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Marianna Haynes
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1 6. A bus is moving with a velocity of 0 m/s on a staight oa. A scooteist wishes to ovetake the bus in 00 secons. If the bus is at a istance of km fom the scooteist, at what velocity shoul the scooteist chase the bus? 50 m/sec 40 m/sec 0 m/sec 0 m/sec 7. The masses of the blocks A an B ae 0.5 kg an kg espectively. These ae aange as shown in the figue an ae connecte by a massless sting. The coefficient of fiction between all contact sufaces is 0.4. The foce, necessay to move the block B with constant velocity, will be (g 0 m/s ) 5 N 0 N 5 N 0 N 8. A o of length L is place on x-axis between x 0 an x L. the linea ensity i.e., mass pe unit length enote by ρ, of this o, vaies as, ρ a + bx. What shoul be the imensions of b? M L T 0 M L T 0 M L T M L T 9. A boy is thown vetically upwas fom the suface of eath in such a way that it eaches upto a height equal to 0 R e. The velocity impate to the boy will be 0.6 km/s 0.06 km/s.06 km/s zeo 40. A metallic wie of ensity is lying hoizontal on the suface of wate. The maximum length of wie so that it may not sink will be Tg π T πg A B Tg π any length 4. Two points of a o move with velocities v an v pepenicula to the o an in the same iection, sepaate by a istance. Then the angula velocity of the o is v/ 4 v/ 5 v/ v/ 4. A tansfome is use to light a 40 W, 4 V bulb fom a 40 V a.c. mains. The cuent in the main cable is 0.7 A. the efficiency of the tansfome is 6.8 % 8.% 6.7% 6.% 4. A flat plate P of mass M executes SHM in a hoizontal plane by sliing ove a fictionless suface with a fequency V. A block B of mass m ests on the plate as shown in figue. Coefficient of fiction between the suface of B an P is µ. What is the maximum amplitue of oscillation that the plate block system can have if the block B is not to slip on the plate: µ g 4 V π µ g V µ V g µ g V 44. What is the atio of the cicumfeence of the fist Boh obit fo the electon in the hyogen atom to the e Boglie wavelength of electons having the same velocity as the electon in the fist Boh obit of the hyogen atom? : : : 4 : 45. P-V plots fo two gases uing aiabatic pocesses ae shown in the figue. Plots an shoul coespon espectively to He an A He an O

2 O an N O an He 46. Two ientical thin ings, each of aius R metes, ae coaxially place at a istance R metes apat. If Q coulomb an Q coulomb ae espectively, the chages unifomly spea on the two ings, the wok one in moving a chage q fom the cente of one ing to that of the othe is zeo ( Q Q )( )/ πε R q 4 0 ( Q + Q )/ πε R q 4 0 ( Q + Q )( + )/ πε R q A paticle of mass m collies hea-on with anothe stationay paticle of mass m (m > m ). The collision is pefectly inelastic. The faction of kinetic enegy which is convete into heat in this collision is m /( m + m) m ( m + m) m /( m m) m /( m m) 48. A wooen block of volume 000 cc is suspene fom a sping balance. It weighs N in ai. It is then hel suspene in wate with half of it insie wate. What woul be the eaing in sping balance now? 0 N 9 N 8 N 7 N 49. A sphee, a cube an a thin cicula plate all mae of the same mateial an having the same mass, ae initially heate to a tempeatue of 00 o C. Which of these objects will cool slowest when left in ai at oom tempeatue? the sphee the cube the cicula plate all will cool at same ate 50. A cyline of aius R mae of a mateial of themal conuctivity K is suoune by a cylinical shell of inne aius R an oute aius R mae of a mateial of themal conuctivity K.The two ens of the combine system ae maintaine at two iffeent tempeatues. Thee is no loss of heat acoss the cylinical suface an the system is in steay state. The effective themal conuctivity of the system is K + K K K /( K + K) K + )/ 4 K + )/ 4 ( K ( K 5. Figue shows a close suface which intesects a conucting sphee. If a positive chage is place at the point P, the flux of the electic fiel though the close suface will emain zeo will become positive will become negative will become unefine 5. In the cicuit shown, the total cuent supplie by the battey is ampee 4 ampee ampee 6 ampee 5. The instantaneous values of cuent an voltage in an A.C. cicuit ae I 4sinω t an π E 00 cos ωt + espectively. The phase iffeence between voltage an cuent is π 5π 6 π 7π 6

3 54. In figue, what is the magnetic fiel inuction at point O? µ 0 i µ 0 i µ 0i + 4 π µ 0 i µ 0i + 4 µ 0 i µ 0i A poton, a euton an an α paticle acceleate though the same potential iffeence ente a egion of unifom magnetic fiel, moving at ight angles to B. What is the atio of thei K.E.? : : : : : : : : 56. Two peioic waves of intensities I an I pass though a egion at the same time in the same iection. The sum of the maximum an minimum intensities is ( I + I) I + I ) ( I I + ( I ) I 57. A wie of length l is bent in the fom of a cicula coil of some tuns. A cuent I flows though the coil. The coil is place in a unifom magnetic fiel B. The maximum toque on the coil can be IBl IBl π IBl π IBl π 58. A potentiomete wie of length 00 cm has a esistance of 0 Ω. It is connecte in seies with a esistance of 0 Ω an an accumulato of emf 6 V having negligible intenal esistance. A souce of.4 V is balance against a length L of the potentiomete wie. The value of L is 00 cm 0 cm 0 cm 40 cm 59. The plane faces of two ientical planoconvex lenses each having a focal length of 50 cm ae place against each othe to fom a usual biconvex lens. The istance fom this lens combination at which an object must be place to obtain a eal, invete image which has the same size as the object is 50 cm 5 cm 00 cm 40 cm 60. A conucting cicula loop is place in a unifom magnetic fiel, B 0.05 T with its plane pepenicula to the loop. The aius of the loop is mae to shink at a constant ate of mm s. The inuce emf when the aius is cm is π µ V π µ V π µ V µ V 6. An electon an a poton ae sepaate by a lage istance an the electon appoaches the poton with a kinetic enegy of ev. If the electon is captue by the poton to fom a hyogen atom in the goun state, the wavelength of photon emitte in this pocess will be.6 Å 79. Å 04.6 Å 94.6 Å 6. Thee ae two aioactive substances A an B. Decay constant of B is two times that of A. Initially both have equal numbe of nuclei. Afte n half lives of A ate of isintegation of both ae equal. The value of n is 4 none of these 6. Two shot ba magnets of magnetic moments M each ae aange at the opposite cones of a squae of sie such that thei centes coincie with the cones an thei axes ae paallel. If the like poles

ae in the same iection, the magnetic inuction at any of the othe cones of the squae is µ 0 M µ 0 M µ 0 M µ 0 M 64. In Young s ouble slit expeiment, the wavelength of light use is 6000 Å.

4 ae in the same iection, the magnetic inuction at any of the othe cones of the squae is µ 0 M µ 0 M µ 0 M µ 0 M 64. In Young s ouble slit expeiment, the wavelength of light use is 6000 Å. If the path iffeence between waves eaching a point p on the sceen is.5 micons, then at the point P. secon bight ban occus secon ak ban occus thi ak ban occus thi bight ban occus 65. In a galvanomete thee is a eflection of 0 ivisions pe ma. The intenal esistance of the galvanomete is 60 Ω. If a shunt of.5 Ω is connecte to the galvanomete an thee ae 50 ivisions in all, on the scale of galvanomete, what maximum cuent can this galvanomete ea? 5 ma 00 ma 5 ma 50 ma 66. An electic bulb ate fo 500 W at 00 V is use in cicuit having a 00 V supply. Fin the esistance R that must be put in seies with the bulb, so that the bulb elives 500 W. 00 Ω 0 Ω 5 Ω 0 Ω 67. The mean fee path of electons in a metal is m. The electic fiel which can give on an aveage ev enegy to an electon in the metal will be 5 0 V m 8 0 V m V m V m 68. It is possible to poject a paticle with a given velocity in two possible ways so as to make it pass though a point P at a istant fom the point of pojection. The pouct of the times taken to each this point in the two possible ways is then popotional to / 69. A thin unifom isc has mass M an aius R. A cicula hole of aius R/ is mae in the isc as shown in figue. The moment of inetia of the emaining potion of isc about an axis passing though O an pepenicula to the plane of the isc is MR 9 MR 9 MR 4 MR A mass m is moving with a constant velocity along a line paallel to the x-axis, away fom the oigin. Its angula momentum with espect to the oigin. is zeo emains constant goes on inceasing goes on eceasing 7. A wie is stetche between two igi suppots with a cetain tension. It is obseve that the wie esonates in the nth hamonic at a fequency of 40 Hz. The next highe fequency at which the wie esonates is 490 Hz. The value of n is A ban playing music at a fequency f is moving towas a wall at a spee u. A motoist is following the ban with the same spee u. If v is the spee of soun, the beat fequency hea by the motoist is

5 f u f ( v + u) f ( u + v) ( v u) fu ( v u) 7. The cuent gain (β) of a tansisto in common emitte moe is 40. To change the collecto cuent by 60 ma at constant V the necessay change in the base CE, cuent is 0.5 µa 4 µa 4 ma 40 ma 74. The combination of gates shown in figue yiels whee A an k ae constants. The angle between the foce an momentum is 0 o 0 o 45 o 90 o 77. A sping is compesse between two blocks of masses m an m place on a hoizontal fictionless suface as shown in figue. When the blocks ae elease, they have initial velocity of v an v as shown. The blocks tavel istances x an x espectively befoe coming to est. The atio x /x is m m m m NAND gate OR gate NOT gate XOR gate 75. Rain is falling vetically with a spee of 4 ms. Afte some time, win stats blowing with a spee of ms in the noth to south iection. In oe to potect himself fom ain, a man staning on the goun shoul hol his umbella at an angle θ given by θ tan with the vetical towas 4 south θ tan with the vetical towas 4 noth. θ cot with the vetical towas 4 south θ cot with the vetical towas 4 noth 76. A paticle moves in the x-y plane une the influence of a foce such that its linea momentum is p( t) A[ˆcos( i kt) jˆsin( kt)] m m m m 78. Two paticles A an B, initially at est, move towas each othe une a mutual foce of attaction. At the instant when the spee of A is V an that of B is V, the spee of the cente of mass of the system is 0 V.5 V V 79. Lights of two iffeent fequencies, whose photons have enegies ev an 0 ev espectively, successively illuminate a metal of wok function ev. The atio of the maximum spees of the emitte electons will be : 5 : : 9 : 80. Which of the following pais of space an time vaying E( ie ˆ x + ˆjE y + kˆ Ez ) an B ib ˆ + ˆjB + kˆ E woul geneate a ( ) x y z plane electomagnetic wave tavelling in the z-iection? E x, B z E y, B z E z, Bx E x, B y

6 ANSWERS KEY 6 D 46 B 56 A 66 B 76 D 7 B 47 A 57 A 67 C 77 B 8 B 48 D 58 B 68 B 78 A 9 A 49 A 59 A 69 D 79 D 40 D 50 C 60 B 70 B 80 B 4 D 5 B 6 B 7 C 4 B 5 B 6 A 7 D 4 D 5 C 6 A 7 C 44 A 54 C 64 C 74 B 45 D 55 D 65 A 75 B 6. let the scooteist velocity be v. Then (0 00) v v 000 v 0 m/s Hee m A 0.5 kg; m B kg Foce on block A T µm A g () Foce acting on block B F T + µm A + µ(m A + m B )g () Fom () an () F µm A g + µm A g + µm A g + µm B g F µm A g + µm B g µg(m A + m B ) ( ) 0 N 8. In the given equation [ρ] [b] [x]; [b] [ρ]/[x]. But ρ is mass pe unit length an x is istance, theefoe [b] ML /L ML T Wok one in going fom a istance to a istance away fom cente of the eath, by a boy of mass m, is, W GMm(/ / ), Fo ou case we shoul have / mv GMm [(/R e ) (/0R e )] (GMm/R e ) (9/0) v [(GM/R e ) (9/0)] (9/0) escape velocity (9/0). km/s 0.6 km/s. 40. Mg TL π Lg TL π g T This elation is inepenent of L. vel 4. ω o ωpoint v el epesents the velocity of one point w..t. v v othe. an being the istance v between them. 4. Powe of souce EI Efficiency η 8.% f max µmg, a max µg. If A is the amplitue a max Aω AV µg µ g Theefoe, A. V nh h 44. mv, λ ; π mv nh Using the two concept we get, mv π (whee n ) h π (); mv h λ () mv π h mv Divie () by (), : λ mv h 45. In the gaph given, slope of cuve is geate than the slope of cuve. γ P γ P > γ > γ V V γ > He γ O Since, γ monoatomic > γ iatomic Hence, cuve coespons to helium an cuve coespons to oxygen. Q 46. Q V A + ; 0 R R V Q Q + B 0 R R Q + Q V A VB Q Q R Wok one Q V q (V A V B ) q Q + Q Q Q 0 R q Q + Q Q Q 4 π 0 R [ ]

7 q( Q Q )( ) ( 0 R) 47. (A) 48. Appaent wt. Real wt. Upthust 6 (000 0 ) N 49. Rate of cooling suface aea an fo a given mass, suface aea of sphee is minimum. 50. Heat flowing pe sec. though cyline of T T aius R, Q K R (π ) l Heat flowing pe sec though oute shell of aius R. T T Q K R R ( π ( ) π ) l Total Q Q + Q (K + K ) πr T T () l Let K be the equivalent themo conuctivity of the system. Then Q Kπ (R) T T () l Fom eqs. () an (), we have K ( K + K) 4K o + K K 4 5. The positive an negative chages evelope on iffeent pats of conucting sphee ue to inuction. Hence the flux though the close suface is positive. 5. (B) 5. I I0 sin( ω t + φ); E E0 sin( ω t + φ) ; I 4sinωt; π π E 00 sin ωt + + π π 5π Phase iff. between I an E B at O will be ue to the following potions (i) vetical staight potion. This is zeo. (ii) cicula potion. This is given by µ 0 i µ i B cicula 0 4 (iii) staight hoizontal potion. This is given by µ i B staight 0 µ i B Total 0 i µ K.E. gaine by chage paticle of chage q when acceleate une a pot, iff. V will be E k qv; Fo a given V, E q. Fo potion, euton an α-paticle, the atio of chages is : : o 56. Hee, I max I + I + I cos0 I o I min I + I + II cos80 I max + I min ( I + I) 57. Let N be the numbe of tuns an R the aius of the coil. Then l l πrn o R () πn Now magnetic moment of the coil is M NIA NI( πr ) l Il ( NIπ ) N N Maximum value of M can be Il M max (fo N ) o IBl τmax M maxb sin The cuent in the potentiomete wie AB is 6 I 0. A The potential iffeence acoss the potential wie is V cuent esistance V The length of the wie is l 00 cm. So, the potential gaient along the wie is V 4 k 0.0 V cm l 00 The emf.4 V is balance against a length L of the potentiomete wie. i.e.,.4 kl.4.4 o L 0 cm k (A) 60. Hee, Magnetic fiel, B 0.05 T Raius of the loop, cm 0 m Constant ate at which aius of the loop shinks, 0 ms t Magnetic flux linke with the loop is o φ BA cosθ B( π )cos0 Bπ The magnitue of the inuce emf is φ ε ( Bπ ) Bπ t t t

8 0.05 π 0 0 π 0 6 V π µ V 6. E i ev E f. 6eV E (.6) 5. 6eV 75 o λ Å 79. Å Let λ A λ an λb λ Initially ate of isintegation of A is λn 0 an that of B is λn 0 an that of B is λn 0. Afte one half-life on A, ate of isintegation λn of A will become 0 an that of B woul λn also be 0 (Qhalf-life of B half-life of A). So, afte one half-life of A o two half-lives of B N t A N t B n 6. Magnetic inuction at point A ue to magnet µ 0 M at B (axial point) B (along AB) Magnetic inuction at point A ue to magnet at D (equatoial point) µ 0 M B (along BA) µ 0 M Resultant B B B 64. λ 6000 Å, 6 path iffeence, x.5 0 m λ Fo minima, x (n ) (n ) o n 65. As the galvanomete has 50 ivisions, cuent equie to pouce full scale eflection is Ig 50 ma 5 ma A 0 R 60 Ω an R. 5 Ω g s 0 Let I be the maximum cuent that the galvanomete can ea. R Then s Ig I R + R g s ( Rg + Rs ) Ig (60 +.5)5 o 5 Rs.5 I ma 66. Resistance of the bulb, V R 0 Ω P 500 Cuent though the bulb, V 00 I 5A R 0 Fo the same powe issipation, the cuent though bulb must be 5A. When the bulb is connecte to 00 V supply, the safe esistance of the cicuit shoul be V' 00 R ' 40 Ω I 5 Resistance equie to be put in seies with the bulb is R ' R Ω. V E V m 68. The ange of a pojectile is v 0 cosθ sinθ / g, the two possible angles of pojection ae θ an (90 o θ). The time of flight flight coesponing to these two angles v ae t 0 sinθ g an o v sin(90 θ ) v cosθ t 0 0 g g 4v sin cos so that t t 0 θ θ. Thus t t. g g Hence the coect choice is (. M 69. Mass pe unit aea of the isc. πr Theefoe, mass of the emove potion (hole of aius R/) is M R M m π π R 9 The moment of inetia of the complete isc about an axis passing though its cente O an pepenicula to its plane is I MR Using the paallel axes theoem, the moment of inetia of the emove potion of the isc about the axis passing though O an pepenicula to the plane of the isc is I ' MI of mass m about O ' + m OO' R R m + m M R M 4R + MR Theefoe, the moment of inetia of the emaining potion of the isc about

9 4 O I I' MR MR MR. Hence the 8 9 coect choice is ( 70. Refe to figue. The angula momentum of the mass at point P (x, y) about oigin O is efine as L m v m ( x iˆ + yj ˆ) ( viˆ ) myv( kˆ) ( Q iˆ iˆ 0 & jˆ iˆ kˆ ) Now m an v ae constant. Also y emains constant as the mass moves paallel to the x- axis. Hence L emains constant. Thus the coect choice is ( 7. The fequency of the nth hamonic is 40 Hz. The fequency of the (n + )th hamonic is 490 Hz. Theefoe n T ( n + ) T 40 an 490 L m L L Diviing, we have 490 ( n + ) which gives n n 7. Let u m spee of motoist an u b spee of the ban. The motoist will hea two souns one coming iectly fom the ban an the othe eflecte fom the wall. The appaent fequency of the iect soun is given by (the obseve is appoaching a eceing souce of soun v + u f f m f v u ( Q um ub u) + b The eflecte soun can be egae as coming fom the mio image which is appoaching the motoist with a spee v b. Hence the paent fequency of the eflecte soun is given by (the obseve an the souce of soun ae both appoaching each othe) v + u v + u f f m f v ub v u v + u Beat fequency ( f f) f f v u fu v u Thus the coect choice is (. VI 7. By efinition, β C at constant V CE. IB Theefoe, I 60 ma I C B β 40 4 ma, which is choice (C) 74. If the inputs A an B ae invete an then applie to a NAND gate, the output of the NAND gate will be the same as that an OR gate. The input of the last NAND gate is A A an B B. Hence the coect choice is (. 75. Velocity of ain ( v ) 4 ms vetically ownwas. Velocity of win ( v w ) ms fom noth to south iection. A ain op is acte upon by two velocities v an v w as shown. Fom the tiangle law, the esultant velocity of the ain op is v OW. In oe to potect himself fom ain, he must hol his umbella at an angle θ with the vetical (towas noth) given by RW v tan θ w OR v 4 Thus, the coect choice is (. p 76. Foce F t [ A{ iˆcos( kt) jˆsin( kt) ] t Ak[ iˆsin( kt) ˆcos( j kt)] Now F p Ak[ iˆsin( kt) jˆcos kt] A[ˆcos( i kt) jˆsin( kt)] A k[ sin( kt)cos( kt) + cos( kt)sinkt] 0 ( Q iˆ iˆ ˆj ˆj an ˆ j 0) jˆ. Hence angle between F an P is 90 o, which is choice ( 77. Fom the pinciple of consevation of momentum, we have v m v mv o m () v m When the sping is elease, it exets an equal an opposite foce F on each block. Let

10 a an a be the acceleations of blocks m an m espectively. Then a F ma ma o m () a m Also v ax an v ax, which give x x v. v a a m m m m [Use Eqs. () an ()] m m Hence the coect choice is ( 78. Since no extenal foce acts on the system, the cente of mass will emain at est. Hence the coect choice is (. 79. E mv hv0 W0. Now E ev an E 0 9eV. Theefoe E E / 9, / mv i.e., 9 mv v o. Hence the coect choice is (. v 80. The choice is (.

( )( )( ) ( ) + ( ) ( ) ( )

( )( )( ) ( ) + ( ) ( ) ( ) 3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13