giai chi tiet de ly 2011

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GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c1 Pliku Gia lai THI TUYN SINH I HC KHI A NM 2011 Mn thi : VT L M 817(Thi gian lm bi : 90 pht) Chobit:hngsPlngh=6,625.10-34J.s;lnintchnguynte=1,6.10-19C;tcnhsng trong chn khng c = 3.108 m/s; 1u = 931,5 MeV/c2. I. PHN CHUNG CHO TT C TH SINH (40 cu, t cu 1 n cu 40) Cu 1:t inp u =2 cos 2 U ft (Ukhngi,tnsfthayi c)vohaiu onmch mc ni tip gm in tr thun R, cun cm thun c t cm L v t in c in dung C. Khi tn s l f1 th cm khng v dung khng ca on mch c gi tr ln lt l 6O v 8 O. Khi tn s l f2 th h s cng sut ca on mch bng 1. H thc lin h gia f1 v f2 lA. f2 = 12.3f B. f2 = 13.2f C. f2 = 13.4 f D. f2 = 14.3 fCu 2: Ln lt t cc in p xoay chiu u1 = 12 cos(100 ) U t + ; u2 =22 cos(120 ) U t +v u3 =32 cos(110 ) U t +vo hai u on mchgm in tr thun R, cun cm thun c t cm L v t in c in dung C mc ni tip th cng dng in trong on mch c biu thc tng ng l: i1 =2 cos100 I t ; i2 = 22 cos(120 )3I t +v i3 = 2' 2 cos(110 )3I t . So snh I v I, ta c: A. I = I.B. I =' 2 I .C. I < I.D. I > I. Cu 3: Gi s trong mt phn ng ht nhn, tng khi lng ca cc ht trc phn ng nh hn tng khi lng cc ht sau phn ng l 0,02 u. Phn ng ht nhn ny A. thu nng lng 18,63 MeV.B. thu nng lng 1,863 MeV. C. ta nng lng 1,863 MeV.D. ta nng lng 18,63 MeV. Gii: M0 < M : phn ng thu nng lng .W= M.931,5MeV A ChnA Cu 4: Bn mt prtn vo ht nhn 73Ling yn. Phn ng to ra hai ht nhn X ging nhau bay ra vi cng tc v theo cc phng hp vi phng ti ca prtn cc gc bng nhau l 600. Ly khi lng ca mi ht nhn tnh theo n v u bng s khi ca n. T s gia tc ca prtn v tc ca ht nhn X l A. 4.B. 14.C. 2.D. 12. Gii: 02 . os60p X XP Pc P = = p p x xm v m v = 4pxx pvmv m= = ChnA Cu 5: Khi lectron qu o dng th n th nng lng ca nguyn t hirc xc nh bi cng thc En = 213, 6n (eV) (vi n = 1, 2, 3,). Khi lectron trong nguyn t hirchuyn t qu o dng n = 3 v qu o dng n = 1 th nguyn t pht ra phtn c bc sng 1. Khi lectron chuyn t qu o dng n = 5 v qu o dng n = 2 th nguyn t pht ra phtn c bc sng 2. Mi lin h gia hai bc sng 1 v 2 l A. 272 = 1281.B. 2 = 51.C. 1892 = 8001.D. 2 = 41. Gii: 3 115 22hcE EhcE E = = 2 3 11 5 2E EE E=thay s vo ta chn p n C Cu 6: Khi ni v tia , pht biu no sau y sai? A. Tia khng phi l sng in t. B. Tia c kh nng m xuyn mnh hn tia X. C. Tia khng mang in. GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c2 Pliku Gia lai D. Tia c tn s ln hn tn s ca tia X. Gii: Bn cht ca Tia ( gamma ) l sng in t. Cu 7: Nguyn tc hot ng ca quang in tr da vo A. hin tng tn sc nh sng.B. hin tng quang in ngoi. C. hin tng quang in trong.D. hin tng pht quang ca cht rn. Gii: Chn CCu 8: Trong nguyn t hir, bn knh Bo l r0 = 5,3.10-11m. mt trng thi kch thch ca nguyn t hir, lectron chuyn ng trn qu o dng c bn knh l r = 2,12.10-10m. Qu o c tn gi l qu o dng A. L.B. O.C. N.D. M. Gii: 02rnr= = ChnA Cu 9: Mtkhungdydnphngquayuvi tc gcequanhmttrcc nhnmtrongmt phngkhungdy,trongmtttrngucvectcmngtvunggc vitrc quaycakhung. Sut in ng cm ng trong khung c biu thc e = 0cos( )2E t + . Ti thi im t = 0, vect php tuyn ca mt phng khung dy hp vi vect cm ng t mt gc bng A. 450.B. 1800.C. 900.D. 1500. Cu 10: Mt cht im dao ng iu ha trn trc Ox. Khi cht im i qua v tr cn bng th tc ca n l 20 cm/s. Khi cht im c tc l 10 cm/s th gia tc ca n c ln l40 3 cm/s2. Bin dao ng ca cht im lA. 5 cm.B. 4 cm.C. 10 cm.D. 8 cm. Gii: ax2 224 220mv Aa vA = = = + thay s gii ra ta c p n A Cu 11: Mt cht pht quang c kch thch bng nh sng c bc sng 0,26 um th pht ra nh sng c bc sng 0,52 um. Gi s cng sut ca chm sng pht quang bng 20% cng sut ca chm sng kch thch. T s gia s phtn nh sng pht quang v s phtn nh sng kch thch trong cng mt khong thi gian l A. 45.B. 110.C. 15.D. 25. Gii: P1, N1, 1nh sng pht quang P2, N2, 2nh sng kch thch Theo 121 1 1 1 22 2 2 2 115. ..PPP N NP N N == =thay s ta chn D Cu12:Mtchtimdaongiuhatheophngtrnhx= 24cos3t(xtnhbngcm;ttnh bng s). K t t = 0, cht im i qua v tr c li x = -2 cm ln th 2011 ti thi im A. 3015 s.B. 6030 s.C. 3016 s.D. 6031 s. Gii: Trong mt chu k T vt qua v tr li x = - 2cm hai lnN Khong thi gian 11005 ( ) t Ts =vt qua v tr c li x = -2cm2010 ln + Ti M : t = 0 , x = 4cm ; Ti N : x = -2cm . Vt qut gc 23 =- M 23 2 GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c3 Pliku Gia lai

2231( )23t s = = =Vy :1 21005.3 1 3016( ) t t t s = + = + = Cu 13: Nu ni hai u on mch gm cun cm thun L mc ni tip vi in tr thun R = 1O vo haicccanguninmtchiucsut inngkhngivintrtrong rthtrongmchc dng in khng i cng I. Dng ngun in ny np in cho mt t in c in dung C = 2.10-6F. Khi in tch trn t int gi tr cci, ngt t inkhingun ri ni t invi cun cm thun L thnh mt mch do ng th trong mch c dao ng in t t do vi chu k bng t.10-6 s v cng dng in cc i bng 8I. Gi tr ca r bng A. 0,25 O.B. 1 O.C. 0,5 O.D. 2 O. Cu 14: Mt lng knh c gc chit quang A = 60 (coi l gc nh) c t trong khng kh. Chiu mt chm nh sng trng song song, hp vo mt bn ca lng knh theo phng vung gc vi mt phng phn gic ca gc chit quang, rt gn cnh ca lng knh. t mt mn E sau lng knh, vung gc vi phng ca chm tia ti v cch mt phng phn gic ca gc chit quang 1,2 m. Chit sut ca lng knh i vi nhsng ln= 1,642 v i vi nh sng tm lnt = 1,685. rng t mu n mu tm ca quang ph lin tc quan st c trn mn l A. 4,5 mm.B. 36,9 mm.C. 10,1 mm.D. 5,4 mm. Gii: B rng quang ph. ( )t dl d D dn n A = A = (vi A chuyn v n v Rad ) Chn D Cu 15: Mt cht im dao ng iu ha trn trc Ox vi bin 10 cm, chu k 2 s. Mc th nng v tr cn bng. Tc trung bnh ca cht im trong khong thi gian ngn nht khi cht im i t v tr c ng nng bng 3 ln th nng n v tr c ng nng bng 13 ln th nng l A. 26,12 cm/s.B. 7,32 cm/s.C. 14,64 cm/s.D. 21,96 cm/s. Gii: M V tr ti c W = n Wt: 1Axn= +N t1d t 23W51W W 5 33dWx cmx cm= = = = Da vo hnh v tnh c 1( )6. 65 3 521,96 /16tbt ssv cmst = = == = = Cu 16: Mt on mch AB gm hai on mch AM v MB mc ni tip. on mch AM gm in tr thun R1 mcni tip vi t in c in dungC, on mch MBgm in tr thunR2 mcni tip vi cun cm thun c t cm L. t in p xoay chiu c tn s v gi tr hiu dng khng i vo hai u on mch AB. Khi on mch AB tiu th cng sut bng 120 W v c h s cng sut bng 1. Nu ni tt hai u t in th in p hai u on mch AM v MB c cng gi tr hiu dng nhng lch pha nhau 3, cng sut tiu th trn on mch AB trong trng hp ny bng A. 75 W.B. 160 W.C. 90 W.D. 180 W. Cu 17: Chiu t nc ra khng kh mt chm tia sng song song rt hp (coi nh mt tia sng) gm 5 thnh phn n sc: tm, lam, , lc, vng. Tia l n sc mu lc i l l mt nc (st vi mt phn 55 3GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c4 Pliku Gia lai cch giahai mi trng). Khngk tia n scmu lc, cc tial ra ngoikhngkhl cc tia n sc mu: A. tm, lam, .B. , vng, lam.C. , vng.D. lam, tm. Cu 18: Khi ni v mt vt dao ng iu ha, pht biu no sau y sai? A. Lc ko v tc dng ln vt bin thin iu ha theo thi gian. B. ng nng ca vt bin thin tun hon theo thi gian. C. Vn tc ca vt bin thin iu ha theo thi gian. D. C nng ca vt bin thin tun hon theo thi gian. Cu 19: Thc hin th nghim Y-ng v giao thoa vi nh sng n sc mu lam ta quan st c h vngiao thoa trn mn. Nu thay nhsng nsc mulam bngnh sng n sc mu vng vcc iu kin khc ca th nghim c gi nguyn th A. khong vn tng ln.B. khong vn gim xung. C. v tr vn trung tm thay i.D. khong vn khng thay i. Gii: khong vn Dia=khong vn t l thun vi bc sng ; m v lam > Chn A Cu 20: Pht biu no sau y l sai khi ni v sng in t? A. Khi sng in t gp mt phn cch gia hai mi trng th n c th b phn x v khc x. B. Sng in t truyn c trong chn khng. C. Sng in t l sng ngang nn n ch truyn c trong cht rn. D. Trong sng in t th dao ng ca in trng v ca t trng ti mt im lun ng pha vi nhau. Gii : Sng in t l sng ngang, truyn c trong mi mi trng k c chn khng Cu 21: Mt mch dao ng LC l tng gm cun cm thun c t cm 50 mH v t in c in dung C. Trong mch ang c dao ng in t t do vi cng dng ini = 0,12cos2000t (i tnh bngA, t tnh bngs). thi im mcng dng in trong mch bng mt nacng hiu dng th hiu in th gia hai bn t c ln bng A. 12 3 V.B.5 14 V.C.6 2 V.D.3 14 V. Gii: 2 20 00 0012 2 2i uI UU L II Ii| | | | + = ||\ . \ .= = = 011 3 148u L I V = =Cu 22: Pht biu no sau y l ng khi ni v sng c? A. Bc sng l khong cch giahai im trncng mt phng truynsng m dao ng ti hai im cng pha. B. Sng c truyn trong cht rn lun l sng dc. C. Sng c truyn trong cht lng lun l sng ngang. D. Bc sng l khong cch gia hai im gn nhau nht trn cng mt phng truyn sng m dao ng ti hai im cng pha. Cu 23: mt cht lng c hai ngun sng A, B cch nhau 18 cm, dao ng theo phng thng ng vi phng trnh l uA = uB = acos50tt (vi t tnh bng s). Tc truyn sng ca mt cht lng l 50 cm/s. Gi O l trung im ca AB, im M mt cht lng nm trn ng trung trc ca AB v gn O nht sao cho phn t cht lng ti M dao ng cng pha vi phn t cht lng ti O. Khong cch MO l A. 10 cm.B.2 10cm.C.2 2 .D. 2 cm. Gii:2vcmf = = GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c5 Pliku Gia lai Phngtrnhsngtnghptimtimbtkdo2nguntruynn 2 1 2 12 os ( ) os 2 ft+ ( ) u Ac d d c d d | | | |= + ||\ . \ .M Pha ti O : 09 = ; Pha ti im M : 1 2( )Md d= + M cng pha vi O khi : 02Mk =; M gn O nhtnn chn k = 1 O B

1 211 d d cm = = MO=2 10cm Cu 24: Mt con lc n c treo vo trn mt thang my. Khi thang my chuyn ng thng ng i ln nhanh dn u vi gia tc c ln a th chu k dao ng iu ha ca con lc l 2,52 s. Khi thang my chuyn ng thng ng i ln chm dn u vi gia tc cng c ln a th chu k dao ng iu ha ca con lc l 3,15 s. Khi thang my ng yn th chu k dao ng iu ha ca con lc l A. 2,96 s.B. 2,84 s.C. 2,61 s.D. 2,78 s. Gii:2lTg = ;12lTg a =+; 22lTg a = 211T g aT g aT g aT g+=+= 2, 78 T s = Cu 25: Khi ni v h Mt Tri, pht biu no sau y sai? A. Sao chi l thnh vin ca h Mt Tri. B. Cc hnh tinh chuyn ng quanh Mt Tri theo cng mt chiu. C. Hnh tinh xa Mt Trinht l Thin Vng tinh. D. Hnh tinh gn Mt Tri nht l Thy tinh. Gii: Hnh tinh xa Mt Trinht l Hi Vng tinh. Cu 26: Dao ng ca mt cht im c khi lng 100 g l tng hp ca hai dao ng iu ha cng phng, c phng trnhli lnlt lx1 = 5cos10t v x2 = 10cos10t (x1 v x2 tnh bng cm, t tnh bng s). Mc th nng v tr cn bng. C nng ca cht im bng A. 0,1125 J.B. 225 J.C. 112,5 J.D. 0,225 J. Gii: Bm 1 1 2 2A A Z + Z 15 0 A Z= Z C nng : 21W= 0,11252m A J = Cu 27: Mt si dy n hi cng ngang, ang c sng dng n nh. Trn dy, A l mt im nt, B l mt im bnggn Anht, Cl trung im ca AB, vi AB =10cm. Bitkhong thigianngn nht gia hai ln m li dao ng ca phn t ti B bng bin dao ng ca phn t ti C l 0,2 s. Tc truyn sng trn dy l A. 2 m/s.B. 0,5 m/s.C. 1 m/s.D. 0,25 m/s. Gii:40cm = V C l trung im ca AB nn bin dao ng ca phn t ti C l5 2cm khong thi gian ngn nht gia hai ln m li dao ng ca phn t ti B bng bin dao ng ca phn t ti C l 0,2 s. 2.2t T = =0,8 T s = 0, 5 / v msT= =Cu 28: Mt hc sinh qun mt my bin p vi d nh s vng dy ca cun s cp gp hai ln s vng dy ca cun th cp. Do s sut nn cun th cp b thiu mt s vng dy. Mun xcnh s vng dy thiu qun tip thmvo cun th cp cho ,hc sinhny t vo hai u cun s cp mt in p xoay chiu c gi tr hiu dng khng i, ri dng vn kt xc nh t s in p cun th cp h v cun s cp. Lc u t s in p bng 0,43. Sau khi qun thm vo cun th cp 24 vng dy th t s in p bng 0,45. B qua mi hao ph trong my bin p. c my bin p ng nh d nh, hc sinh ny phi tip tc qun thm vo cun th cp A. 40 vng dy.B. 84 vng dy.C. 100 vng dy.D. 60 vng dy. 2d9 GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c6 Pliku Gia lai Cu 29: Cht phng x plni 21084Po pht ra tia o v bin i thnh ch 20682Pb. Cho chu k bn r ca 21084Po l 138 ngy. Ban u (t = 0) c mt mu plninguyn cht. Tithi im t1, t s gia s ht nhn plniv s ht nhn ch trong mu l 13. Ti thi im t2 = t1 + 276 ngy, t s gia s ht nhn plniv s ht nhn ch trong mu l A. 115.B. 116.C. 19.D. 125. Gii: 12''2 1 32 1 15tPb TPotPb TPoNNNN= == = '1115PoPbNN =Cu 30: Mt con lc l xo t trn mt phngnm nganggm l xo nh c mt u c nh, u kia gn vi vt nh m1. Ban u gi vt m1 ti v tr m l xo b nn 8 cm, t vt nh m2 (c khi lng bngkhilngvtm1) trnmtphngnmngangvstvivtm1.Bungnhhaivtbtu chuyn ng theo phng ca trc l xo. B qua mi ma st. thi im l xo c chiu di cc i ln u tin th khong cch gia hai vt m1 v m2 l A. 4,6 cm.B. 2,3 cm.C. 5,7 cm.D. 3,2 cm. Gii: Giai on t ( A1 n O ) h dao ng vi chu k 1122mTk =Ti O vt m1 v m2 cng t vn tc ax 1 1 mv A = +Giaion2(tOnA2):m2chuynngthngucqungng: 2ax ax. . 2 2 ( )4m mTs v t v cm = = = 1mdao ng vi chu k 122mTk = ; V tnh lin tc nn vn tc ti bn phi O bng vn tc bn tri O ngha l : 1 1 2 2A A =1 1 1224 22A AA cm = = =khong cch gia hai vt m1 v m2 l :2 2 4 2 3, 2 s cm A = =Cu 31: t in p xoay chiu u =U 2 cos100 t vo hai u on mch mc ni tip gm in tr thun R, t in c in dung C v cun cm thun c t cm L thay i c. iu chnh L in p hiu dng hai u cun cm t gi tr cci th thygi trcc i bng 100 V v in p hiu dng hai u t in bng 36 V. Gi tr ca U l A. 80 V.B. 136 V.C. 64 V.D. 48 V. Cu 32: Trong th nghim Y-ng v giao thoa nh sng, khe hp S pht ra ng thi ba bc x n sc c bc sng l 1 = 0,42um, 2 = 0,56um v 3 = 0,63um. Trn mn, trong khong gia hai vn sng lin tip c mu ging mu vn trung tm, nu hai vn sng ca hai bc x trng nhau ta ch tnh l mt vn sng th s vn sng quan st c l A. 21.B. 23.C. 26.D. 27. Gii: iu kin trng vn : 1 2 3k l m = = Lp t l : 43 38932lk l lm lk m= = +==t3 l n = 3483l nk nm n = = =

Trng ln u ti vn trung tam O : n =0 ; l = 0 ; k = 0 ; m = 0 GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c7 Pliku Gia lai ln haitin = 3; l = 9 ; k = 12 ; m = 8 Vy trong khong gia hai vn trung c 26 vn sng ca 3 mu trong C 2 vn trng ca h hai bc x 1v 2ng vi3; 4 l k = =v6; 8 l k = =C 3 vn trng ca h hai bc x 1v 3ng vim = 2; k = 3 v m = 4; k = 6 v m = 6; k = 9 KT LUN : theo bi ta s c:26 - ( 2 + 3 )= 21 vn Cu 33 : t in p2 cos u U t = vo hai u mt t in th cng dng in qua n c gi tr hiu dng l I. Ti thi im t, in p hai u t in l u v cng dng in qua n l i. H thc lin h gia cc i lng lA. 2 22 2u i 1U I 4+ = B. 2 22 2u i1U I+ = C. 2 22 2u i2U I+ = D. 2 22 2u i 1U I 2+ =Cu 34 : Theo thuyt tng i, mt lectron c ng nng bng mt na nng lng ngh ca n th lectron ny chuyn ng vi tc bng A. 2,41.108 m/sB. 2,75.108 m/sC. 1,67.108 m/sD. 2,24.108 m/s Gii: Ta c : W = 01 02EE E =1 00122321E EEEvc= = 82, 24.10 / v ms =Cu35:tinpxoaychiuu=U0coset(U0khngivethayic)vohaiuon mch gm in tr thun R, cun cm thun c t cm L v t in c in dung C mc ni tip, vi CR2 < 2L. Khi e = e1 hoc e = e2 th in p hiu dng gia hai bn t in c cng mt gi tr. Khi e = e0 th in p hiu dng gia hai bn t in t cc i. H thc lin h gia e1, e2 v e0 l A. 0 1 21( )2e = e +e B. 2 2 20 1 21( )2e = e + e C. 0 1 2e = e e D. 2 2 20 1 21 1 1 1( )2= +e e e Cu 36 : on mch AB gm hai on mch AM v MB mc ni tip. on mch AM gm in tr thun R1 = 40 O mc ni tip vi t in c din dng 310C F4=t, on mch MB gm in tr thun R2mcnitipvicuncmthun.tvoA, Binpxoaychiucgitrhiudngvtns khngithinptcthihaiuonmchAMvMBlnltl: AM7u 50 2 cos(100 t ) (V)12t= t v MBu 150cos100 t (V) = t . H s cng sut ca on mch AB lA. 0,86.B. 0,84.C. 0,95.D. 0,71. Cu 37:TrongthnghimY-ngvgiaothoanhsng,haikhecchiubngnhsngnsc, khong cch gia hai khe l 0,6 mm. Khong vn trn mn quan st o c l 1 mm. T v tr ban u, nutnhtinmnquanstmton25cmlignmtphngchahaikhe thkhongvnmitrn mn l 0,8 mm. Bc sng ca nh sng dng trong th nghim lA. 0,64 umB. 0,50 umC. 0,45 umD. 0,48 um Gii: 1 12 21 20, 25i Di DD D== +11, 25 D m =11.0, 48a imD = =Cu 38 : Hin tng quang in ngoi l hin tng lectron b bt ra khi tm kim loi khi A. chiu vo tm kim loi ny mt chm ht nhn heli. B. chiu vo tm kim loi ny mt bc x in t c bc sng thch hp. C. cho dng in chy qua tm kim loi ny. D. tm kim loi ny b nung nng bi mt ngun nhit. Cu 39: Trong mch dao ngLC l tng angc daong in t t do. Thigianngnnht nng lng in trng gim t gi tr cc i xung cn mt na gi tr cc i l 1,5.10-4s. Thi gian ngn nht in tch trn t gim t gi tr cc i xung cn mt na gi tr l A. 2.10-4s.B. 6.10-4s.C. 12.10-4s.D. 3.10-4s. GV: L Vn c Gii chi tit l 2011 Tell : 01642.032.372 Thy c8 Pliku Gia lai Gii: Ta c W = Wt 02Qq =. Thi gian t Qo n 02Ql: 41,5.108Tt s= =410( / )6rad s =Thi gian t Qo n 02Q : 42.103.t s= =Cu 40:MtngunimOphtsngmccngsutkhngitrongmtmitrngtruynm ng hng v khng hp th m. Hai im A, B cch ngun m ln lt l r1 v r2. Bit cng m ti A gp 4 ln cng m ti B. T s 21rr bng A. 4.B. 12.C. 14.D. 2. Gii: C : 22 11 24r Ir I| |= = |\ .

212rr =II. PHN RING [10 cu] Th sinh ch c lm mt trong hai phn (phn A hoc B) A. Theo chng trnh Chun (10 cu, t cu 41 n cu 50) Cu 41 : Cng thot lectron ca mt kim loi l A = 1,88 eV. Gii hn quang in ca kim loi ny c gi tr l A. 550 nmB. 220 nmC. 1057 nmD. 661 nm Gii: C 0661hcnmA = =( A i ra n v Jun ) Cu 42 :Mtchtimdao ngiuhatrntrcOx.Trongthigian31,4schtimthchin c 100 dao ng ton phn. Gc thi gian l lc cht im i qua v tr c li 2 cm theo chiu m vi tc l40 3cm/s. Ly t = 3,14. Phng trnh dao ng ca cht im l A.x 6cos(20t ) (cm)6t= B.x 4cos(20t ) (cm)3t= +C.x 4cos(20t ) (cm)3t= D.x 6cos(20t ) (cm)6t= +Gii: Gc thi gian l lc cht im i qua v tr c li 2 cm theo chiu m , nu bin l 6cm th 3 2 <