IIT-JEE 2009 Physics Paper - I I Questions and Solutions

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PARTIII:PHYSICS

SECTION�IStraightObjectiveType

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Thissection contains4 multiple choicequestions. Eachquestion has 4 choices (A), (B), (C) and(D), out of which ONLY ONEiscorrect.

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*39.The mass M shown in the figure oscillates in simple harmonicmotionwithamplitude A. The amplitude ofthe pointPis
(A)k₁A/k₂(B)k₂/k₁

(C)k₁A/k₁+k₂(D)k₂A/k₁+k₂
Key,(D)
Sol.

x1 + x2 =A
k₁x1=k₂x2
amplitude of Point=k₂A/k₁+k₂
(D) iscorrect.

*40. A Piece of wire is bent inthe shape of a Parabola y =kx2 (y�axis vertical) with a bead of mass mon it.The
bead can slide on the wirewithout friction. It stays at thelowest Point of the Parabola when the wireisat
rest. The wire is nowaccelerated Parallel to the x�axis withconstant acceleration a. The distanceofthe
new equilibrium Position of thebead, where the bead can stayat rest with respect to the wire, form they�axisis

(A)a/gk(B)-a/2gk

(C)2a/gk(D)4a/gk

Key(B)

SOl:

tanθ =a/g

slope of tangent =-tanθ =2kx

=>x=-a/2gk

41. Photoelectric effectexperiments are performed using threedifferent metal Plates p, q andr havingwork
function P2.0 eV φ = , q 2.5 eVφ = and r 3.0 eVφ = , respectively. A light beamcontaining wavelengthof
550 nm and 350 nmwith equal intensities illuminates each ofthe P lates. The correctI�V graph forthe
experimentis

Key(A)

Sol.The work functionfor P issmallest.stopping Potentialfor P is largest. Secondly, not allwavelengths will be able toejectphotoelectron
from all threei.e., the saturationcurrent will bedifferent.

(A) iscorrect.

*42. A uniform rod of length Land mass M is pivotedat the centre. Its two endsare
attached to two springs ofequal spring constants k. Thesprings are fixed torigid
supports as shown inthe figure, and the rod is freeto oscillate in thehorizontal
plane. The rod is gently Pushed through a small angleθ in one directionand
released. The frequency ofoscillationis
(A) 1/2 π*√2k/M(B) 1/2π*√k/M

(C) 1/2 π*√6k/M(D) 1/2π*√24k/M

Key.(C)

Sol.Restoring torquer

=>-k*L/2*θ.L/282

So FromFigure f=1/2 π*√6k/M

Therefore(C)iscorrect

SECTION�IIMultiple CorrectAnswerType

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Thissection contains 5 multiple correctanswer(s) type questions. Each questionhas 4 choices (A),(B), (C) and (D), out of which ONE OR MORE is/arecorrect.

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43. Two metallic rings A andB, identical in shape and sizebut havingdifferent
resistivity A B and ρρ , are kept ontop of twoidentical solenoids asshown inthe
figure. When current I isswitched on in both the solenoids inidentical manner,the
rings A and Bjump toheights hA and hB,respectively, with hA > hB. ThePossible
relation(s) between theirresistivities and their masses mAand mB is(are)

(A)ρA> ρ B and m A=mB(B)ρA < ρ Band m A=mB
(C) ρA >ρ B and m A>mB(D)ρA <ρ B and m A

*44. A student performed theexperiment to measure the speedof sound in air using resonanceair�column
method. Two resonances in theair�column were obtained bylowering the water level. The resonancewith
the shorter air�column is thefirst resonance and that withthe longer air�column is thesecondresonance.
Then,
(A) the intensity of the soundheard at the first resonancewas more than that at the secondresonance
(B) the Prongs of the tunning fork werekept in a horizontal planeabove the resonancetube
(C) theamP litudeof vibration of the ends of theP rongsistyP icallyaround 1 cm
(D) the length of theair�column at the first resonance wassomewhat shorter than1/4th of the wavelengthof
the sound inair.
Key. (A,D)
Sol. As length ofair-column increases intensitydecreases.
Hence (A) iscorrect.l+e=λ/4=>l<λ/4
Hence (D) iscorrect.

*45. The figure shows theP �VP lot ofan ideal gas takenthrough a cycle ABCDA.The
Part ABC is a semi�circle andCDA is half of anelliPse.Then,
(A) the process during theP ath A→ B isisothermal
(B) heat flows out of the gasduring thenP ath B→ C →D
(C) work done during theP ath A→ B →C is zero
(D) Positive work is done by thegas in the cycleABCDA.Key. (B,D)
Sol.temperature at B >temperature atD

∆U is negative (forB → C →D)
Also W is negative (for B→ C →D)
Tracing is clockwise onPVdiagram.
W is Positive.
(B) and (D) arecorrect.

46. Under the influence of theCoulomb field of charge +Q, acharge �q is moving around it in anelliPtical
orbit. Find out the correctstatement(s)
(A) the angular momentum ofthe charge �q isconstant
(B) the linear momentum of thecharge �q isconstant
(C) the angular velocity ofthe charge �q isconstant
(D) the linear speed of thecharge �q isconstant.
Key.(A)
Sol.Force iscentral.
So, option (A)iscorrect.

*47. AsP here isrolling withoutslipping on a fixed horizontal plane surface.Inthe
figure, A is the point ofcontact, B is the centre of thesP hereand C is its top mostpoint then(A )Vc-Va =2(Vc-V_b)(B)Vc-V_b=(V_b-Va)
(C)|Vc-Va|=2|Vc-V_b|(D)|Vc-V_b| =|(V_b-Va)|
Key.(B,C)

SECTION�IIIMatrixMatchType

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Thissectioncontains 2 questions. Each question contains statements givenintwocolumns, which have to bematched. The statements in Column Iare labeled A, B, Cand D,while the statements in Column IIare labelled p, q, r, s and t. Any givenstatement inColumn I can havecorrect matching with ONE OR MOREstatement(s) in ColumnII. Theappropriate bubbles correspondingto the answers to these questionshave to bedarkened as illustrated inthe followingexamPle:If the correct matches are A� p, s and t; B � q and r; C �pand q; and D � s and t;then the correctdarkening of bubbleswill look like thefollowing:

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48. Column II givescertain systems undergoing aprocess. Column I suggests changesin some of theparameters related to the system. Match the statementsin Column I tothe appropriate process(es)from
ColumnII

Key. (A) �(p , q, t)[When current will passthrough loopits temperaturewillincrease]
(B) �(q)
(C) �(s)
(D) �(s)49.Column I shows four situations ofstandard Young's double slitarrangement with the screenP laced faraway from theslitsS₁andS₂. In each of thesecasesS₁P0=S₂P0,S₁P₁=S₂P₁= λ/2andS₁P₂= λ/3, whereλ is the wavelength of the light used.In the cases B, C and D, atransParent sheet of refractiveindex � andthickness t is Pasted onslitS₂. The thicknesses of thesheets are different in differentcases. The Phase difference betweenthe light waves reaching a point Pon thescreen from the two slits isdenoted by δ(P) and theintensity by I(P). Matcheach situation given in Column I with thestatement(s) in Column IIvalid
for thatsituation.

SECTION�IV
IntegerAnswerType

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Thissection contains 8 questions. Theanswer to each of the question is asingle digit integer, ranging from 0 to9. The appropriatebubbles below the respective questionnumbers in the ORS have to be darkened.For example, if the correct answers toquestion numbers X,Y, Z and W (say) are 6, 0, 9 and 2,respectively, then the correct darkeningof bubbles will looklike thefollowing:

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*50. A metal rod AB of length10x has its one end A in ice at 0�C andthe other end B inwater at 100�C. If apoint P on the rod is maintainedat 400�C, then itis found that equal amounts of waterand ice evaporateand meltper unit time. The latent heat of evaporation of water is540 cal/g and latentheat of melting of ice is80
cal/g. If the point P is at adistance of λx from theice end A, find the value ofλ.[Neglect any heatloss tothesurrounding.]
Key.9.
Sol.(∆Q/∆t)l= 300/10x-λx/KA = mLv....................→(1)

(∆Q/∆t)w =400/λx/KA = mlf......................→(2)

dividing we getλ =9

*51. A cylindrical vesselof height 500 mm has anorifice (small hole) at its bottom.The orifice isinitially closedand water is filled in it up toheight H. Now the top iscompletely sealed with a cap andthe orifice atthe bottomis opened. Some water comes out from the orifice andthe water level in thevessel becomesteady
with height of water columnbeing 200 mm. Find the fall inheight (in mm) of water level due to openingoftheorifice.
[Take atmospheric pressure =1.0 � 105 N/m2, density of water= 1000 kg/m3 and g = 10 m/s2. Neglectany
effect of surfacetension.]
Key. 6mm.
Sol.

*52. Two soap bubblesA and B are kept in a closedchamber where the air ismaintained at pressure 8 N/m2.The radii of bubbles A and Bare 2 cm and 4 cm, respectively. Surface tensionof the soap�water used to makebubbles is 0.04 N/m. Find the ratio nB/nA,where nA and nB are the number ofmoles of air in bubbles A and B, respectively.[Neglect the effect ofgravity.]
Key.6.

*53. Three objects A, B and Care kept in a straight line ona frictionless horizontalsurface. These havemasses m, 2m and m,respectively. The object A movestowards B with aspeed 9 m/s and makesan elastic collision with it. Thereafter,Bmakes completely inelasticcollision with C. All motions occuron the samestraight line. Find the finalspeed (in m/s) of the objectC.
Key.4m/s.

Sol:collision between A andB

m*9+2m*0= mv1+mv2

9 = V1 +2V2
e =1
So
Solving (1) and(2)
V2 = 6m/s
For collision between B andD
2m*6 = (2m+m)ν
=>^V=4m/s

54. A steady current I goesthrough a wire loop PQR havingshape of a right angle triangle with PQ = 3x,PR=
4x and QR = 5x. If themagnitude of the magnetic field at Pdue to this loopisk(�0I/48Πx) find the valueofk?

Key. K =7.
Sol. d = 4x cos37

=4x*3/5

NowBp = k(�0I/48Πx)[sin37+sin53]

By solving we getk=7

*55. A light inextensiblestring that goes over a smooth fixedpulley as shown in thefigure
connects two block of masses0.36 and 0.72 kg. Taking g = 10m/s2, find the work done(in
joules) by the string on theblock of mass 0.36 kg during thefirst second after thesystem is released fromrest.

=>SoW = T.S = 4.8*5/3 =8J

56. A solid sphereofradius R has a charge Q distributed in itsvolume with a charge density a rρ = κ ,where
and a κ are constantsand r is the distance from itscentre. If the electric field atr=R/2 is 1/8times that
r = R, find the valueofa.

Key.2

*57. A 20 cm longstring, having a mass of 1.0 g, isfixed at both the ends. Thetension in the string is0.5 N. The
string is set into vibrationsusing an external vibrator offrequency 100 Hz. Find the separation (incm)
between the successive nodes onthestring.
Key. 5cm.

Sol:l=20cm, m = 1 gm, T = 0.5N,f-=100hz

�=0.5*10^-2

v =√0.5/ 0.5*10^-2=10m/s ,λ=0.1

λ/2=0.05m=5cm