[1] J EEMain2014Physi cs 1. Thepressurethat has to beapplied to theends of a steel wireof length10cmto keepitslengthconstant whenitstemperatureisraisedby100 0 C is (For steel Young's modulus is 2×10 11 N m –2 and coefficientofthermalexpansionis1.1×10 –5 K –1 ) (1) 2.2×10 7 Pa (2) 2.2×10 6 Pa (3) 2.2×10 8 Pa (4) 2.2×10 9 Pa Sol. [3] 2. A conductor lies alongthez-axis at ÷ s < 15 15 . . z m andcarriesafixedcurrentof10.0A in ÷ a z direction (seefigure). Forafield B e a x y = × ÷ ÷ 30 10 4 02 . . T, findthe power required to move the conductor at constant speedtox =2.0m, y =0min5×10 –3 s. Assumeparallel motionalongthex-axis. / (1) 14.85W (2) 29.7W (3) 1.57W (4) 2.97W Sol. [4] 3. A bobofmassm attachedtoaninextensiblestringof length is suspended froma vertical support. The bobrotatesinahorizontalcirclewithanangularspeed e rad/s about the vertical. About the point of suspension (1) angular momentumchangesindirectionbutnotin magnitude (2) angular momentumchangesbothindirectionand magnitude (3) angular momentumisconserved (4) angular momentumchanges inmagnitudebut not indirection Sol. [1] 4. The current voltage relationof diode is givenby I e V T = ÷ 1000 1 / e j mA, wheretheappliedvoltageV is involtsandthetemperatureT isindegreekelvin. Ifa students makes anerror measuring ±001 . V while measuringthecurrentof5mA at300K, whatwillbe error inthevalueofcurrentinmA? (1) 0.5mA (2) 0.05mA (3) 0.2mA (4) 0.02mA Sol. [3] 5. Anopenglasstubeisimmersedinmercuryinsucha waythat alengthof 8 cmextendsabovethemercury level. The openend of the tube is thenclosed and sealedandthetubeisraisedverticallyupbyadditional 46 cm. What will belengthof theair columnabove mercuryinthetubenow? (Atmosphericpressure=76cmofHg) (1) 38cm (2) 6cm (3) 16cm (4) 22cm Sol. [1] 6. MatchList- I (Electromagneticwavetype)withList-II (Its association/application) and select the correct optionfromthechoicesgivenbelowthelists List-I List-II (a)infraredwaves (i)Totreatmuscularstrain (b) Radiowaves (ii)Forbroadcasting (c)X-rays (iii) Todetectfractureof bones (d)Ultraviolet (iv) Absorbedbythe rays ozonelayer ofthe atmosphere a b c d (1) (iii) (ii) (i) (iv) (2) (i) (ii) (iii) (iv) (3) (iv) (iii) (ii) (i) (4) (i) (ii) (iv) (iii) Sol. [2] 7. Aparallelplatecapacitorismadeoftwocircularplates separatedbyadistanceof5mmandwithadielectricof dielectricconstant2.2betweenthem. Whentheelectric fieldinthedielectricis3×10 4 V/m, thechargedensityof thepositiveplatewill becloseto (1) 3×10 4 C/m 2 (2) 6×10 4 C/m 2 (3) 6×10 –7 C/m 2 (4) 3×10 –7 C/m 2 Sol. [3] 8. A studentmeasuredthelengthofarodandwroteitas 3.50cm. Whatinstrumentdidheusetomeasureit? (1) Ascrewgaugehaving100divisionsinthecircular scaleandpitchas1mm (2) A screwgaugehaving50divisions inthecircular scaleandpitchas1mm (3) A meterscale (4) Averniercalliperwherethe10divisionsinvernier scale matches with9 divisions in main scale and mainscalehas10divisionsin1cm. Sol. [4] [2] J EEMain2014 9. Four particles, eachof mass M and equidistant from eachother, movealongacircleof radiusR under the actionof their mutual gravitational attraction. The speedofeachparticleis (1) GM R 1 2 2 + e j (2) 1 2 1 2 2 GM R + e j (3) GM R (4) 2 2 GM R Sol. [2 10. Inalargebuilding, thereare15bulbsof40W, 5bulbs of100W, 5fansof 80Wand1heater of1kW. The voltageof theelectric mainsis220V. Theminimum capacityofthemainfuseofthebuildingwillbe (1) 12A (2) 14A (3) 8A (4) 10A Sol. [1] 11. A particles moves withsimpleharmonic motionina straightline. Infirst t s afterstartingfromrestittravels adistancea, and innext t s it travels 2a, insame direction, then (1) amplitudeofmotionis4a (2) timeperiodofoscillationsis 6t (3) amplitudeofmotionis3a (4) timeperiodofoscillationsis 8t Sol. [2] 12. Thecoercivityofasmallmagnetwheretheferromagnet getsdemagnetizedis3×10 3 Am –1 . Thecurrentrequired toapassedinasolenoidoflength10cmandnumberof turns100, sothatthemagnetgetsdemagnetizedwhen insidethesolenoid, is (1) 3A (2) 6A (3) 30mA (4) 60mA Sol. [1] 13. Theforwardbiaseddiodeconnectionis (1) (2) (3) (4) Sol. [3] 14. Duringthepropagationofelectromagneticwavesina medium (1) Electric energydensityis equal to themagnetic energy density (2) Bothelectricandmagneticenergydensitiesarezero (3) Electric energydensityisdoubleof themagnetic energy density (4) Electricenergydensityishalfofthemagneticenergy density Sol. [1] 15. Inthecircuitshownhere, thepointCiskeptconnected to point A till thecurrent flowingthroughthecircuit becomes constant. Afterward, suddenly, point C is disconnected frompoint A andconnectedto point B attimet =0. Ratioofthevoltageacrossresistanceand theinductoratt =L/R willbeequalto (1) –1 (2) 1÷ e e (3) e e 1÷ (4) 1 Sol. [1] 16. A mass m is supported bya massless stringwound aroundauniformhollowcylinderofmassm andradius R. Ifthestringdoesnotsliponthecylinder, withwhat accelerationwillthemassfallonrelease? (1) 5 6 g (2) g (3) 2 3 g (4) g 2 Sol. [4] [3] J EEMain2014 17. One mole of diatomic ideal gas undergoes a cyclic process ABC as showninfigure. Theprocess BC is adiabatic. ThetemperaturesatA, BandC are400K, 800 K and 600 K respectively. Choose the correct statement. (1) Thechangeininternal energyintheprocessABis – 350R (2) Thechangeininternal energyintheprocessBCis –500R (3) The change ininternal energy inwhole cyclic processis250R (4) ThechangeininternalenergyintheprocessCAis 700R Sol. [2] 18. FromatowerofheightH, aparticleisthrownvertically upwardswithaspeedu. Thetimetakenbytheparticles, tohittheground, isntimesthattakenbyittoreachthe highest pointof its path. TherelationbetweenH, uandnis (1) 2 2 2 gH nu n = ÷ b g (2) g H n u = ÷ 2 2 b g (3) 2 2 2 g H n u = (4) g H n u = ÷ 2 2 2 b g Sol. [1] 19. A thinconvexlens madefromcrownglass µ = F H G I K J 3 2 has focallengthf. Whenitismeasuredintwodifferent liquidshavingrefractiveindices 4 3 and 5 3 , ithasthe focal lengths f 1 and f 2 respectively. The correct relationbetweenthefocal lengthsis (1) f f 2 > and f 1 becomesnegative (2) f 1 and f 2 bothbecome negative (3) f f f 1 2 = < (4) f f 1 > and f 2 becomesnegative Sol. [4] 20. Three rods of Copper, Brass and Steel are welded togethertoformaY- shapedstructure. Areaofcross- sectionof eachrod =4 cm 2 . End of copper rod is maintained at 10 0 C.Lengths of thecopper, brass and steelrodsare46, 13and12cmsrespectively. Therods are thermallyinsulated fromsurroundings except at ends. Thermalconductiviesofcopper, brassandsteel are0.92, 0.26and0.12CGSunitsrespectively. Rateof heatflowthroughcopper rodis (1) 4.8cal/s (2) 6.0cal /s (3) 1.2cal/s (4) 2.4cal/s Sol. [1] 21. Apipeoflength85cmisclosedfromoneend. Findthe numberofpossiblenaturaloscillationsofaircolumnin thepipewhosefrequencies liebelow1250 Hz. The velocityofsoundinairis340m/s. (1) 6 (2) 4 (3) 12 (4) 8 Sol. [1] 22. Thereisacirculartubeinaverticalplane. Twoliquids whichdonotmixandofdensities d 1 and d 2 arefilled int hetube. Eachliquid subtends 90° angleat centre. Radiusjoiningthereinterfacemakesanangleo with vertical. Ratio d d 1 2 is (1) 1 1 + ÷ tan tan o o (2) 1 1 + ÷ sin cos o o (3) 1 1 + ÷ sin sin o o (4) 1 1 + ÷ cos cos o o Sol. [1] [4] J EEMain2014 23. Agreenlightisincidentfromthewatertotheair-water interfaceat thecritical angle(u ) . Select thecorrect statement (1) Thespectrumof visiblelight whosefrequencyis morethanthatofgreenlightwillcomeouttotheair medium (2) Theentirespectrumofvisiblelightwillcomeoutof thewater atvariousanglestothenormal (3) Theentirespectrumofvisiblelightwillcomeoutof thewateratanangleof90°totenormal (4) Thespectrumof visiblelight whosefrequencyis lessthanthatofgreenlightwillcomeouttotheair medium Sol. [4] 24. Hydrogen 1 1 H e j, Deuterium 1 2 H e j, singlyionised Helium 2 4 He e j + and doublyionisedlithium 3 6 Li e j ++ all haveoneelectronaroundthenucleus. Consider an electrontransitionfromn=2 to n=1. If the wave lengths of emitted radiationare ì ì ì 1 2 3 , , and ì 4 respectivelythenapproximatelywhich one of the followingiscorrect? (1) ì ì ì ì 1 2 3 4 4 9 = = = (2) ì ì ì ì 1 2 3 4 2 3 4 = = = (3) 4 2 2 1 2 3 4 ì ì ì ì = = = (4) ì ì ì ì 1 2 3 4 2 2 = = = Sol. [1] 25. The radiationcorrespondingto 3 2 ÷ transitionof hydrogenatomfalls ona metal surface to produce photoelectrons. Theseelectrons are made to enter a magenticfieldof 3 10 4 × ÷ T . Iftheradiusofthelargest circular pathfollowedbytheseelectrons is10.0mm, theworkfunctionofthemetaliscloseto: (1) 0.8eV (2) 1.6eV (3) 1.8eV (4) 1.1eV Sol. [4] 26. Ablockofmassmisplacedonasurfacewithavertical cross sectiongivenby y x = 3 6 . If thecoefficient of frictionis0.5, themaximumheightabovethegroundat whichtheblock canbeplacedwithoutslippingis: (1) 1 3 m (2) 1 2 m (3) 1 6 m (4) 2 3 m Sol. [3] 27. Whena rubber-band is stretched bya distancex, it exerts a restoringforce of magnitude F ax bx = + 2 where a and b are constants. The work done in stretchingtheunstretchedrubber-bandbyL is: (1) aL bL 2 3 2 3 + (2) 1 2 2 3 2 3 aL bL + F H G I K J (3) aL bL 2 3 + (4) 1 2 2 3 aL bL + e j Sol. [1] 28. Onheatingwater, bubblesbeingformedatthebottom of thevessel detatchandrise. Takethebubblestobe spheres of radius R and makingacircular contant fo radiusr withthebottomofthevessel. If r R << , and thesurfacetensionofwaterisT, valueofr justbefore bubblesdetatchis:(densityof water is µ w ) (1) R g T w 2 µ (2) R g T w 2 3µ (3) R g T w 2 3 µ (4) R g T w 2 6 µ Sol. [3] 29. Two beams, A and B, of planepolarized light with mutuallyperpendicularplanesofpolarizationareseen throughapolaroid. Fromthepositionwhenthebeam A has maximumintensity (and beamB has zero intensity), arotationofpolaroidthrough30°makesthe twobeamsappearequallybright. Iftheinitialintensities of the two beams are I A and I B respectively, then I I A B equals: (1) 1 (2) 1 3 (3) 3 (4) 3 2 Sol. [2] [5] J EEMain2014 30. Assumethatanelectricfield E x i = 30 2 existsinspace. Thenthepotential difference V V A O ÷ , where V O is thepotentialattheoriginandV A thepotentialatx =2 mis: (1) ÷80J (2) 80J (3) 120J (4) ÷120J Sol. [1]