IIT JEE, 2005 (MAINS) SOLUTIONS PHYSICS 1

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1 IIT JEE, 5 (MINS) SOLUTIONS YSIS iscaimer: Tis booket contains te questions of IIT-JEE 5, Main Examination based on te memory reca of students aong wit soutions provided by te facuty of riiant Tutorias. Since te questions are based on recoection, certain inadvertent errors migt ave cropped in. riiant Tutorias is not responsibe for suc errors.. stationary observer receives sound waves from a moving train. Te frequency of sound received by observer is. kz wen te train approaces im and.8 kz wen te train moves away from im. Find te veocity of train. It is given speed of sound is m/s. []. + s v' v,. v,.8 v,, s m/s ± s s + s.8. conducting sperica bubbe of radius a and tickness t (<<a ) is carged to potentia. Now it coapses to form a sperica dropet. Find te potentia of dropet. [] Let te radius of dropet be r. a t r r ( a t) From conservation of carge, ' ε a ε r ' s ' a ( a t) E x. otentia energy of a partice varies as a function of x and is given by U ( x), de-rogie waveengts of x > te partice in te region x and x >are λ and λ respectivey. If tota energy of te partice is E, find λ /λ. [] Tota energy Kinetic energy + otentia energy, E K + E [ in te region x ] K E mk me [ momentum of te partice in te region x ], λ me Tota energy Kinetic energy + otentia energy, E K + [ in te region x > ] mk me [ momentum of te partice in te region x > ], λ ividing equation (i) by (ii), λ λ me. Te smaest division on te main scae of a vernier caipers is mm and t vernier division coincide wit 9 t main scae division. Wen two jaws of te instrument are touced wit eac oter zero of vernier scae coincide wit zero of te main scae. Te side of a cube wen measured wit tis instrument gives divisions on main scae and st division of vernier scae coincides wit main scae division. If mass of cube is.7 gm, find its density (in gm/cm ). Express your answer in correct number of significant figures. [] Least count mm.. mm. Lengt of side of cube +.. mm oume (.). mm. cm.7 ensity.65 gm/cc. In correct significant figures density.65 gm/cc. 5. rod of mass M and engt L is suspended by a frictioness inge at point O, as sown in O figure. buet of mass m moving wit veocity v in orizonta direction strikes te end of te rod and gets embedded in it. Find te anguar veocity acquired by te rod just after te M L coision. v m [] y conservation of anguar momentum about te point O, we ave mvl I ML mvl mv + ml, ML L( M + m) + ml 6. U tube of base engt contains a iquid of density ρ in it. Te tube is rotated about one of its vertica imbs wit anguar veocity, as sown in te figure. Find te difference of eigt of iquid in te two imbs. Te diameter of tube is negigiby sma as compared to engt of te tube. []

2 IIT JEE, 5 (MINS) SOLUTIONS YSIS ressure difference across te eement of widt dx at a distance x is d ρ x dx, ρx ρ g ρx, g x dx 7. Find te minimum vaue of ange of incidence on so tat tota interna refection takes pace at bot te surfaces and. For tota interna refection at surface i sin i 5 For tota interna refection at surface i sin i 6 For tota interna refection at bot te surfaces i 6, so minimum vaue of i 6 i i i i µ µ µ µ µ µ [] 8. Te meter bridge sown in te diagram, is used to measure te vaue of unknown resistance X. It gives nu points at, and wen R R, R R and R R respectivey. Wic one of te arrangements wi give te most accurate vaue of X and wy? X Resistance box R G [] Most accurate vaue wi be obtained for point because (a) te bridge is most sensitive wen four resistances are neary of same magnitude. (b) Reative error wi be minimum wen is maximum (measured from bot sides). (c) it reduces te end errors. 9. transverse mecanica armonic wave is traveing on a string. Maximum veocity and maximum acceeration of a partice on te string are m/s and 9 m/s respectivey. If wave is traveing wit a speed m/s on te string, write wave function describing te wave. Maximum transverse veocity m/s Maximum transverse acceeration 9 m/s eocity of wave K m/s (iii) y (i), (ii) and (iii) we get, rad/s. K.5 rad/m. m. Terefore, wave equation wi be y sin( t ±. 5x + φ) initia pase zero] m [ φ initia pase] or y sin( t ±.5x) m[ taking. soid cyinder of mass M and radius R ros down on an incined pane aving ange of incination θ. Find te acceeration of centre of mass of te cyinder. For transation motion, Mg sin θ f MaM N f For rotationa motion, f. R MR α Mgsinθ Mgcosθ For no sipping a M Rα (iii) Soving (i) (ii) and (iii) Mg sin θ MaM a M gsinθ θ. (a) Ligt is incident on te prism at an ange of incidence i, as sown in figure. Find te vaue of i so tat te deviation produced by prism is minimum. (b) noter simiar prism E is now fixed at point wic can rotate about te axis passing troug and perpendicuar to te pane of paper. y wat ange wi te prism E be rotated, so tat te fina emergent ray soud ave minimum deviation? If it is given tat te refractive index of materia of bot te prism is. i E

3 IIT JEE, 5 (MINS) SOLUTIONS YSIS (a) For minimum deviation r r and + r 6 r sin i So r.nd by Sne s aw,, i 6 sin r (b) For minimum deviation from second prism te ange of incidence on soud aso be 6. Terefore te prism E soud be rotated cockwise or anti cockwise troug 6.. Two adders eac of mass M and engt L are connected by eac oter at te point. point mass m angs troug a massess string at point and te system is paced on a orizonta surface as sown in figure. If te system is in equiibrium, ten find te magnitude and direction of friction force at or. i r r 6 6 M,L m M,L θ θ R x R y N m Mg mg Mg N θ θ f f m For vertica equiibrium N M + g N Mg θ f F.. of adder (were R x and R y are reaction force at point ). For rotationa equiibrium of L fl sin θ NL cos θ + Mg cos θ From equation (i) and (ii) f ( M + m) gcotθ and direction is as sown in figure. ong soenoid of radius a aving n number of turns per unit engt and carrying current I I sin t (were I and are constants) is paced coaxiay inside a cyindrica se of uniform resistivity ρ, engt L, radius R and tickness d (<<R) as sown in figure. Find te vaue of induced current in te se. a d L ρ R Rρ Resistance of cyindrica se R' Ld Ld Magnetic fied due to soenoid µ ni µ ni sin t Fux associated wit cyindrica se φ ( a ) dφ Induced emf e dt µ I na Ld I ' t Rρ cos µ I na cos t, e I'R' (were I ' is te induced current). bock executes SM about mean position y wit an ampitude and anguar frequency. t time t, te bock is at te mean position and moving upwards. t a certain eigt y* from te mean position, te bock get detaced from te spring (wen te bock gets detaced assume tat spring compresses immediatey suc tat it does not interfere wit te subsequent motion of te bock). Find te y* so tat eigt attained by te bock be maximum. [ > g]. y

4 IIT JEE, 5 (MINS) SOLUTIONS YSIS Speed of bock at y* y * ( ) y * eigt attained by te bock after detacment ( ) * Tota eigt attained by te bock + y y * g d For to be maximum, dy * y* g/ y 5. capacitor of capacitance and two resistors R and R are connected R troug a switc S wit a battery of emf, as sown in figure. t t S switc S is cosed and te carge on te capacitor at any time t is αt given by ( t) ( e ). Find te vaue of and α in terms of R given parameters. g y* t time t carge on te capacitor and current troug te resistances are as sown in te figure, ten + ( i + i ) R i R + ( i + i ) R R (i +i ) i R i and d i (iii) dt From equation (i), (ii) and (iii) d dt R + R αt On comparing above equation wit ( t) ( e ) R ( ) e R + R R R α + R R RR +. On soving, ( t) R R, R + R ( R + R ) t RR 6. n unknown atom as neutrons in its nuceus. Ratio of radii of nucei of tis atom and e is ( ). Find te (a) atomic number of unknown atom. (b) frequency of K α X-rays for tis atom. ( Rydberg constant R 7 m, speed of igt 8 m/s) R (a) ( ), 56. tomic number of unknown atom 56 6 R R, 7 5 λ (b) ( Z ) λ n n 7 65, v c λ z 7. J of eat energy is suppied to a metaic object of kg at atmosperic pressure and. Find (a) te fina temperature of te meta. (b) work done by te meta. (c) cange in interna energy of te meta. [6] Given specific eat of meta J/kg /, ensity of te meta 9 kg/ m oefficient of voume expansion 9 5 /, tmosperic pressure 5 N/m. (a) Let fina temperature of te meta is T, ( ) T + W T 5 T 7 (Θ W ) m (b) m, γ T, 9 5 5, d W 5.5 J (c) U + W U J, ( ) 7 m 5, 8. moving coi gavanometer as a coi of area, number of turns N. magnetic fied is appied on it. Te torque acing on it is given by τ Ki, were i current troug coi. If moment of inertia of coi is I about te axis of rotation (a) find vaue of K in terms of gavanometer parameters (N,, ) (b) find vaue of torsiona constant if current i produces anguar defection radian. (c) if a carge is passed amost instantaneousy troug coi, find te maximum anguar defection in it. [6] (a) τ Ni sinθ (were θ is te ange between and ) Ni (In gavanometer te coi is paced in radia fied, i.e. θ ) K N (b) If is torsiona constant and φ is anguar defection. Ten, τ φ Ni. Wen, i i, φ

5 IIT JEE, 5 (MINS) SOLUTIONS YSIS 5 Ni Ni (c) If is anguar speed acieved by te coi wen carge is passed troug it ten K From impuse momentum consideration, I τ t I K t t I If θ max is maximum anguar defection ten From energy conservation max I θ θ K I max I K N I Ii

Previous Years Problems on System of Particles and Rotional Motion for NEET

Previous Years Problems on System of Particles and Rotional Motion for NEET P-8 JPME Topicwise Soved Paper- PHYSCS Previous Years Probems on Sstem of Partices and otiona Motion for NEET This Chapter Previous Years Probems on Sstem of Partices and otiona Motion for NEET is taken