Physics 2007

NANYANG CONCEPT TEST PHYSTCS(ADVAI{CED LEVEL) 14 JULY 2OO7

9.30- 11.30am

Instructionsto participants: 1.

The test comprises60 multiple choice questionson 24 printed pages (including the front and back pages).It has the following sectionsand numberof questions: - 23questions; Mechanics Thermodynamics andMatter- 4 questions; - 11questions; WavesandOscillations - 19questions; ElectricityandMagnetism ModernPhysics3 questions.

2,

All questionscarryequalmarks.

3.

use black lead 28 pencils to shade in the answer sheet provided. Ensurethat the circles are filled in completely. Any erasuremust be done cleanly,and make no stray mark on the answersheet.

4.

U s e g : 9 . 8m s - 2 ; speedof light in vacuumc : 3 x 108m s-r; Planck'sconstant h:6.63 x 10-34 J s; chargeof an electrone: L 6 x 10-leC.

NCTPOT

Mechanics L

Whichof the followins is NOT a baseunit in the SI convention? (i) kilometre (ii) kilogram (iii) coulomb A. B. C. D. E.

2.

(i) only (ii) only (iii) only (i) and(ii) only (i) and(iii) only

Considerthe formula below for the total energyE of a particleof massm as a sum of its kinetic energy and its potential energy @, where v denotesthe particle'svelocity. E=|mv" +e errors in the velocity and potential energy If Av and A(D are the measurement errorAE in the total energy? respectively,what is the measurement A.

M=Av+A@

B.

LE*!m(Lv)'+A@ 6P - mv(Lv)+Ao AO _LE x _ + Av _ Ev@ LE ^[lv) lo

C. D. E.

3.

E *'l; )* *

positionof a pointP on Earthis givenby a coordinatepair of The geographical numbers(1,,9),where,tis the longitudeandE is the latitudeat pointP.Is Q',E)a vector? A. B. C. D. E.

it hasdirectionandmagnitude. Yes,(2,9) is a vectorbecause No, (2,9) is not a vectorbecausealthoughit has direction,its direction changesas the valueofrl or g changes. No, (,1,9)is not a vectorbecause it is actuallya pair of scalars. may may not be a vector, dependingon how it is interpreted. or Q,cp) None of the abovechoicesis correct.

NCTPOT 4.

A skydiverjumps out of a hoveringhelicopter(- 100m abovethe ground).one secondlater, another skydiverjumps out, so they both fall along the same vertical line relativeto the helicopter.Assumeair resistancecan be ignored. While both of themarein the air, doesthe verticaldistancebetweenthem A. B. C. D. E.

5.

In a basketballcourt (- 28.5m long and 15 m wide) on the Moon,an astronaut (- 1.9m) wishesto obtainthe maximumrangefor his throw into a hoopwhich is situatedat a heightof 3.0 m. At what angleshouldthe astronautreleasehis ball? A. B. C. D. E.

6.

increase decrease staythe same cannotbe determinedunlessthe massesof the two skydiversareknown cannotbe determinedunlessthe preciseheight of the helicopteris known.

45 degrees greaterthan45 degrees lessthan45 degrees cannotbe determinedunlessthe massof the ball is known. cannotbe determinedunlessthe gravitationalacceleration on the Moon is known.

Kim and sally are two studentathletes.To help Kim practicefor the Special olympics, Sally runs besidehim for half the requireddistance.She runs the remainingdistanceat her regularspeedand arrives50 s aheadof Kim. What is theratioof Sally'sregularspeedto Kim's speed?lJse t *,, for Kim,s totaltime. A.

tKi./I00

B.

t*,, /(t*,, - 100)

c.

t Ki, /(t Ki^ - 50)

D.

tKi^ /50

E.

cannotbe determined unlessthe totaldistanceis known.

As a basketballplayer startsto jump for a rebound,he beginsto move upward fasterand fasteruntil he leavesthe floor. During this time that he is in contact with the floor, the forceof the floor on his shoesis: A. B. C. D. E.

greaterthanhis weight. equalin magnitudeandoppositein directionto his weight. lessthanhis weight. initially smallerthanhis weight,andthenbecomeslarger. initially largerthanhis weight,andthenbecomessmaller.

NCTPOT 8.

4 is the velocity of a particlemoving along the x axis as shown below. If x : 2 . 0 m at t: 1.0s, whatis thepositionof the particleat t: 6.0 s? t,',

{m/s21

)r1 l^0

t) 1.0 2.{l

A. B. C. D. E.

9.

+7.0m + 3 . 0m + 1 . 0m 0.0m - 1 . 0m

A small car of massm anda largetruck of massM (>m) travelingat the same speedcollidehead-onand sticktogether.Whichvehicleexperiences the larger changein momenfum? A. B. C. D. E.

the smallcar the largetruck bothexperience the samemomentumchange cannotbe determinedunlessthe initial speedsareknown. cannotbe determinedunlessthe precisemassesof the car and truck are known.

1 0 . Car A collideswith Car B on an icy road at a speedlow enoughso that the collisionis essentiallyelastic.Car B, which hastwice the massof A, is initially at rest.CarA hasmassm andspeedv beforethe collision.After the collision A. B. C. D. E.

I l.

eachcarhashalf the momentum. eachcarhashalf of the kineticenergy. carA stopsandcar B hasmomentummv. the momentumof carB is four timesasgreatin magnitudeasthatof carA. the momentumof car B is two timesas greatin magnitudeasthat of car A.

A light stringis usedto suspend a blockof mass5.0kg in an elevator.The string canonly sustainmaximumtensionof 60 N. Otherwise,it will break.Whatis the maximumupwardacceleration of the elevatorsuchthat the stringwill not break? A. B. C. D. E.

2.2mlsz 21.8mlsz 12.0m/sz 9.8mls2 The stringwill neverbreakregardless of the acceleration.

NCTPOT 12. Whichof the following statements is/areTRUE concerninglinearimpulse? (i) The linearimpulseof an objectis alwayspositive (ii) The linearimpulseis a scalarquantity (iii) Impulseandmomentumhavethe sameunit (iv) Impulseand kinetic energyhavethe sameunit A.

(i) only

B . (ii) only C. (iii) only D. (iv) only E. (i) and (iv) 13.

rf u:40", F:60",andm:5.0

A. B. c. D. E.

14.

kg, determinethe tensionin stringI at equilibrium.

24.50N 2 4 . 8 8N 3 1 . 9 8N 3 8 . 1 2N 76.23N

A block with a massr, : 5.0 kg is pushedup a frictionless30o inclineby an externalforce.The forceis parallelto the baseof the incline.If F:30 N, what is the magnitudeof the resultingacceleration of the block?

A. B. C. D. E.

0.3m/s2 3.3m/s2 5.2m/s2 6.0m/s2 10.1m/s2

NCTPOT

1 5 . A basketballwith a massof 600 g is thrown at 54.0km/hour during a game. What is the kinetic energyof the ball? A. B. c. D. E.

4.5I 874.81 16.2J 6 7 . 5I 0.067sJ

1 6 . In the figure below, a springof springconstantk : 50 N/m is being usedto launcha ball with a massrn :200 g suchthat the ball will hit the floor at the "A" zone.At equilibrium,the distancebetweenthe edgeof table and the ball is dt : 0.5 m. The height of the table is h : 1.0 m and dz : 2.25 m. For a from its frictionlesstabletop,find how far the springneedsto be compressed equilibriumpositionin orderto achievea hit.

dr

A. B. C. D. E.

dz

0.05m 0 . 1 4m 0.32m 0 . 3 9m 9.96m

circle at uniform speedv. The 17. A pilot flies a planeand makesa loop-the-loop pilot experiencesan apparentweight at the bottom that is tlvice his apparent weight at the top of the circularpath.What is the radiusof the path? A. B. C. D. E.

u2l3g ,'l2g v2lg 2v2lg 3v2lg

NCTPOT 18. A planetof radiusR containsa uniform distributionof mass.Which of the curves/lineson the graph below showscorrectly the qualitativedependenceof the magnitudeof the gravitationalfield strengthg insidethe planetis a function ofthe distancer from its center?

A. B. C. D. E.

A B C D E

19. Considerthe physicalpossibilityof a shot fired aroundthe world. A bullet is propelledhorizontallyaroundan assumedsphericalEarth of radius Rs. What is theperiodif the bulletattainsa stableorbit of radiusr? A.

x 24 hours

R. E

B.

r

;-

t(-

x 24 hours

f---;-

C.

lr'

.j

. x24hours

VR;

D. E.

jr2 24hours , R: " 24 hours

20. Dueto Earth'srotation,a plumb bob doesnot hangexactlyalonga line directed to the centerof the Earth. How much doesthe plumb bob deviatefrom a radial line at 33.5' north latitudeas shownin the figurebelow wherecr is the angleof deviationand co is the angularvelocity of Earth's rotation?Assumethat the Earthis perfectlysphericalandof radius6.40x 106m.

A. 0.0932" B. 0 .1 6 5 0 " c . 0 .1 0 9 5 " D . 0 .6 6 1 9 . E. 1.5110"

North

NCTPOT 21. Considera point objectO of massm.Point P is locatedat distancerfrom O. Which of the following are the correctexpressions for the gravitationalfield strengthg and the gravitationalpotential rp at P? (k denotesthe unit vector pointingfrom O to P; G denotesthe universalgravitationalconstant.) A. B. C. D. E'

g---(GmF)k f:-(Gm/r)k g: (Gm/r")k R: - Gm/r g: - Gmht

t t i t ;

- Gm/r" A: A:-Gm/l rp: Gm/r - (Gm/tt)k a: A:-$m/r)k

(about15 km altitude)is 10 timesless 22. The pressureat the top of the atmosphere thanthe pressureat the Earth's surface.What is the reason? A.

B. C.

D.

E.

zJ.

is 10timesat 15 km altitude Air pressurebalancesgravity.The pressure gravitational field strengthis 10times thanat Earth'ssurfacebecause weakerat l5 km altitudethanat Earth'ssurface. Earth'sdownward The differencein air pressureis neededto counteract gravitationalpull on the atmosphere. Althoughgravitationalfield strengthis aboutthe sameat 15 km altitude andat Earth's surface,the centrifugalforce dueto Earth's rotationis l0 times strongerat 15 km altitudethanat Earth's surface.This causesair to be "spun out" into space,leadingto low air pressureat the top ofthe atmosphere. The differencehasnothingto do with gravity.Vacuumin spaceis the theair is mainreasonwhy air pressureis low at thetop of the atmosphere: "suckedout" into space. More than oneof the abovereasonsarecorrect.

A car starts from rest at sea level and travels very slowly up to the peak of Mount Kinabalu (altitude 4096m), beforereturningto rest at its startingpoint. Sincethe initial and final total energy(i.e. kinetic + gravitationalpotential energy)of the car are both zero,the driver expectsno energ"yexpenditure.But to his surprise,half the fuel in the tank was consumedin the round trip. Explain why. A. B. C. D. E.

The fuel is mostly consumedto overcomeair drag and ground friction encounteredduring the wholejourney. The fuel is mostly consumedto overcomegravity during part of the journey. The fuel is consumedmostly to overcomeinertia.Gravity, air drag and groundfriction do not affectfuel consumptionsignificantly. Theremustbe a leakin the fuel tank. the final gravitationalpotentialenergyis The questionis not right because actuallymore than the initial gravitationalpotentialenergybecausethe car hastravelledvery high up beforecomingbackto its originalposition.

NCTPOT

Thermodynamics and Matter 24. A balloonis filled with 1 mole of hydrogen.The pressureinsidethe balloonis l.0l atm(1 atm: 1.013x 105pa).which of thestatements is true? A. B'

C. D. E.

The densityof hydrogeninsidetheballoonis 4.2x l0-5e/cm3. -atm The pressureinsidethe balloonwilr be higherthan l.0l if we replace hydrogenwith oxygen. The volumeof the balloonis approximately 2.3 x lOacm3 at25 oC. The volumeof the balloonis approximately 9.2 x l O ac m 3a t 1 0 0 ' C . Noneof the above.

25. On a high mountain,comparedwith the sealevel,which of the followinswill be observed? A. B. C, D. E.

The boiling point of wateris higherthan 100.C. Latentheatduringmeltingis lower. Ice meltsat a temperature lowerthan0 oC. Air moleculesmovefaster. None of the above.

26. Gasinsidea thermallyconductingcylinderis compressed quickly. (Thecylinder is placedin a largebathat constanttemperature.) Which oithe followinsis true? A. B. c. D. E.

27'

The gaswarrnsup immediately. The gas cools since accordingto the ideal gas law the temperatureis proportionalto the volume. The gastemperature remainsthe sameduringthe whole process. The gaspressuredecreases immediately. The intemalenergyof the gaswill increaseafterthe thermalequilibriumis reached.

A quantity of a monatomicideal gas expandsto twice the volume while maintainingthe samepressure.If the internalene.gyof the gas were {/e before theexpansion, what is its valueaftertheexpansioniA. B.

Uo/2 Uo

c. 2uo D. E.

4Uo The temperature changeis alsoneededfor this question.

NCTPOT

Waves and Oscillations 28. A 100 g massattachedto a springmoveson a horizontalfrictionlesstable in simpleharmonicmotion with amplitude16 cm and period2 s. Assumingthat as the massis releasedfrom restat t : 0 s andx : -16 cm, find the displacement a functionof time. A. B. C. D. E.

x: x: x: x: x:

16cos(n/) 16cos(nr* n) -16 cos(ntlZ) -16cos(nr + n) -16 cos(2nt + n)

29. A simpleharmonicoscillatorconsistsof a particleof massm andan idealspring with spring constant ft. The spring-masssystem oscillates with period Z. Suppose,the spring is cut in half and the sameparticle is attachedto it. What is the new periodof this simpleharmonicoscillator? A.

2T

B. ^lzr C.T D. Tl^12 E. TI2

3 0 . The massin the figurebelow slideson a frictionlesssurface.It is connectedby spring 1 and spring 2 with spring constantsftr and ft2respectively.Supposethe massis displaceda small distancex in the positivex-direction(denotedby the affow pointingto the right of the page),the forceexertedon the massis:

A.

-kfi

E.

- k'+k' *

B. -k7 c. -(kr-kr)x D. - (\+ k2)x

Positivex-direction

KtKz

l0

NCTPOT 31. An optical microscopecan resolveobjectsas small as half the wavelensthof light.If the frequency of a lightbeamenteringthe microscope is 6*lOta LLand the speedof light is 3xl0Em/s,whatis the smallestobjectihatthemicroscope canresolve? A. B. C. D. E.

)2.

A bat,flying at 15.00m/s towardsawall, emitsa chirp at 40.0kHz.If this sound pulse is reflectedby the wall, what is the frequencyof the echo receivedby the bat?Speedof soundin air is 340 mls. A, B. C. D. E.

aa

250 nm 500 nm 1000nm 3 x 1014*{z 1.2x l}ts l1z

36.6klrz 4 1 . 8k H z 43.5kllz 43.7krlz 43.9l
A singletravelinglight wavein vacuumcan A. B. C. D. E.

createinterferencepatterns createa standingwave carrymomentum propagateat anyvelocity noneofthe above

34. Superposition of wavescanoccurfor A. B. C. D. E.

J).

only transverse waves only longitudinalwaves only sinusoidalwaves all ofthe above only for (A) and(B) above

A guitar string of lengthz is fixed at its ends.If you pluck the string, a wave traveling at a velocity v will be generatedon the string. what is the smallest frequencyof this wave? A. B. C. D. E.

2v/L v/L v/2L v/4L v/8L

ll

NCTPOT 36. Two loudspeakersplacednext to eachother producepure tones of frequencies 500 and 520 Hz, respectively.At the positionof your ear the two coherent wavesinterferesuchthat you will heara beatfrequencyof A. B. C. D. E.

Jt.

l0 llz ?.0tlz 40Hz 5 1 0H z 1020Hz

Two mirrors are placedat 80oto one another.If an object is placednearthe mirrors,what is the maximumnumberof imagesthatcanbe seen? A.2 B.3 c.4 D.5 E. >5

3 8 . In a two-slit interferenceexperiment,one slit transmitstwice the amptitudeof the other slit. If the maximum intensity of the interferencepattern is 1e,the minimum intensityin the patternwould be A.0 B. C. D. E.

Io/9 Io/4 Io/3 In/z

t2

NCTPOT Electricify and Magnetism 39. consider two systemsof point charges.In the first system,there is a point chargeq at eachcornerof a cubeof sidea. In the secondsystem,thereis a point charge2q at eachcomer of a cube of side 2a. Potentialenergyfor the second systemis: A. B. C. D. E.

sixty-four times of that for the first system eight times of that for the first system four times of that for the first system two times of that for the first system noneofthe above

40. A proton is accelerated from rest by a potentialdifferenceof 10 kV befween point A and point B. An electron,about 2,000 times lighter than a proton, accelerated from restbetweenpointsB andA will acquirea speed,which is: A. B. C. D. E.

about4,000,000timeshigherthanthatof the proton about2,000timeshigherthanthatof the proton about45 times higherthanthat of the proton the sameasthat of the proton about45 times lower thanthat of the proton

4 t . Two concentricconductingsphericalshellsof radii2r andr. Thereis a chargee on the largeshell.what is the chargeon the smallshellif it is grounded?

A. B.

+Q Zero

c. - Qt2 D. -O E. _2Q 42. The following showsthe circuitconnectionof a lead-acidbatteryto a light bulb. As the batterygetsolder,it is observedthat the light bulb dims.This is so even whenthe circuit is replacedwith a new light bulb.This is bestexplainedby: (D a largereductionin the electromotiveforce of the battery (ii) a largeincreasein the intemalresistanceof the bafiery (iii) a largeincreasein theresistance of the light bulb (iv) a reductionin thepotentialdifferenceacrossthe light bulb A. B. C. D. E.

(ii) and(iii) (i) and(iv) (ii) and(iv) (iii) and(iv) (D, (ii) and(iv)

,I 4

l3

NCTPOT 43. Why arebirds not electrocutedwhenthey sit on high voltagepowercablesthat hangbetweentransmission posts? A.

B. C. D. E.

It is becausethe birdsareat the samepotentialasthe cablethey are sitting on. It is becausethe birds are able to withstandthe flow of large current throughtheir bodies. It is becausebirds have very low electricalresistancecomparedto the powercable. It is because birdshaveextremelyhigh electricalresistance. It is becausethe voltagefrom the power cable is not high enoughto electrocutethe birds.

44. A batterywith an emf of 3V andinternalresistance of 0.2Odelivereda powerof 7.2W to an externalresistancewith diameter1.02mmand lensth 38m. The resistivityof the extemalresistance is Qm. A. B. C. D. E.

l.72xl0'8 2.26x l0'8 2.69x l0-8 0.8 1.05

4 5 . To createa four-resisternetwork of any configurationwith a total resistance smallerthan 10 C),which shouldwe choosefrom the following combinations? A. B. c. D. E.

30 Cr,30 Q, 60 Q, 60 Q. 20 9r,40Q, 60 Q, 80 Q. 18Cr,48 Q, 78 C),108O. 35 c), 35 Q, 55 Q, 55 Q. None of the above.

46. Let libe the currentflowingthroughresistor{ in the followingcircuit,then

A. B. C. D. E.

lincreasesif Rr increases. if Rr increases. { increases by 10 O. by 10O andRzdecreases if Rr increases l increases remains constant if Rr decreases. 12 l equalsthe sumof 13 12,and.Is.

t4

NCTPOT 47. An ion beam from a gas dischargepassesthrough the electric field of a (C) anda magneticfield (M) which is orientedparallelto the electric condenser field. In the planeof observation,particlesof the samechargeand mass,but havinedifferentvelocitiesv. aredistributed

A. B. C. D. E.

,n

alonga parabola along a straightline on a dot alonga circle alonga semicircle

48. Whatis the totalpowerdissipated by the circuit?

16V A.

B. C. D. E.

2 5 .0W 3 7 .5W 3 7 .8W 80.2W

t8v

1 0 sw

49. An elementarypanicle of massm and charge+e is projectedat velocity v towards an initially stationaryparticle of mass m of charge +e. What is the closestpossibleapproachdistance& of the incidentparticle? (Electrostatic PotentialEnergy:, = #, Force:F =: Electrostatic

o2

4teof'

., wherer is the distanceande6is a constant)

.e2 A. _--_____-____-= 4tteomv' o2

B."= 2treomv" o2 (\ \,. _-___-__-______= EEomv1a2

D.

""

ftEomv-

E. noneofthe above.

l5

NCTPOT 5 0 . A protonis releasedfrom restin a regionwith a constantelectricfield anda constantmagneticfield. If thetwo fieldsareparallelto eachother,the pathof the particleis bestdescribedby A. B. C. D. E.

a circle a parabola a helix chaoticbehavior a straightline

5 1 . A planeconductingcircularwire loop liesperpendicular to a uniformmagnetic field B, and its areaS(t) is changedasS(r): ,So(1 - crl) for 0 < r < l/cr (Ssand cr areconstants). The wire hasresistance per unit lengthp Q/m. Find the currentin thewire. Magneticflux is givenby O : B S(t),and inducedemf is E: - LQ/LI. n l-

A.

6

1112

tft\=g!l 'oo ,l 2pl"(-at))

B . t ( t \= s o o B 2p

c.

I(t): 0

D.

(r)-constant>0

E.

Noneofthe above.

52. What is the magnitudeof the torqueM actingon the currentloop (seepicture)in a magneticfield B?

A.

B. C. D. E.

M:0 M: YzrlIB M: rlIB M:2rlIB M:2nrllB

-> --> --+

5 3 . A device with a very high internal resistance may be suitablefor useasalan A. B. C. D. E.

ammeter and current source. ammeter and voltmeter. current source and voltmeter. current source and capacitor. voltmeter and capacitor.

t6

NCTPOT 54.

Considerthe simplecircuitas shownin the figure

If the input signalis a sinewave,

Vee

theoutputsignalwill be

A.

VCO

B.

C.

Vco

D.

E.

55. An electricmotordrawsa currentof 2.50A from a 15V batterywhenit runsat normalspeed.If themotor'sarmature(coil) is 'Jammed"so that it cannotrotate the currentsuddenlyrisesto 10.0A. What is the backemf of the motor when it is runningnormally? A. B. c. D. E.

1 0 . 0v 1 1 . 3V 12.5V 1 5 . 0v 1 8 . 8V

t7

NCTPOT 56. Considerthe simpleRC circuitas shownin the figure.

Which figure below showsthe right ratio of outputvoltageto input voltageasa functionof the angularfrequencyof the AC source?

A.

B.

C.

D. E.

h

L L

None of the above

5 7 . Considerthe AC circuit in the figure, The frequencyof the AC source is adjustedbetweenarand a, (a, < a") while its voltageamplitudeis held constant.The light bulb will glow the brightestat

A.

aL

B'

aH

C.

A frequency between at, and ar.The value of the frequency depends on the value of Z. A frequency between a, and ao . The value of the lrequency dependson the applied voltage. The brightnesswill be the sameat all frequencies.

D.

E.

18

NCTPOT

Modern Physics 5 8 . The figure showstheexperimental resultsof doubleslit experimentusing neutrons(Zlinger 1 9 8 8 ) .

scaNNtNo sLtf PostfloN

If Coomolecules(mass- 720 neutrons)with the samekineticenergyas thatof the neutronsareusedto do the experimentin the samecondition,the fringe will spacing A. B. C. D. E.

remainthe same. increase by 720times. increase bv Jln times. decrease by 720times. decrease bv J7n times.

59. An electronwith finite energy,E in regionI movestoward a potentialenergy barrierasshownin the figure.The potentialenergybarrierheight Z is finite.

A. B. C. D. E.

If E> V, the probabilityof the electrongettingto region II is 100%. If E > tr/,the probabilityof the electrongettingto region II is 0%. If E < V, the probabilityof the electrongettingto region II is 0%. lf E < Z, the probabilityof the electrongettingto regionII is 100%. Noneof the aboveis rieht.

I9

NCTPOT 60. A deuteron(2H nucleus)consistsof a proton and a neutron.If the bindins energyof a deuteronis1.12MeV pernucleonwhat is themassof the deuteron? Giventhat

I eV :1.60xlO-reJ; 1 u : 1 . 6 6 x 1 0 -k' 'g ; tflproton: 1.007825 u; m n e u t r o n1: . 0 0 8 6 6 5 u

A. B. C. D. E.

2.015291u 2.014091u 2.016490 u 2.018889 u 2 . 0 1 0 0 8z9

- END OF TEST.

20