An infinitely lng slid cylinder f rdius R hs unifrm lume chrge density. t hs sphericl city f rdius R/ with its centre n the xis f the cylinder, s shwn in the figure. he mgnitude f the electric field t the pint, which is t distnce R frm the xis f the cylinder, is gien by the expressin 3 R 16k. he lue f k is x x R 45 R/ R R y y Sl. [6] Electric field t = E R ( R / ) E 3 tl Sphericl prt 0 R 3 0( R) R R 3R = E sphericl prt E tl Cmpring, k = A prtn is fired frm ery fr wy twrds nucleus with chrge Q = 10 e, where e is the electrnic chrge. t mkes clsest pprch f 10 fm t the nucleus. he de Brglie welength (in unit f fm) f 1 the prtn t its strt is: (tke the prtn mss, m p = (5/3) 10 7 kg; h/e = J.s/C; 910 m/f, 4 1 fm = m) Amity : hnes: /44, //3/4, /4-7 -

7 hysics, Chemistry & Mthemtics (per-) Cde-5 -JEE-01 Sl. [7] K.E. f prtn = e e 10 4 h (m 108e 10 ) 4 1/ ( ) / = m = 7 fm 19. A lmin is mde by reming smll disc f dimeter R frm bigger disc f unifrm mss density nd rdius R, s shwn in the figure. he mment f inerti f this lmin but xes pssing thrugh nd is nd, respectiely. Bth these xes re perpendiculr t the plne f the lmin. he rti integer is p t the nerest R R Sl. [3] 0 M ( R) ( M / 4)( R ) M.( R) 4 = M ( R) M R M 37MR MR. ( R 5) MR 13MR MR A cylindricl city f dimeter exists inside cylinder f dimeter Sl. [5] s shwn in the figure. Bth the cylinder nd the city re infinitely lng. A unifrm current density J flws lng the length. f the mgnitude f the mgnetic field t the pint is gien by N J 1, then the lue f N is 0J 0 J( / ) B 3 50J B = 1 Cmpring, N = 5 Amity : hnes: /44, //3/4, /4-8 -