GATE-PH 7 Q. Q.5 : Cy ONE mk ech.. In he nucle ecion 6 e 7 PHYSICS-PH C v N X, he picle X is () n elecon n ni-elecon (c) muon (d) pion. Two idenicl msses of gm ech e conneced by mssless sping of sping consn N/m. The noneo ngul eigen fequency of he sysem is d/s. (up o wo deciml plces).. Conside iomic molecule of he shpe shown in he figue below in hee dimensions. The he cpciy of his molecule high empeue (empeue much highe hn he vibionl nd oionl enegy scles of he molecule bu lowe hn is bond dissociion enegies) is: () k B k B (c) 9 k B (d) 6k B. Fo he Hmilonin H I b. whee R, b is el veco, I is he ideniy mi nd e he Puli mices, he gound se enegy is () b b (c) b (d) 5. The Poisson bcke, p y yp is equl o () y (c) p (d) py 6. The wvefuncion of which obil is spheiclly symmeic: () p p y (c) s (d) d y 7. A monochomic plne wve in fee spce wih elecic field mpliude of /m is nomlly inciden on fully eflecing mio. The pessue eeed on he mio is P. (up o wo deciml plces) ( 8.85 F/m). 8. The eleconic gound se enegy of he Hydogen om is.6 e. The highes possible eleconic enegy eigense hs n enegy equl o () e (c) +.6 e (d) 9. Conside one-dimensionl lice wih wek peiodic poenil U ( ) U cos. The gp he edge of he Billouin one k is: () U U (c) U. Idenicl chge q e plced five veices of egul hegon of side. The mgniude of he elecic field nd he elecosic poenil he cene of he hegon e especively q q (),, q 5q (c), (d) U 5q 5q (d),
GATE-PH 7. A evesible Cno engine is opeed beween empeues nd woking subsnce. The efficiency of he engine is T T T T wih phoon gs s he () T T T T (c) T T / (d) T T /. The bes esoluion h 7 bi A/D convee wih 5 full scle cn chieve is m. (up o wo deciml plces). dq dq. If he Lgngin L m m q is modified o L L q, which one of he following is d d TRUE? () Boh he cnonicl momenum nd equion of moion do no chnge Cnonicl momenum chnges, equion of moion does no chnge (c) Cnonicl momenum does no chnge, equion of moion chnges (d) Boh he cnonicl momenum nd equion of moion chnge. A pllel ple cpcio wih sque ples of side m seped by mico mee is filled wih medium of dielecic consn of. If he chges on he wo ples e C nd - C, he volge coss he cpcio is k. (up o wo deciml plces). ( 8.85 F/m) 5. The conou inegl d evlued long conou going fom o long he el is nd closed in he lowe hlf-plne by hlf cicle is equl o. (up o wo deciml plces). 6. In he figue given below, he inpu o he pimy of he nsfome is volge vying sinusoidlly wih ime. The esiso R is conneced o he cene p of he secondy. Which one of he following plos epesens he volge coss he esiso R s funcion of ime? C R () (c) (d) 7. Ligh is inciden fom medium of efcive inde n.5 ono vcuum. The smlles ngle of incidence fo which he ligh is no nsmied ino vcuum is degees. (up o wo deciml plces). 8. Elecomgneic inecions e : () C conseving C non-conseving bu CP conseving (c) CP non-conseving bu CPT conseving (d) CPT non-conseving
GATE-PH 7 9. The Compon wvelengh of poon is fm. (up o wo deciml plces). 7 9 8 ( mp.67 kg, h 6.66 Js, e.6 C, c ms ). Which one of he following consevion lws is violed in he decy () Angul momenum Tol Lepon numbe (c) Elecic chge (d) Tu numbe. The coefficien of ik e in he Fouie epnsion of sin u A fo k is () A/ A / (c) A / (d) A/. The phse spce jecoy of fee picle bouncing beween wo hd wlls elsiclly in one dimension is () sigh line pbol (c) ecngle (d) cicle. The omic mss nd mss densiy of Sodium e nd.968 g cm, especively. The numbe densiy of vlence elecons is cm. (Up o wo deciml plces.) (Avogdo numbe, N 6. ). A. The degenecy of he hid enegy level of -dimensionl isoopic qunum hmonic oscillo is () 6 (c) 8 (d) 5. A one dimensionl simple hmonic oscillo wih Hmilonin H p k m is subjeced o smll pe- ubion, H. The fis ode coecion o he gound se enegy is dependen on () only nd (c) nd (d) only Q.6 Q.55 : Cy TWO mks ech. 6. Thee chges ( C, C, C) e plced he veices of n equilel ingle of side m s shown in he figue. The componen of he elecic dipole momen bou he mked oigin long he ŷ diecion is cm. y C m -C.5m 7. An objec vels long he -diecion wih velociy c/ in fme O. An obseve in fme O sees he sme objec velling wih velociy c /. The elive velociy of O wih espec o O in unis of c is. (up o wo deciml plces). 8. The enegy densiy nd pessue of phoon gs e given by u T nd P u /, whee T is he empe- ue nd is he diion consn. The enopy pe uni volume is given by T. The vlue of is. (up o wo deciml plces). 9. A peson weighs w p Eh s noh pole nd w e he equo. Teing he Eh s pefec sphee of dius 6 km, he vlue ( w w )/ w is. (up o wo deciml plces). (Tke g ms ). p e p -C
GATE-PH 7. The minimum numbe of NAND ges equied o consuc n OR ge is: () (c) 5 (d).5. The ol enegy of n ine-gs cysl is given by E( R) 6 R R (in e), whee R is he ine-omic spcing in Angsoms. The equilibium sepion beween he oms is Angsoms. (up o wo deciml plces).. The imginy p of n nlyic comple funcion is v(, y) y y. The el p of he funcion is eo he oigin. The vlue of he el p of he funcion +i is. (up o wo deciml plces).. Conside N non-inecing, disinguishble picles in wo-level sysem empeue T. The enegies of he levels e nd, whee. In he high empeue limi ( kbt ), wh is he populion of picles in he level wih enegy? () N N (c) N (d) N. Fo he nsiso mplifie cicui shown below wih R k, R k, R k, nd 99. Neglecing he emie diode esisnce, he inpu impednce of he mplifie looking ino he bse fo smll c signl is k. (up o wo deciml plces). CC in R C B E R R ou 5. Which one of he following gses of diomic molecules is Rmn, infed, nd NMR cive? () H H C O (c) H 5 Cl (d) 6 O 6 6 6. Le X be column veco of dimension n wih les one non-eo eny. The numbe of non-eo eigenvlues of he mi M T XX is () n (c) (d) n 7. A fee elecon of enegy e is inciden upon one-dimensionl finie poenil sep of heigh.75 e. The pobbiliy of is eflecion fom he bie is (up o wo deciml plces). 8. An infinie solenoid cies ime vying cuen I ( ) A, wih A. The is of he solenoid is long he ẑ diecion. ˆ nd ˆ e he usul dil nd pol diecions in cylindicl pol coodines. B B ˆ B ˆ B ˆ is he mgneic field poin ouside he solenoid. Which one of he following semens is ue? () B, B, B B, B, B (c) B, B, B (d) B, B, B O
GATE-PH 7 9. Conside wo picles nd wo non-degenee qunum levels nd. Level lwys conins picle. Hence, wh is he pobbiliy h level lso conins picle fo ech of he wo cses: (i) when he wo picles e disinguishble nd (ii) when he wo picles e bosons? () (i) / nd (ii) / (i) / nd (ii) / (c) (i) / nd (ii) / (d) (i) nd (ii). The el spce pimiive lice vecos e ˆ nd ˆ yˆ b nd b fo his lice e, especively 5. The ecipocl spce uni vecos () yˆ ˆ nd yˆ yˆ ˆ nd yˆ (c) ˆ ˆ nd yˆ (d) ˆ ˆ nd yˆ. The geomeic coss-secion of wo colliding poons lge enegies is vey well esimed by he poduc of he effecive sies of ech picle. This is closes o () b mb (c) µb (d) pb. A unifom volume chge densiy is plced inside conduco (wih esisiviy m ). The chge densiy becomes /(.78) of is oiginl vlue fe ime femo seconds. (up o wo deciml plces) ( 8.85 F/m) 5. We feees ºC mospheic pessue (. P). The densiies of we nd ice his empeue nd pessue e kg/m nd 9 kg/m 5 especively. The len he of fusion is. J/kg. The pessue equied fo depessing he meling empeue of ice by ºC is GP. (up o wo deciml plces). The inegl e d is equl o. (up o wo deciml plces). 5. P J fo he gound se of he C 6 nucleus is () (c) (d) 6. A unifom solid cylinde is elesed on hoionl sufce wih speed 5 m/s wihou ny oion (slipping wihou olling). The cylinde evenully ss olling wihou slipping. If he mss nd dius of he cylinde e gm nd cm especively, he finl line velociy of he cylinde is m/s. (up o wo deciml plces) 7. Conside one-dimensionl poenil well of widh nm. Using he unceiny pinciple. p / esime of he minimum deph of he well such h i hs les one bound se fo n elecon is 9 ( me 9. kg, h 6.66 J s, e.6 C) : () µe me (c) e (d) Me 8. Conside n idel opeionl mplifie s shown in he figue below wih R 5 k, R k, R L k. Fo n pplied inpu volge m, he cuen pssing hough R is µa. (up o wo deciml plces)., n
GATE-PH 7 6 R R L R 9. The decys es o nd. Assuming he neuino o be mssless, he momenum of he neuino is Me/c. (up o wo deciml plces) m 9Me/ c, m 5 Me/ c. 5. Conside he diffeenil equion dy / d y n( ) cos( ). If y(), y( / ) is. (up o wo deciml plces). 5. Conside mel wih fee elecon densiy of 6 cm. The lowes fequency elecomgneic diion 6 o which his mel is nspen is.8 H. If his mel hd fee elecon densiy of.8 cm insed, he lowes fequency elecomgneic diion o which i would be nspen is 6 H. (up o wo deciml plces). 5. Using Hund s ule, he ol ngul momenum qunum numbe J fo he eleconic gound se of he niogen om is () / / (c) (d) 9 5. Conside -dimensionl elecon gs wih densiy of m. The Femi enegy of he sysem is e. (up o wo deciml plces). m h e e 9 9. kg, 6.66 Js,.6 C 5. Which one of he following opeos is Hemiin? () i p p i p p (c) ip e (d) e ip 55. Posionium is n om mde of n elecon nd posion. Given h he Boh dius fo he gound se of he Hydogen om o be.5 Angsoms, he Boh dius fo he gound se of posionium is Angsoms. (up o wo deciml plces).