fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NET December 2016 Part A

Size: px

Start display at page:

Download "fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NET December 2016 Part A"

Mary Patterson
6 years ago
Views:

Q. Find out the missing pttern. 5 7? NET December 6 Prt A 8 6 9 7 SET- 7 7 7 4 4 4 4 7 Q. Seeds when soked in wter gin bout % by weight nd % by volume. y wht fctor does the density increse?....9 Q.

1 Q. Find out the missing pttern. 5 7? NET December 6 Prt A SET Q. Seeds when soked in wter gin bout % by weight nd % by volume. y wht fctor does the density increse?....9 Q. Retrding frictionl force, f, on moving bll, is proportionl to its velocity, V. Two identicl blls roll down identicl slopes A& from different heights. Compre the retrding forces nd the velocities of the blls t the bses of the slopes. A f f ; V V f f ; V V A A A A f f ; V V f f ; V V A A A A Q4. Two cockroches of the sme species hve the sme thickness but different lengths nd widths. Their bility to survive in oygen deficert environments will be compromises if their thickness increses, nd the rest of the size remins the sme. their thickness remins unchnged, but their length increses. their thickness remins unchnged, but their width decreses. their thickness decreses, but the rest of the size remins unchnged. fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

2 Q5. The br chrt shows number of sets won by four politicl prties in stte legisltive ssembly sets prty Which of the following pie-chrts correctly depicts this informtion? Q6. The rndom errors ssocited with the mesurement of P nd Q re % nd % respectively, Wht is the percentge rndom error in P Q? Q7. In how mny distinguishble wys cn the letters of the word CHANCE be rrnged? Q8. Which of the following grphs correctly shows the speed nd the corresponding distnce covered by n object moving long stright line? speed, distnce speed speed, distnce distnce, time, time fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

3 speed, distnce speed, distnce, time, time Q9. A norml TV screen hs width to height rtio of 4:, while high definition TV screen hs rtio of 6 : 9. Wht is the pproimte rtio of their digonls, if the heights of the two types of screens re the sme? 5:9 5:8 5:5 5:6 Q. Compring numericl vlues, which of the following is different from the rest? The rtio of the circumference of circle to its dimeter. The sum of the three ngles of plne tringle epressed in rdins. 7. The net volume of hemisphere of unit rdius, nd cone of unit rdius nd unit height Q. A river is 4.km wide. A bridge built cross it hs 7 of its length on one-bnk nd 8 of its length on the other bnk. Wht is the totl length of the bridge? 5.km 4.9km 5.6 km 5.4km Q. OA, O, nd OC re rdii of the qurter circle shown in the figure. A is lso equl to A the rdius. wht is ngle OC? O? C fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

4 Q. Intrvenous (IV) fluid hs to be dministered to child of kg with dehydrtion, t dose of mg of fluid per kg of body weight, in hour. Wht should be the drip rte (in drops/min of IV fluid? (mg drops) Q4. A hll with high roof is supported by n rry of identicl columns such tht, to person lying on the floor nd looking t the ceiling, the columns pper prllel to ech other. Which of the following designs conforms to this? ROOF ROOF FLOOR FLOOR ROOF ROOF FLOOR FLOOR Q5. The sum of digits of two-digit number is 9. If the frction formed by tking 9 less thn the number s numertor nd 9 more thn the number s denomintor is, wht is the 4 number? fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 4

5 Q6. The distnce between X nd Y is km. A person flies from X t 8 A.M. locl time nd reches Y t A.M. locl time. He flies bck fter hlt of 4 hours t Y nd reches X t 4 P.M. locl time on the sme dy. Wht is his verge speed for the durtion he is in the ir? 5 km/hour 5 km/hour 75 km/hour cnnot be clculted with the given informtion Q7. If person trvels % fster thn norml, he reches y minutes erlier thn norml. Wht is his norml time of trvel? y minutes y minutes y minutes minutes y Q8. A nd wlk up n escltor one step t time, while the escltor itself moves up t constnt speed. A wlks twice s fst s. A reches the top in 4 steps nd in steps. How mny steps of the escltor cn be seen when it is not moving? Q9. Two iron spheres of rdii cm nd cm re melted nd fused. Two new spheres re mde without ny loss of iron. Their possible rdii could be 9 nd 4cm 9 ndcm 8 nd5cm ndcm Q. A mn buys lcohol t Rs 75 / cl, dds wter, nd sells it t Rs.75 / cl mking profit of 5%. Wht is the rtio of lcohol to wter? : : : : fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 5

6 Prt Q. A bll of mss m is dropped from tll building with zero initil velocity. In ddition to grvity, the bll eperiences dmping force of the form, where is its instntneous velocity nd is constnt. Given the vlues m kg, kg/ s,, nd g m/ s the distnce trvelled (in metres) in time t in seconds, is t e t t e t t 5t e 5t Q. The mtri M stisfies the eqution M M M I M M M I M M M I Q. The Lplce trnsform of is e st st f t t, t T T t T e st st M M M I e st st e st Q4. A reltivistic prticle moves with constnt velocity v with respect to the lbortory frme. In time, mesured in the rest frme of the prticle, the distnce tht it trvels in the lbortory frme is st v c v c v v c v v c fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 6

7 Q5. A prticle in two dimensions is in potentil V, y y. Which of the following (prt from the totl energy of the prticle) is lso constnt of motion? p p p p y p p p p y Q6. The dynmics of prticle governed by the Lgrngin L m k kt describes n undmped simple hrmonic oscilltor dmped hrmonic oscilltor with time vrying dmping fctor n undmped hrmonic oscilltor with time dependent frequency free prticle Q7. The prbolic coordintes, re relted to the Crtesin coordintes, y y y by nd y. The Lgrngin of two-dimensionl simple hrmonic oscilltor of mss m nd ngulr frequency is m 4 m m m 4 Q8. Consider two rdioctive toms, ech of which hs decy rte of per yer. The probbility tht t lest one of them decys in the first two yers is 4 4 e 4 e fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 7

8 Q9. The Fourier trnsform df e ik of the function f is e k e k e k e k Q. A screen hs two slits, ech of width w with their centres t distnce w prt. It is illuminted by monochromtic plne wve trvelling long the -is. The intensity of the interference pttern, mesured on distnt screen, t n ngle w w w n to the -is is w zero for n,,... mimum for n,,... mimum for 5 n,,... zero for n only Q. The electric field of n electromgnetic wve is E z, t E cos kzt iˆe sin kzt ˆj where nd k re positive constnts. This represents linerly polrised wve trvelling in the positive z -direction circulrly polrised wve trvelling in the negtive z -direction n ellipticlly polrised wve trvelling in the negtive z -direction n unpolrised wve trvelling in the positive z -direction Q. Consider the two lowest normlized energy eigenfunctions nd * dimensionl system. They stisfy nd fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / of one d, where is rel d constnt. The epecttion vlue of the momentum opertor in the stte is 8 /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 8

9 Q. Consider the opertor,cos is d cting on smooth functions of. The commuttor d sin cos cos ip nd ip be the lowering nd rising opertors of simple hrmonic oscilltor in units where the mss, ngulr frequency nd hve been Q4. Let set to unity. If is the ground stte of the oscilltor nd is comple constnt, the * epecttion vlue of in the stte ep, is i * * Q5. Consider the opertor p qa, where p is the momentum opertor, A A, A, A is the vector potentil nd q denotes the electric chrge. If y z,, is y z denotes the mgnetic field, the z -component of the vector opertor iq z qap y Ayp iq z q Ap y Ayp iq z iq z Q6. A conducting circulr disc of rdius r nd resistivity rottes with n ngulr velocity in mgnetic field perpendiculr to it. A voltmeter is connected s shown in the figure below. Assuming its internl resistnce to be infinite, the reding on the voltmeter depends on,, r nd depends on, nd r but not on is zero becuse the flu through the loop is not chnging is zero becuse current the flows in the direction of r V fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 9

10 Q7. The chrge per unit length of circulr wire of rdius in the y -plne, with its centre t the origin, is cos, where is constnt nd the ngle is mesured from the positive -is. The electric field t the centre of the circle is E iˆ E iˆ 4 4 E ˆ j E kˆ 4 4 Q8. The prtition function of two-level system governed by the Hmiltonin is sinh cosh H cosh sinh cosh sinh Q9. A silic prticle of rdius. m is put in continer of wter t T K. The densities of silic nd wter re / kg m nd / kg m, respectively. Due to therml fluctutions, the prticle is not lwys t the bottom of the continer. The verge height of the prticle bove the bse of the continer is pproimtely m 4 4 m m 5 5 m fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

11 Q4. Which of the following circuits implements the oolen function FA,, C,,4,6? C I I I 4 MUX F C I I I 4 MUX F I S S I S S A A C I I 4 MUX I F I I I 4 MUX F I S S C I S S A A Q4. A pir of prllel glss pltes seprted by distnce d is illuminted by white light s shown in the figure below. Also shown is the grph of the intensity of the reflected light I s function of the wvelength recorded by spectrometer. spectrometer prtilly reflecting mirror incident white light d ir gp glss pltes fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

12 .8 Intensity Assuming tht the interference tkes plce only between light reflected by the bottom surfce of the top plte nd the top surfce of bottom plte, the distnce d is closest to m 4 m 6 m m V Q4. The I V chrcteristics of device cn be epressed s I Is ep T, where T is the temperture nd nd I s re constnts independent of T nd V. Which one of the following plots is correct for fied pplied voltge V? log log V / T V / T fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / log log V / T 4 V / T 8 /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

13 Q4. The ctive medium in blue LED (light emitting diode) is GIn N lloy. The bnd gps of GN nd InN re.5ev nd.5ev respectively. If the bnd gp of GIn vries pproimtely linerly with, the vlue of required for the emission of blue light of wvelength 4nm is (tke hc ev -nm ) Q44. Consider gs of N clssicl prticles in two-dimensionl squre bo of side L. If the totl energy of the gs is E, the entropy (prt from n dditive constnt) is N Nk ln LE N Nk LE ln N Nk L E ln N Lk E ln N Q45. Consider continuous time rndom wlk. If step hs tken plce t time t, the probbility tht the net step tkes plce between t nd t is constnt. Wht is the verge time between successive steps? dt is given by bt dt, where b b b b b fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

14 PART C Q46. Given the vlues sin 45.77, sin 5.766, sin nd sin 6.866, the pproimte vlue of difference method, is sin 5, computed by Newton s forwrd Q47. Let f, t be solution of the het eqution condition t t is, f e for f t f D in one dimension. The initil. Then for ll t, f, t is given by [Useful integrl: d e ] Dt e Dt Dt e Dt 4Dt Dt e e 4Dt Q48. After perfectly elstic collision of two identicl blls, one of which ws initilly t rest, the velocities of both the blls re non zero. The ngle between the finl, velocities (in the lb frme) is Q49. Consider circulr orbits in centrl force potentil n V r k, where k nd r n. If the time period of circulr orbit of rdius R is T nd tht of rdius R is T T, then T n n n n fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 4

15 Q5. Consider rdioctive nucleus tht is trvelling t speed c with respect to the lb frme. It emits -rys of frequency v in its rest frme. There is sttionry detector, (which is not on the pth of the nucleus) in the lb. If -ry photon is emitted when the nucleus is closest to the detector, its observed frequency t the detector is v v v v Q5. Suppose tht free chrges re present in mteril of dielectric constnt nd resistively m. Using Ohm s lw nd the eqution of continuity for chrge, the time required for the chrge density inside the mteril to decy by e is closest to 6 S 6 S S S Q5. A prticle with chrge q moves with uniform ngulr velocity in circulr orbit of rdius in the y - plne, round fied chrge q, which is t the centre of the orbit t,,. Let the intensity of rdition t the point,, R be I nd t R,, be I I The rtio I for R, is Q5. A prllel plte cpcitor is formed by two circulr conducting pltes of rdius seprted by distnce d, where d. It is being slowly chrged by current tht is nerly constnt. At n instnt when the current is I, the mgnetic induction between the pltes t distnce from the centre of the plte, is I I I I 4 fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 5

16 Q54. Two uniformly chrged insulting solid spheres A nd, both of rdius, crry totl chrges Q nd Q, respectively. The spheres re plced touching ech other s shown in the figure. If the potentil t the centre of the sphere A is V A nd tht t the centre of is V then the difference VA V is A Q 4 Q Q Q55. A stble symptotic solution of the eqution n n Q 4 is. If we tke n n n nd n n, where n nd n re both smll, the rtio pproimtely 4 y z Q56. The identity mtri I nd the Puli mtrices,, do not form group under mtri multipliction. The minimum number of mtrices, which includes these four mtrices, nd form group (under mtri multipliction) is 8 6 Q57. The dynmics of free reltivistic prticle of mss m is governed by the Dirc Hmiltonin H c. pmc,,, where p is the momentum opertor nd y z nd re four 4 4 Dirc mtrices. The ccelertion opertor cn be epressed s n is ic cp H ic H ic ic cp H fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 6

17 Q58. A prticle of chrge q in one dimension is in simple hrmonic potentil with ngulr frequency. It is subjected to time- dependent electric field E t t Ae, where A nd re positive constnts nd. If in the distnt pst t the prticle ws in its ground stte, the probbility tht it will be in the first ecited stte s t is proportionl to e e Q59. Consider rndom wlk on n infinite two-dimensionl tringulr lttice, prt of which is shown in the figure below. If the probbilities of moving to ny of the nerest neighbour sites re equl, wht is the probbility tht the wlker returns to the strting position t the end of ectly three steps? Q6. An tom hs non-degenerte ground-stte nd doubly-degenerte ecited stte. The energy difference between the two sttes is. The specific het t very low tempertures is given by k ke k e k Q6. The electrons in grphene cn be thought of s two-dimensionl gs with liner energy-momentum reltion E pv p p, p nd v is constnt. If is the, where y number of electrons per unit re, the energy per unit re is proportionl to / / fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 7

18 Q6. In the circuit below, the input voltge V i is VV, cc 6 VR, k nd RL k V CC V i R R R L The vlue of R required to deliver mw of power cross R L is k 4k 8k 4 k Q6. Two sinusoidl signls re sent to n nlog multiplier of scle fctor V followed by low pss filter (LPF). V 5cos t Multiplier LPF f 5Hz C V out V cos t / If the roll-off frequency of the LPF is f 5 Hz c, the output voltge V out is 5V 5V V 5V Q64. The resistnce of smple is mesured s function of temperture, nd the dt re shown below. T C R The slope of R vs T grph, using liner lest-squres fit to the dt, will be 6 C 4 C fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / C 8 C 8 /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 8

19 Q65. A prticle is scttered by centrl potentil V r V re r, where V nd re positive constnts. If the momentum trnsfer q is such tht q q, the scttering crosssection in the orn pproimtion, s q, depends on q s [You my use 8 q n n d e d e d n d ] q Q66. A prticle in one dimension is in potentil V A. Its wvefunction q 6 q is continuous everywhere. The discontinuity in d d t is m A A A m Q67. Consider hegonl lttice with bsis vectors s shown in the figure below. y If the lttice spcing is, the reciprocl lttice vectors re 4,,, 4,,, 4,,,,,, fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com 9

20 Q68. In the L S coupling scheme, the terms rising from two non-equivlent p -electrons re S, P, P, D, D S, S, P, D S, S, P, D S, S, P, P, D, D Q69. The totl spin of hydrogen tom is due to the contribution of the spins of the electron nd the proton. In the high temperture limit, the rtio of the number of toms in the spin- stte to the number in the spin- stte is Q7. A two level system in therml (blck body) environment cn decy from the ecited stte by both spontneous nd thermlly stimulted emission. At room temperture K, the frequency below which therml emission domintes over spontneous emission is nerest to Hz 8 Hz 5 Hz Hz Q7. Wht should be the minimum energy of photon for it to split n -prticle t rest into tritium nd proton? (The msses of He, 4 H nd respectively, nd mu 98MeV ) H re 4.6 mu,.6mu nd.7mu. MeV MeV 9.MeV 9.5MeV Q7. Which of the following rection(s) is/re llowed by the conservtion lws? (i) n K (ii) p K both (i) nd (ii) only (ii) only (i) neither (i) nor (ii) fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

21 Q7. A prticle, which is composite stte of three qurks ud, nd s, hs electric chrge, spin nd strngeness respectively, equl to,,,,,,, Q74. Consider one-dimensionl chin of toms with lttice constnt. The energy of n electron with wve-vector k is k cosk, where nd re constnts. If n electric field E is pplied in the positive -direction, the time dependent velocity of n electron is (In the following is the constnt) ee Proportionl to cos t proportionl to E ee independent of E proportionl to sin t Q75. A thin rectngulr conducting plte of length nd width b is plced in the y -plne in two different orienttions s shown in the figures below. In both cses mgnetic field is pplied in the z -direction nd current flows in the direction due to the pplied voltge V. y b V V b V V If the Hll voltge cross the y -direction in the two cses stisfy V V the rtio : b must be : : : : fiziks, H.No. 4 D, G.F, Ji Sri, Ner IIT, Huz Khs, New Delhi 6 Phone: / /6, Ji Sri, Ner IIT Huz Khs, New Delhi 6 Emil: fiziks.physics@gmil.com

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write