WBJEE (Answers & Hints) ANSWERS & HINTS for WBJEE SUB : PHYSICS

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1 WBJEE - (Answes & Hints) Coe- ANSWES & HINTS fo WBJEE - SUB : PHYSICS CATEGOY - I Q. Q. 45 cay one mak each, fo which only one option is coect. Any wong answe will be lea to euction of / mak. a. The equation of state of a gas is gien by P + (V- b ) ct, whee P, V, T ae pessue, olume an tempeatue espectiely, an a, b, c ae constants. The imensions of a an b ae espectiely ML 8 T an L / ML 5 T an L ML 5 T a L ML 6 T an L / a [P] a ML T 9 a ML 8 T L [] [b ] L b b L. A capacito of capacitance C is chage to a pot ntia V an is connecte with anothe capacito of capacitance C as shown. Afte closing the switch S, the common potential acoss the two capacitos becomes V. The capacitance C is gien by s V C C c( ) c( ) c(+ ) c( ) Chage on isolate plates emains same C V C V + CV CV CV C V C(V V) C V. The.m.s. spee of the molecules of a gas at C is ν. The tempeatue at which the.m.s. spee will be ν is 546 C 646 C 746 C 846 C

2 WBJEE - (Answes & Hints) V ms T 7 T T T V V T 7 9K M M M 7 7 T ( C) 846 C 4. As shown in the figue below, a chage +C is situate at the oigin O an anothe chage +5C is on the x-axis at the point A. The late chage fom the point A is then bought to a point B on the y-axis. The wok one is (gien 4πε 9 9 m/f) B(,) m A(,) m (+ C) 45 9 J 9 9 J Zeo 45 9 J Wok one U final U initial 5 4πε 5. A fictionless piston-cyline base enclosue contains some amount of gas at a pessue of 4 kpa. Then heat is tansfee to the gas at constant pessue in a quasi-sta ic pocess. The piston moes up slowly though a height of cm. If the piston has a coss-section aea of. m, the wok one by the gas in this pocess is 6 kj kj 7.5 kj 4 kj W const Pess P ΔV 4 4 kj 6. An electic cell of e.m.f. E is connecte aco s a coppe wie of iamete an length l. The ift elocity of electons in the wie is. If the length of the wie is change to l, the new ift elocity of electons in the coppe wie will be ν ν ν / ν /4 i ν an nea E l n e ν ρ E E A nea ρ l n e A E ρ l n e ν ν ν ν 7. A NO gate an a NAND gate ae connecte as shown in the figue. Two iffeent sets of inputs ae gien to this set up. In the fist case, the input to the gates ae A, B, C. In the secon case, the inputs ae A, B, C. The output D in the fist case an secon case espectiely ae A B D C an an an an

3 WBJEE - (Answes & Hints) 8. A ba magnet has a magnetic moment of A.m. The magnet is suspene in a magnetic fiel of. NA m. The toque equie to otate the magnet fom its equilibium position though an angle of, will be N m N m 6 N m 6 N m ΤΜ Β Τ M Β sinθ.. Nm 9. Two soap bubbles of aii an ae connecte by a capillay tube-ale aangement as shown in the iagam. The ale is now opene. Then which one of the following will esult: Vale the aii of the bubbles will emain unchange the bubbles will hae equal aii The aius of the smalle bubble will incease an tha of the bigge bubble will ecease The aius of the smalle bubble will ecease an hat of the bigge bubble will incease Pessue Diffeence 4T 4T Fo smalle soap Patm Pi Fo bigge soap 4T Patm Pi As pessue insie smalle bubble is geate than pessue insie bigge bubble. so ai flows fom smalle to bigge.. An ieal mono-atomic gas of gien mass is heate at constant pessue. In this pocess, the faction of supplie heat enegy use fo the incease of the intenal enegy of the gas is /8 /5 /4 /5 Faction Δ U CV ΔQ C ϒ 5 P. The elocity of a ca taelling on a staight oa is 6 kmh at an instant of time. Now taelling with unifom acceleation fo s, the elocity becomes exactly ouble. If the wheel aius of the ca is 5 cm, then which of the following numbes is the closest to the numbe of eolutions that the wheel makes uing this s?

4 WBJEE - (Answes & Hints) f i θ π n a f i n 95 (a)π. Two glass pisms P an P ae to be combine togethe to pouce ispesion without eiation. The angles of the pisms P an P ae selecte as 4 an espectiely. If the efactie inex of pism P is.54, then that of P will be δ + δ (μ )A (μ )A μ.7. The ionization enegy of the hyogen atom is.6 ev. The potential enegy of the electon in n state of hyogen atom is +.4 ev.4 ev ev 6.8 ev E.6z.4 e, PE E n n 6.8e n 4. Wate is flowing in steamline motion though a hoizontal tube. The pessu at a point in the tube is p whee the elocity of flow is. At anothe point, whee the pessue is p/, the elocity of flow is [ensity of wate ρ] p ν + ρ ν ρ p p ν + ρ p p p+ ρ + ρ + ρ 5. In the electical cicuit shown in figue, the cu ent though the 4Ω esisto is 9V Ω Ω 8Ω Ω 4Ω.5 A.5 A Ω A.5 A.5 A. A A p ν ρ 6. A wie of initial length L an aius is stetche by a length l. Anothe wie of same mateial but with initial length L an aius is stetche by a length l. The atio of the stoe elastic enegy pe unit olume in the fist an secon wie is, : 4 : : : U (stain) l 4L U (stain) L 4l :

5 WBJEE - (Answes & Hints) 7. A cuent of A is flowing along positie x-axis though a staight wie of length.5 m place in a egion of a magnetic fiel gien by B (i ˆ+ 4j) ˆ T. The magnitue an the iection of the foce expeience by the wie espectiely ae 8N, along positie z-axis N, along positie x-axis N, along positie z-axis 4N, along positie y-axis il ˆ i ; B ( i ˆ+ 4j ˆ) T F il B k N ( ) ˆ 8. Two sphees of the same mateial, but of aii an ae allowe to fall etically ownwas though a liqui of ensity σ. The atio of thei teminal elocities is : : 6 : 9 : V V V 9 9. S an S ae the two coheent point souces of light locate in the xy-plane at points (,) an (,λ) espectiely. Hee λ is the waelength of light. At which one of the following points (gien as cooinates), the intensity of intefeence will be maximum? (λ, ) (4λ, ) (5λ/4, ) (λ/, ) (, λ) (,) 4λ 5λ ( 4λ,) Δx nλ (n ) I I max. An alpha paticle ( 4 He)has a mass of 4. amu. A poton has mass of.78 amu an a neuton has mass of.867 amu espectiely. The bining enegy of alpha paticle estimate fom these ata is the closest to 7.9 MeV. MeV 5. MeV.4 MeV ΔM (m p + m n ) m He. amu E ΔM C. 9 MeV 7.9 Me. Fou small objects each of mass m ae fixe at the cones of a ectangula wie-fame of negligible mass an of sies a an b (a > b). If the wie fame is now otate about an axis passing along the sie of length b, then the moment of inetia of the system fo this axis of otation is ma 4ma m(a + b ) m(a b ) m a m m m b I ma

6 WBJEE - (Answes & Hints). The equialent esistance between the points a an b of the electical netwok shown in the figue is a b 6 4. The e Boglie waelength of an electon (mass kg, chage.6 C) with a kinetic enegy of ev is (Planck s constant J s) 9.6 m 8.5 m 6.5 m 5. m 4 h 6.6 λ mk m 4. An object place at a istance of 6 cm fom a con x lens pouces an image of magnification m (m > ). If the object is moe towas the lens by 8 cm then again an image of magnification m is obtaine. The numeical alue of the focal length of the lens is cm 4 cm 8 cm cm f m f + u As magnification can be same fo two iffeent alues of u only if they ae of opposite sign. f f 6 f f 8 f 6 f 8 f 4, f cm 5. The numbe of atoms of a aioactie substance of half-life T is N at t. The time necessay to ecay fom N / atoms to N / atoms will be 5 T t N(t) N e λ Tln 5 5 Tln ln5 T ln N N e λt an N N e λt

7 WBJEE - (Answes & Hints) n λt, t n n T λ n t, T n n n n n t t T T n n ( ) n5 T n 6. A taelling acoustic wae of fequency 5 Hz is moing along the positie x-iection with a elocity of ms. The phase iffeence between two points x an x is 6º. Then the minimum sepaation between the two pints is mm cm cm m λ 5 5 π π φ Δ λ Δx cm π λ ( x), ( Δx) 7. A mass M at est is boken into two pieces haing masses m an (M-m). The two masses ae then sepaate by a istance. The gaitational foce between them will be the maximum when he atio of the masses [m:(m-m)] of the two pats is : : : : 4 Gmm F F [m(m m)] m m M m m, M m 8. A shell of mass 5M, acte upon by no e tenal foce an initially at est, busts into thee fagments of masses M, M an M espectiely. The fist tw fagments moe in opposite iections with elocities of magnitues V an V espectiely. The thi fagment will moe with a elocity V in a iection pepenicula to the othe two moe with a elocity V in the iection of elocity of the fist fagment be at est moe with a elocity V in the iection of elocity of the secon fagment By conseation of momentum M V MV+ MV V 9. A bullet of mass m taelling with a spee hits a block of mass M initially at est an gets embee in it. The combine system is fee to moe an thee is no othe foce acting on the system. The heat geneate in the pocess will be Zeo m Mm (M m) mm (M + m)

8 WBJEE - (Answes & Hints) mm Mmu (m + m ) (M + m) Loss in K.E. ( u u). A paticle moes along X-axis an its isplacement at any time is gien by x(t) t t + 4t in SI units. The elocity of the paticle when its acceleation is zeo, is.5 ms.5 ms 4.5 ms 8.5 ms x(t) (t t + 4t) x +, t (6t 6t 4) a (t 6) t t 6, 6 t sec, (6t 6t + 4).5 m/s. A planet moes aoun the sun in an elliptical obit with the sun at one of its foci. The physical quantity associate with the motion of the planet that emains constant with time is elocity centipetal foce linea momentum angula momentum Planet S F g SUN Toque about the sun, S Angula momentum is consee. The funamental fequency of a close pipe is equal to the fequency of the secon hamonic of an open pipe. The atio of thei lengths is : : 4 : 8 : 6 f cp f cp op 4 op 4 cp op. A paticle of mass M an chage q is elease fom est in a egion of unifom electic fiel of magnitue E. Afte a time t, the istance taelle by the chage is S an the kinetic enegy attaine by the paticle is T. Then, the atio T/S emains constant with time t aies linealy with the mass M of the paticle is inepenent of the chage q is inepenent of the magnitue of the electic fiel E qe S t m qe T T m t qe m S 4. An altenating cuent in a cicuit is gien by I sin (πt +.5π) A. The.m.s. alue an the fequency of cuent espectiely ae A & Hz A & 5 Hz A & 5Hz A & Hz

9 WBJEE - (Answes & Hints) I sin ( πt +.5π) Ims w π f 5 Hz 5. The specific heat c of a soli at low tempeatue shows tempeatue epenence accoing to the elation c DT whee D is a constant an T is the tempeatue in kelin. A piece of this soli of mass m kg is taken an its tempeatue is aise fom K to K. The amount of the heat equie in the pocess in enegy units is 5 4 Dm (/4) 4 Dm (65/4) 4 Dm (5/4) 4 Dm T 65mD Q Q mct mdt T 4 T 4 6. Fou ientical plates each of aea a ae sepaate by a istance. The connection is shown below. What is the capacitance between P an Q? P aε / aε /() aε / 4aε / P P C Q C εa Ceq. C 7. The least istance of ision of a longsighte peson is 6 cm. By using a spectacle lens, this istance is euce to cm. The powe of the len is +5. D +(/) D (/) D +. D Hee, 6 cm, u cm 6 f f 5cm 5m P D 5 8. A paticle is acte upon by a constant powe. Then, which of the following physical quantity emains constant? spee ate of change of acceleation kinetic enegy ate of change of kinetic enegy Q Q

10 WBJEE - (Answes & Hints) w k By efinition, P constant t t 9. A paticle of mass M an chage q, initially at est, is acceleate by a unifom electic fiel E though a istance D an is then allowe to appoach a fixe static chage Q of the same sign. The istance of the closest appoach of the chage q will then be qq 4πε D Q 4πε ED qq πε D Q 4πε E qq Q (qed) 4 πε 4 πε ED 4. In an n-p-n tansisto the emitte has highe egee of oping compae to that of the collecto the collecto has highe egee of oping compae to that of the emitte both the emitte an collecto hae same egee of oping the base egion is most heaily ope 4. At two iffeent places the angles of ip ae espectiely º an 45º. At these two places the atio of hoizontal component of eath s magnetic fiel is : : : : H Bcos H Bcos45 Note : Infomation is not sufficient in the gien question. It can be sole only when magnetic fiel at these two places ae equal. 4. Two ectos ae gien by A iˆ + j + kˆ an B iˆ + 6 ˆj + kˆ. Anothe ecto C has the same magnitue as B but has the same iection as A. Then which of the following ectos epesents C? 7 ( iˆ ˆj kˆ + + ) ( iˆ ˆj kˆ 7 + ) ( iˆ ˆj + kˆ ) 7 9 ˆi + j ˆ+ kˆ C ˆi + j ˆ+ kˆ 49 7 (i ˆ j ˆ k) ˆ ( iˆ + ˆj + kˆ ) 7

11 WBJEE - (Answes & Hints) 4. An equilateal tiangle is mae by unifom wies AB, BC, CA. A cuent I entes at A an leaes fom the mi point of BC. If the lengths of each sie of the tiangle is L, the magnetic fiel B at the centoi O of the tiangle is A O B C μ 4I 4π L I μ 4I π L B + B μ I 4π L Zeo B ue to left pat B ue to ight pat 44. A ca moing at a elocity of 7 ms towas an appoac ing bus that blows a hon at a fequency of 64 Hz on a staight tack. The fequency of this hon appeas to be 68 Hz to the ca ie. If the elociy of soun in ai is 4 ms, then elocity of the appoaching bus is ms 4 ms 8 ms ms Ca 7 m sec Bus on soling, 4ms 45. A paticle is moing with a unifom spee in a cicula path of aius with the cente at O. When the paticle moes fom a point P to Q on the cicle such that POQ θ, then the magnitue of the change in elocity is θ θ sin (θ) Zeo sin cos Δ + cosθ sin θ

12 WBJEE - (Answes & Hints) CATEGOY - II Q. 46 Q. 55 cay two maks each, fo which only one option is coect. Any wong answe will lea to euction of / mak 46. Two simple hamonic motions ae gien by x a sin ωt + a cos ωt an x a sin ωt + a cosωt The atio of the amplitues of fist an secon motion an the phase iffeence between them ae espectiely a an π a π/4 a fo fist S.H.M an π a a π an π/6 a fo secon S H M a π π π atio of amplitue phase iffe nce i a 4 6 an π A small mass m attache to one en of a sping with a negligi le mass an an unstetche length L, executes etical oscillations with angula fequency ω. When the mass is otate with an angula spee ω by holing the othe en of the sping at a fixe point, the mass moes unifomly in a cicula path in a hoizontal plane. Then the incease in length of the sping uing this otation is ω L ω ω Kxcosθ θ mg Kx Kxsinθ ω L ω ω ω L ω Kxsinθ mω (L + x) sinθ Kx mω (L + x) an K m ω K mω ω L ω m/ ω x m / ω (L+ x) ω L x ω ω

13 WBJEE - (Answes & Hints) 48. A cylinical block floats etically in a liqui of ensity ρ kept in a containe such that the faction of olume of the cyline insie the liqui is x. then some amount of anothe immiscible liqui of ensity ρ (ρ < ρ ) is ae to the liqui in the containe so that the cyline now floats just fully immese in the liquis with x faction of olume of the cyline insie the liqui of ensity ρ. The atio ρ /ρ will be x x x x x + x x x x + x x x x ( x ) p x fist case p x g p x g + p ( x )g, as Bouyant foce in both the cases ae same p x on soling, p x x 49. A sphee of aius has a olume ensity of chage ρ k, whee is the istance fom the cente of the sphee an k is constant. The magnitue of the electic fiel which exists at the su ace o the sphee is gien by (ε pemittiity of the fee space) 4π k ε 4 By Gauss s theoem E(4π ) p 4π ε k 4π ε K E 4ε k ε 4π k ε 5. A paticle of mass M an chage q is at est at the mipoint between two othe fixe simila chages each of magnitue Q place a istance apat. The system is collinea as shown in the figue. The paticle is now isplace by a small amount x (x<< ) along the line joining the two chages an is left to itself. It will now oscillate about the mean position with a time peio (ε pemittiity of fee space) Q q Q k 4ε π Mε Qq π ε Qq M π ε Qq M π Mε Qq estoing foce on isplacement of x,

14 WBJEE - (Answes & Hints) q Qq F K ( x) ( x) + KQq ( x) ( x) + 4x KQq ( x ) 4x KQq If ( x) 4 KQq 4x F 4KQq acceleation a x m m 4KQq ω m T π ω m π 4KQq π m ε Qq 5. A boy is pojecte fom the goun with a elocity ( ) iˆ + ˆj ms The maximum height attaine an the ange of the boy espectiely ae (gien g ms ) 5 m an 6 m m an m 6 m an 5 m m an 5 m V i + j V x V y y V H 5m g V y V x T V x g 6m 5. The stopping potential fo photoelect ons fom a metal suface is V when monochomatic light of fequency is incient on it. The stopping potential becomes V when monochomatic light of anothe fequency is incient on the same metal suface. If h be the Planck s onstant an e be the chage of an electon, then the fequency of light in the secon case is e h ( V + ) + ( V + ) ( V ) + ( V ) V hν φ + e () hν φ + e () h (ν ν ) e ( ) e ν ( ) h e h V e h V + ν e h V

15 WBJEE - (Answes & Hints) 5. A cell of e.m.f. E is connecte to a esistance fo time t an the amount of heat geneate in it is H. If the esistance is eplace by anothe esistance an is connecte to the cell fo the same time t, the amount of heat geneate in is 4H. Then the intenal esistance of the cell is + + I H I 4H E ( + ) H ( ) ( ) an ( + ) ( + ) E ( + ) 4H 54. moles of a mono-atomic gas (γ 5/) is mixe with mole of a iatomic gas (γ 7/). The alue of γ fo the mixtue will be 9/ /7 /7 5/7 Degee of feeom n f + nf + 5 f mix n + n 4 ie. f 7 γ + f Note : If we take γ 7/ fo iatomic gas as gien in the question, none of the options ae coect 55. The magnetic fiel B t + 4t (whee t time) is applie pepenicula to the plane of a cicula wie of aius an esistance. If all the units ae in SI the electic chage that flows though the cicula wie uing t s to t s is 6π π π 48π

16 WBJEE - (Answes & Hints) ΔQ Δφ π (B B ) π [ + 4 4] π CATEGOY - III Q. 56 Q. 6 cay two maks each, fo which one o moe than one options may be coect. Making of coect options will lea to a maximum mak of twoon po ata basis. Thee willbe no negatie making fo these questions. Howee, any making of wong option will lea to awa of zeo mak against the espectie question iespectie of the numbe of coet options make. 56. If E an B ae the magnitues of electic an magnetic fiels espectiely in some egion of space, then the possibilities fo which a chage paticle may moe in that space with a unifom elocity of magnitue ae E B E, B E, B E, B Ans : (A, C, D) 57. An electon of chage e an mass m is moing in cicula path of aius with a unifom angula spee ω. Then which of the following statements ae coect? The equialent cuent flowing in the cicula path is popotional to The magnetic moment ue to cicula cuent loop is inepenent of m The magnetic moment ue to cicula cuent loop is equal to e/m time th angula momentum of the electon The angula momentum of the paticle is popotional to the aeal eloc ty of electon. Ans : (B, D) Magnetic moment μ IA e e π π Angula momentum m A t 58. A biconex lens of focal length f an aii of cu atue of both the sufaces is mae of a mateial of efactie inex n. This lens is place in a liqui of efactie inex n. Now this lens will behae like eithe as a conex o as a concae len epening solely on a conex lens epening on n an n a concae lens epening on n an n a conex lens of same foc l length iespectie of, n an n Ans : (B, C) 59. A block of mass m (. kg) is hanging oe a fictionless light fixe pulley by an inextensible sting of negligible mass. The othe en of the sting is pulle by a constant foce F in the eticaly ownwa iection. The linea momentum of the block incease by kg ms in s afte the block stats fom est. Then, (gien g ms ) m F The tension in the sting is F The tension in the sting is N The wok one by the tension on the block is J uing this s The wok one against the foce of gaity is J Ans : (A, B, D)

17 WBJEE - (Answes & Hints) T F m F mg F mg F + mg N unbalance foce a m/s mass. S at m W by tension F J W against gaity mg s J 6. A ba of length l caying a small mass m at one of its ens otates with a unifom angula spee ω in a etical plane about the mi-point of the ba. Duing the otation, at some instant of time when the ba is hoizontal, the mass is etache fom the ba but the ba continues to otate with same ω. The mass moes etically up, comes back an eches the ba at the same point. At that place, the accele ation ue to gaity is g. This is possible if the quantity is an intege g The total time of flight of the mass is popotiona to ω The total istance taelle by the mass n ai is popotional to ω The total istance taelle by the mass in ai an its total time of flight ae both inepenent on its mass. Ans : (A, C, D) m ω, π ω n ω g T g ω g (as completes n otations within T) ω n π g ω Distance taelle h. g 4g

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to