CJC Pr€lims 2009- Paper 1 Solulions

I Penelope measures ihe mass and speed ol a glider The perceniage unc€rtanty in hermeaslrement ol lhe mass s 3% a.d n the measur€menl oJ lhe sp€ed is l0o/o Her calculaledv€lue ofthe krnellc ene€y of the g der wr have an unceda nlyof

B 130/0 c 23e/a D 30%

-.- --.'. t 1"" -0ul ',u.10, 0/r rhJs 061 e1 5s€ Ln-edd r J - 2 r.KFMr2 The sze otan aIom soitheorderotmagniludeol

The nlc/eris of the alofi has a d amete. of abo!1 10 '" m, whgreas lh€ atomlc diam€ter is about 1010 m

3 Abal wesprojecledfromthegroundwilhaveloclyval.nangeOlolhehoizoila.lltracesaFaraboic paih as shown below, reachnga marmum helghtHaftera lioe Iand the.f.lsb:ckdownto llreground. Ar rcsstance may be assumed lo be negigibre wh ch graph bestshowslheva allon olkinelice.ergy aof the balrwrh lme t

Nole lhat ai m€x mum he qhl,lhe bal sllllhas a sp€od ofr si, A. Hef6 trE s nol equalslo z€ro al I = tOptionsA 6nd C ar6 out

\EdEloFor'-onra lelocr/ @Gla l ) "or'zola l.e r',

KE d!€ to lgd&aL ve ocity - % m (u + ar': t qlad€l . cuRe ---- (2)

Sumnino up {1)and {2) olr answeris D.

Aslation:ry1a00k9lruckshitlrcmb€hindbya900kgcarThelwobecomeentangedandmoveofi at the same spe€d logether. lf the sma ercarwas mov ng al a sp6ed of 20 m sr inila y what sthe lnalspeed of lhe two veh c es after lhe co son?

(goox2o) - (1800+9oo)(r)

5 T@salelles collde in spa.e inelasticaly Whalsrslem of the lwo satellites?

Kinetic eneqy

happens to the krherlc er6qy and naneftun d lne

Momentum

B

A slone was thrown venca ly lpwardsrepres€nts th€ varation ol the stone s

and subsequenl yla s nto a pond. Which qraph bestac€leralion awth tme l? Assume an resislance to be

aelore impa.t w th waler, dowrward aceleralio. a = g = conslantAt point ol mpsct wfth waier, ,pwad acceleration is maxlmlm.As stone slows doM, dbg lorce decreases, hence hagnitude of ac€leralion decrea6es.When drag lorce + uplhrusl = welghl. a = 0 {i.e. termlnal velociiv €ach€d).Nere, vecto6 doMwatd iaken as posili!€.

7 The graph below shows the Jorc€ acling on: bodyol2 kg ov€r a perod of4 s

lf the bodywas n lia y moving at 1 m sr whatwould be Is velocitv llter 4 s?

A lrlmsr B llms' C 2omsi

tola cnanaern no-e-lui - ! ea Jroe q dph -,. (rJ(toj - 20 t9 r s'D,=D + di= r2)ll) + 20 = 22 rq m sl

a A parlicl€ of mass m sldes down an incined p ane wth an average ac@Leraton 6 The ncined p ane

makes an ang6 a wlh the honzonta The av€rage fiicliona force exeded by lhe pLan€ on the mass is

7a. a .tat 4 .-a..t\a.\ q" r'o("ioa".ooiI <-o' *.ro--qqdp. .Fo1 'e adolo eYoro oole P^ a(Y',\l

I ---'

tf-I'a:

L-P = Fv: F(! + a0- FIO + a0= Fars'nce F and aaraconslants Pv!.esln€arvw(hl

lo An eleciic motor s r€quned Io hauLa cage ot mass 4oo kg up a m ne shait through a lenica helghl of- lnno - .:.r,r* vin"r

"ilbe irs eleArcalpower required I ls overa Lefic€ncv is 87%?

c 213kW D 251kW

P@erolloul=mqh/t={4OOx9.61 x1OO0)/(3:601'21300W=21 3klvPeeroulourPorer npul=047Powerrnoul = Pow€rodoui/0 37 = 21 0 / 0 37 = 25 1 (W

D'"aen n c Lob'r o r glla eo oole end or a aq \r 'oa'.lolq.aq'j.lo:^dsToo'hoo.io'd1o.J.dre9ntWLrdagi.r"."-...-heLbbd rc$ w 1" Looe' bu a s se ' 'o d r o''o r,nro - r-- a. o on *r.n ai,qL : peeo u r. e I e'-s- or r' r"r I oe,6nd r\e -pb''

"p." "s ;r li" sl"* l,u. " r ind thl; porlion ot ihe stins makes an ans e e with the vencd as

Wh ch oi the following slalemen(s) is/are corect?

(1) lf L is kepl constanl e w ldecrease as o sincre.sed(2) lf€ iskepl cofstanl Lwil ncreaseaso s incr*sed(3) When W is ncr$sed swilincrease

B (2)onry

D (2)aid (3)o.y

I6os s. Fs (i)

llorzonlalyCentpeial for.€ = T s n€ = m(L s nB)d'

From (ii):When6is ncreased and L is kept constanl ) TincreasedFom (i): T increased > cos 0mustdecrease sincemslnchnsod >0must ncre.se Hence{1) is frrse

F.om (i): I kept consl.nt .> Tkeptconslanl, s nc€ ms unchanqedFrom (i): lf d is in.reased and e s keptcoNtant(and hen@ T ls kept constant), Lmlstdecrease Hen@

when w is lncreased, the lension in lh€ str ng inc.eas€s 8nd hence 6 sma rer of ils venl*lcomponenr isneded to ha ane lhe woiqht of ihe rubber bun! He.€ 6 will inc.ease

Whe.Tinc€a*s .ince m! lnchanged, Smust nsease. Hence{3)is t.!e

12 A m.rb e ol mass 20 q s re eas€d lrom rest from lhe rm ola sem -crcllar bow ol rad !s RDeterm n€ n newlons lhe norma reacton force exerted by lhe bowlon lhe marb e when lhe marbles at the bottom of th€ bow .

AO.2B

ByC.O.E, mqR= %mv? )mv':=

Alihe boticm oflfe bowl,N m9=mf/R=2msRlR=2mgN = 3m9 = 0.6 N

o6 0a

13 Two sla6 of equrlfrass M move wlh constanl speed v n a c.cllar orb l of radius R aboul the rcommon c.rre ofmsssas shown .ihedaqram beow

what sthe net force on each slar?

A au, B M,, C zerc

4n' 2R

J!s1 eFply Newlon's Law ot gravilalion lo the two slars.

D 2!!

r.1 The diegrem below shows how lhe gravlatio.rlpolen(ialvares betwe€n lhe moon and Eafth At whichposlonwl eFarticLeexperencezeronelforce?

Earth

Sln@ g = -d9/dr. At C. g€dienr = 0 > g:0 > Fe: m9:0.

This isthe point where the sravitauonal field due lo Eanh cancels oul lhe g.av lalio.alli€ d d!6 to lhe lvloo.so that lh6 resulra.tg€vllaliona!field strength I is zero.

15 Anobjeclplacedonahorzonlalplailormsvibrallngledcayinsimp€harmoncmoiionwlhatequencyof2.0llz ThemarimumampllldeolosclatonthatwL alowlheobleclloremaln nconlaclwth the pl€tfo.fr throlgrrolt the motion s

l,

Take v€ciors upwards as Positive,

To llnd nax. atrp llude, sel N=0 at x = x"

Heice)q = g/o': = g/(2ni)'? = 9 81 /(4r)' =6.2cm

A padce of mass 4 kg doves wlhpostoi r as shown in the dLagram

smple hamonic motion and its potenlia energy u vaies with

What is the per od of osciLhl on ol the mass?C 1.00 s O 2.50 s

11-o) =% (4x@':Xo.?)'z6t- 12.5 > (ZFll)'z lZ.5 >t = Ltas

'r7 a toel.1 brock x. of mass fr. al o'c com€s ntoconlaclwth.nothermetalbockY.ofnass2n atl00'c. Heal conduclion lakes p ace w(h no loss lo lhe surcundings Tlre lina equi br un lemperallre oflhe bLocks is 20 'c. flhespeclficheatmpacliesolthetwomelasarec,andcrrespeclvev th€n

c c,=2c, o c,- It ct

Heat Loss by Y = Heat qaln byxl2mlq{100-20)=mcJ20 0)160 c\ = 20 c^ -) 8q=q

la A. deal las has an inil a volumeofl2rlO3ffsandalapressureoliOxl05Pa Wh€na0Joienergy s slppied to th€ gas. ls volume increases to I 5 r 10'm'whie ts p@ssure remains consbnt.Asa resul.the nlernal energy of the ges s

A ncreased by 110 J B lncreases by 30 J C ncreases by50 J D decreases by50 J

w = -p dv =, (1.0 x 101(1 5- 1 2)(1Ol = - 30 J

^lJ - o + w = {+30) + ( 30) = + 50 J

19 Th.ee polamd sheels P QandRarepacedalonga

PQ

slraghlln€ wilh a ampand ! detecloras

,,. ''__ __tt____-,- -'l . r. ,n':1 L

nr d.rheorc((o. olood uaoororPctOr'epdal" b deDo oro' otFro R Wralr"pp""s-: "i" .r''eod"Fdo.I aoce.rorirtalP oera odreoso^'rl o 9"0,rnrr r\.lre. on.l ooa zLon s oaral€lto rhaiofFT

A /rehains unchanged.B 1 ncrcases throughoutC / ncreas€slnd the. decreasesD /decreases andlhen increases

S nce ihe pohnzing axis olO and R emal.s pelpend.datlo each oherlhroughoul, intensilv Itemainsconstanl at zero ihrcughout.

20 Two waves P and Q are mov fg towards the rghtas showi in the ligure be ow

Which of lhe fol ow n! corecty describes the

PlagsO by radians.

P eadsO by radians.

c P Edso bv l'- rad ans

P eadsO bv : rad ans

phas€ difie€nce between lhe twowaves?

L .ad. Equlval€nlly, P bads Q by;

21 a beam olwh le ighl was prolected onto a d ffraclon grat.g wlh 500 nes per 16ord€rs oi th€ entire vs b e specltuh (.100 nm 700nm)canitproduce?

5

(O OO1/500)sln0= m{700 i 1Oi)Noler Use l = 7oo nm nol40o nh si.ethe longerwavelength llght wllbedlll€cled more. Hence on ihescreen we wllobserye mo.€ ordo6 olbrighltnngos @rresponding lo the shonerwavelenglh lghl.llencelhe nlmber ofCOMPLETE speclrlms we wllobsefr€ is imited by the longer wavelenglh lglrl.

Io lnd the nax. order. sine = 1

9 n= 2.9 a ffax order = 2' .0 19 .-s zeror ' o der oLdlrL- oe dooeso'e1r'e\sbespe.r!-,ee "- - .

Asludenl prepares a dolbe-sitsel-up as shown below Howeve., no inle.f€renc€ fr.ge.a. be

Is

a\r

\r;I d:001N

t1f{----.-- r:10

A suitabL€ mprolementmaybe

A us ng a mercury lamp to prcvide rad aton of a shorler w:ve ength.B reducng xc educng d.D ndeasing a

Fo. obsefrabie diff€ction, l >> d and I >> a

23 The d agram be ow shows electic f e d ines qith po nts PQR on one ol ihe f e d nee. The distancePO=OR fthepotenlia alP s0Va.dlhepolenta alQ s 200V,whal s a poss b e va !e ol the

B -400v c -350 v

Fled inesare n:nowlng m€a.inq ncreasingfield sLonglh.Sne E = dv/dx. poleniialqradienllsste€perbetweenQand Riha. b€M€en Pand OHen@ the polentia d@p from Q to R is grealer than that lrom P to O. Only posslb e answer is 450 V

24 Oererdine the e ectc field slrength al rhe m d-point berween th€ rwo chaaes be ow.

+2.0 !C -2.0 pC

1.0 rn

_ I 2 tao l'-;;['s; ro-a ru5i -4'(8.8s rd]

pA to a cock fo.300 days

(0.5)

25 A batlery, dlring ts usabe lfetime. suppies a conslanl curent ol 10How much chaBe doee the battery suppiy during lrr s l,me?

a 12000 pC D 2400 c

O= tt = 40 x lodAxsoor 24x60 x60=2764.8 C :2800 C

26 A gen€rator prcdlces 100 kw ol power at a p d of 10kV Theof tora ressrance 5J). What is the power oss in the cables?

cu €nroasseshro,ohm6.r-Ll s -PA/- loo"w roN/- IoAP.wer ;* m lhe d:bies s=l'R= l0x lor5=5OoW

power lransm rted through cabl€s

The matera of: wre has res stivity I 3 r r03 om. The wne has d am6l€r 0 50 mm and its lenglh is

lusr enough to enable tto be wound tqhuy rolnd an ins! ati.q rod 30 umes The rcd has d amel€r 1.5

u,lE mu.d.ound iod 30 timod

Whal s the resistanceofllrewre?A l.lx1orO B 9.1 tlono

The enslhorthe d€ s(2trDl2IN)- N

Thc.hsc-se.l ona :rca is tu'/l4Re5 sfance = riua = p(nDN)/ indl4l= 4pON/d'

= 4 t(r 3' r0! Qm)(r.tro0 m)r30)l / (0.5/io0ox0 t10001l

23 Th€esimlar ight bu bs are connecled to a consla.t_voLtage d c supplvasshown nlhedaEamEach bu b.peEtesel norma brightness and lrreamm€ler(of neglq b € r€slstance)reqislersa

Thellame ofoneoflhebubsbreaks what happens to the ammeter reading and lo the

brOhlness ol lhe rema n.g buLbs?

ffi.1

When one nlament br*ks, tolalcjrcuit r€sjst:nce incrcases{.om R/310 FV2. Hen@ ammoler readifg

sin@ bulbs are connect€d in parallol, rclage a@ss e€ch emalns lhe same when there s on€ l€ss bulb.

Powerdissipll€d by each b!lb, siven by P = VtR , @mains lnchanged

o q-r" -a ldnee le 19a Foo-o r'loir .da P llaldci.en lhal.n€ oa.e or Inr rFra o l " 1 "q' ' . I e d !.d th"r rl e 1 F'd

trame moves ar a constant speed whch graph b€ow besl shows th€ varaton with time lofthe.urenr / ind!.€d nlheliafre

I

@o@o@oo60€r00ooo300ooo€oo

l-==-i

L,,- --...t-I

whe.lhe.olisfullyinlhe magneli.tield, the.e snochangeinl!vanditlhereisnolnducedomtcurentwnenreml ""nGars €'ri19rersg.e elo lle aleol(re.g.o r'lrage s6 "dtr ielce

ft a oer _ sroDoo\'e d'efton

.o Afon_o b [d9l^r.o Fro ,ll, !u91" "rcr'ol '0r 10 0( -h€'o.orlalm, po el o!l€'d Yag ' 'to e'ol atfsrorior' -0 r0 -^'"

ar.on 30 0 - W1d r -ea e4e' f i-d 'dd!rcssthe ends ot th€ w re?

A zeo B 0024mV

t.dued EiilF = Btv = (2.0 x 1or){2)(3/ 0.20) - 0.60 frv

The diagram shows three ongskaghtwr€sP OandRnormaltolhepaneotlhepaper WresP and R *rry cu(ents drccted nto the pan€ oJ rhe paper and wre O cafies a curenld rec.ted oul oflhe paper. Al threecurenls h6vethe sane magnlude.

^o

t9tn

Wh ch affow best shows the d recl on of the resultanl force on wlre P ?

oireclion oI resuliant lield due ro cur€nt R and a d P is in dlrecton of D. LJsing Fteming,s !€fr H6nd R! e.lhe 10rce is in d e.ton B.

32 A charge moves ln a cncular orbl n a un lom magnel c t e dWh ch one ol the fo lowing statements s corect?

A Theiorce on the cha.ge is paralello lhe fieLdB Theperod n the orbll s nd€p€ndenlof thespeed of lhechargeC The fromenlud olth€ charge is ndep€ndenl ollh€.irc e radiusD The€dusofthecrcle s direclly poporlionate to the charge

Manipulatino Bqv= nf / r slves Bqr= mv ) henc c is:i{jlfq.Man pulallng Bqr= sv = mro = m(2nlT)gives l = 2d lBq > hence B s @rect

33 A sleady cuirent r d ss pates a c€rla n power navarabler€sstor The resista.ce has io be hatv€d rooblain the same pow€rwhen a sinuso dalalternatinq curcnt s used

What ls the r.m.s. va ue of the a ter.at ng curenl?

B .I/2 1cr

D 1)r

13

34 The power dissipaled in a I ght bu b cofnecled ac.oss an a c sourceolpeakvoltagelS0V s50W. flwosuch ightbulbsareconnecr€dins€restotheerectrica fransof230Vr.m.s..whatwoudb€lhelotal power d ss paled n bolh lhe amps?

a 316 Wo 61.6 W

Since % = 130 V, V* = 130/J2.R = V*,/ P = (130/!2f / 50 = 324 OPowe. dissipalBd in on€ lishtbllb is - V:/R ; (230 / 2): / 324 = 40.3 WPser dissipated in two ight butbs is = 40.3 x 2 - a1 6w.

A specl@meter s set up lo obserye ihe speclrumFigu€36.1 Theene.gy evels olthe lowesl slales

lhe sodium amp as shown

I

I

Howmany spe.lra inesofunqle wavelengths corespo.d ng ro thes€ energy evescan b€

a 4 B I C t0 2A

Ans: C because j'C= 1o

36 Theqraph b€owshowsa lvpca X ravspeclrum produced when electronsare accee€ledihrolgh a potenlal dfie.enceand a.eth€nslopped na freta tergel

l4

wh ch leaturc of lhe graph enab es th s pole.tald fferen€ to be delerm ned?

A Thewav€lenglh oflhe peaks on lhe g€phB The maxhufi wav€Lenglh ollhe X €ys prodlc€dC The maxmum nlensity ofthe X{ays producedD - €r ,n

'T^a.eerq o .,.crso'od .d

Xralswith th€ shodest Mvelenqth haveihe hiolrestenergy Bycoisedation of energv lhisene€y@ossfro;$6 situalio. when th6 e €itron has a siaqe h€ad-on colso. wilh rhe iarset atons losiiis al its

energy, wlth ths re can determine th€ energy that I gslns thbugh the potenlia d fferen@ and hence the

37 Why slaser ighlcoherent?

The excledel€ctrons are n a melastable slaleThesystem s n a state ot popu ation inversion.stm! ated emisson celses the emitled photon and lhe ncdeft pholon to be of lhe same

D Photons olthe same energy as thal ofthe ncid€nt photons are emitled when the e ectronslransit dow. iiom a h ghere.ergy elel

The incidenland the emllled photon are ln phase and ol lhe eheirequencv H€nce c is the answer'

38 Whch slatement about somlcondlctors s corecl?

A Th€nresislivity s.ormaly somewhat grealer lhan that of mosl melasB A rrole" n a s€mcondlctor s due lo th6 removalof a protonc Electica conducton n an n rype sem conductor is due lo lhe transfer of n€utronsD A p lypesemconduclotis produced bydopng p type implrlies caled donors

B ls wronq. A hoL6 !s duelo lhe r€movalofan elec{ron lrcm th€ valence ba.d.C a^ro19.risau6E.lela sfe o' oo" €l€.(o sl.'e.o d-aonoa d)a-dhoe- i 'e Elonc€band).bui wLihel€ckonsasihemaionly.harq€.a ie4D iswong.llls cal €d ameplors.

15

Bc

.ot. 1.do.dpod.r6sor eo..ag aro 9hr6ooldrD ioerl€ leo Ahc odo o ( L ot 1ort5'c ' 'l

Bc

Mosl0f lhe mass ofthealom swithlnth€ atomThe d ameterollhe nucl€us s duch ess than the diameler ol the atom

The nuceus has a pos lv€ chargelhe alom s overa neut€

40 A Rad oactive nuceus x decays by re eas nq a P_padcle -rh€

B li/,

D,li,ls

daughternlceus s rrlaii.whal sx?