-

TOPIC1 PhysicaI Quantities&Units 1If`CX C

I;CD

12W :c

uI

A

B

CD

13Tl~cwhen

1t

ABCD

14Whic

ABCD

15 Vhic

AB CD

16F( rC(l11 t

I cht c

ABCD

17A tha tby th(` s

th tr

181 ^(

E l n1 stst

1Phy )r .

Unit.s' l ' l rc

c.rn. l ' . fo ol 'a batte'ry is givcn by IL, = P/l where P rs t l tcpo\r 'er dissipated rvltert a current / f ' lorv.s. The e.rn. l ' . E.rnduccd i r t l co i l hy a chaneing mugnct ic { lux is cquul to thclr i tc o1'chiutgc ol- l lux, l . = i l r l>/41Whic :h o l ' thc lb l lo rv ing is l un i t fbr nragnct ic l lu .x?

A ms - r Ai l rns-2 A-tC kg rn2 s-2 AI) kg rn.sr A-rE kg rn2 s-2 A-l

' l 'he e,rperimental nreasurement 01' the hent capacity C ol ' a

so l id as a I 'unct ion o( ' ternDeraturc 7 ' is to bc f i t ted to thecx oressi on

/l1t"C thC1lllits()f ftnd /`?

rr /,A Pa nr6n O12 n13mol

B Pa n16mo 2 n13n1c)l

C Pa nr6nlo12 I 3nlO |

I) l)a ll6111o12 n 3nlo l

E nOnc bccausc they arc diI11cnsioncss constant.

J84/II/27

6 In which nc otho|ollOwing ptirs of clec1rical units arc thc

uni ts not cqLr iva lcnt?

A Wb rn - l :B JsC JC l

D AsE CVl

An a l ternat ive fornr o f the un i t o l ' res is tance, the ohm (Q) , isV A_ I .

Which ol ' thc lbl lowing exanrplcs shorvs a sirni lar correctalternative forrn of unit ' l

ttrtit altcrnativc fonnA cO111OI b(C) As

B fllmd(F) VCIC pt scal(Pa) N nr2

D volt(V) JCE wmt(W) Js

Which expression could be correct l 'or t l re velocity v ofocean waves in terms of p the density of sea-water, g theaccelerat ion of l iee fal l , /r the depth o[ ' the ocean and /" thewavclcngtlr?

D

N91/I/2;

Which of the lbl lowing cluanti t ies has a unit that can bcexpressed in term.s of just two dif ferent Sl base units?A arcil D lbrccI l charge l l resistanceC current J92l l l2

The Lrase units ol ' the SI systelx include those of

tn i tss , kg; lcngth , rn ; t i rnc , s ; e lcc t r ic cur re n t , A.

Which basc un i ts would bc r rccc lcd to cxDrcss the SI un i t o flrotential di l ' lercncc (the volt)?A nr and A on lyB .s arrd A onlyC nr , s , i lnd A on lyD kg, rn , s , and A N93/l/l;J98/I/3

A Physics Topical Pal)er

J79/II/25;N79/lI/17;J90/I/3

C= r /JT3

units o| and/J? 7

K 2

J3

KJ J79/Il/29

N82/II/29 N96/F/

?

??

WIrat are poss ib le

J87/I/2

J9I/I/l

1iCDE

J JJK2JK JJK2 J

J

AI tc rnperatures c lose to 0 K, thc spcc i l ' i c hcat capnc i ty o fa par t icu lar so l id is

-9 iven by t - r r7 ' r , wherc I is thethernrodynttmic tenrperature and c i .s zr constant characferist icof the so l id . What are the un i ts o f constant n expressed in S lbascd1Inits?

A m2s

2K l

B n12s

2K3

C m 2K

D kg

2s^2K 3

E kg n12s9K C

In tclrns ol ' thc ki lograrn (kg), mctrc (nr), second (s), andkc lv in (K) , what are t l i c base un i ts o f spcc i l ' i c l reat capac i ty?A rns-2 K-lR ms- l K- lC r-r-,2

"-2 6-lD tn2 s- l K- lE kg-t n12 6-t J$l lv2g; J93lv2

Tlrc behavioLrr ol ' many real gases cleviatcs l i r l rn p(,, = I ITbut can be rcprcscutcd c1r-r i tc closcly ovcr ccrtairr nirrges oftcnrl)cr i l tul 'e and prcssurc by an cquation ol ' t l rc lbrur

' t p + J + \ , u . _ b t = R . r\ u,; / ,,,

in which thc va l r res o l ' n anc l b l t rc c l taractcr is t ic o l ' t i rcl) i l r t icular ! las.

'hys ica l Quant i t ie .s & Uni ts

10

14

[ 1 t r ' p r s t h c " r ) r o r ] r c n t u n r

o 1 '

cx l rcss ion / ' - 1 . ,a , basc r tn i ts'

I l l

A c l ) L : l g Y .I i l i rrcc.C l)o\\'cr.D i ,e loc i ty .

12 Wtr icn cxprcss ion does not l rave t l rc s t :cor rc l (s ) ls i ts b lseun i t ' J

. lI fecluency

B cl l lacitrrnc'c x rcsist i .urce

C \ lcngtlr +- accelentt iorrD nrAss + spr ing constan l " J95 l I / l

l3 fne encfgy o f i r photon o1 ' l ight o [ l ' rec luency/ is g ivcn by l { ,wltere /r is the Pl i tnck constant.

Wlrat arc the basc units ol ' /r ' l

19 ' i ' t r c t i l r g coe l ' f i c i cu t Cs g l ' i t cn r i n l v ipg r i , i t i t : t pccd yI l t rouq l t a i r o l ' r l e r t s i t v p i s g i vcn [ r y ,

. J ;T -. r ,_ r l r . r )

r,, 'hcrc F- is tlrc cllag lirrc:c cxelted on tltc cru' ; ln(l .;1 i:; Lt'rcrr iax inrurr . r cross-sect ic l r ra l i t rca o1' the c 'c i r pcrpencl icru l l r to thcd i rec t i on o f t rave l . Show tha t Cp i s r l i r l ens ion less ( i . c . t hu r i tdoes no t have a un r t ) .

Whcn a cc l ta in ca r i s t rave l l i ng l t l r s l t eec l t l 1 ' 20 n t s - ' li t cxpcr icnccs a c l rag l 'orcc ol '350 N, What c l rag 1 'orcc u 'ouldbe expected when t l rc car is t ravel l ing at i ts top speed ol '40rn s l? J87/II/2

' i '20 The unit J s- l ctrn lrc uscct as t lre unit ol 'powcr instei icl o1'the wat t . Give a un i t {br eac l i o f the lo l lowing quant i t icsusing applopriate cornbinations of rnetre (t tr), second (.s),arxpere (A) , jo i r le (J) , and vo l t (V) on ly .

Qttt tr t t i t l , renelgypressu reclectr ical chargeelect r ica l les is tance 4]

J88/II/l

21 Bernoul l i ' s cquat ion, w l i ich appl ics to l lu ic l l ' low, s ta lcs th i t t

p + h p g + t l r p v 2 = l t

where y; is a prcssure, /r a height, p a density, g an i tccelera-t i

ce ad` llt,lc= m3

spe cr l o f ' l r w l lvc = 4 .

ddm " d =2WT

pressure of a gas = \ p"t '>

t ' , l , ) " are d is tanccs, c is a speed, g is an acce lerat ion,7 i s a t r r ne l nd p i s a dens i t y .

Cive arr SI Lrnit and an crst i lxate of the rtragnitude of 'eac l r o l ' the fb l lowi r rg phys ica l quant i t ies . (Marks wi l lbe irwar-ded lbr t l rc correct orcler of rnaqnitucle of cachcst i rnatc , r ro t { 'o r i ts accuracy. ) [7j

rnagnitut le unItt hc wc i sh t o f an adu l tthe polver ol 'a hair drierthe energy required to bring tot lre boi l a kett lel ir l of waterthe resi.starrce of a dornestict i larnent Iarnpthc r,vavelength of visible l ight

t99i lUl

' fhc ki logrzun, {-he rnetre and the sccond are base units.Nartre two other base units. t?l

Explain why the unit ol 'enel 'gy is said to be a derit ,et lt r r r i t . l2 l' f l ic dcrisi ty p tn' td t lre pressurc;; ol 'a gas are rclated bytlrc expression

r.l,here r-' and yare constants.

( i ) l . Deter rn ine the base un i ts o1 'dens i ty p .2 . Show that the base un i ts o l ' p ressure / i i r re

kg In-l 5-2'

( i i ) C i i ,c r t that the constant y h l ts no Lrn i t , dc ter rn incthe un i t o l 'c .

( i i i ) Usirtg your nnswer Lo ( i i ) , suggest rvhat quanti tynray be represerrted by the syrlbol r.'. t6l

N2000/rr/l

D i s c u s s t r r i e l ' l y r v h e t l r e r , i l r g e n e r a l , t h c n t e t h o r . l o l 'd inrens ion l l check ing c ln pos i t ive ly cor r f inn the cor rc :c tncsso l ' a t t c c l u t r t i on .

W l r cn a l i qu id (o f ' dens i t y 1 .0 x l 0 r kg r l - r and v i scos i t y1.0 x l0{ Pa s) f lo rvs past un obstac le o f w id th l -5 n t tn ,turbu lencc occurs lbr l low-specds greater than 80 rn l r s - r .What cri t ical l low speed would be expected for ar l iquid ofdcns i t y 13 .6 x l 0 r kg m- l and v i scos i t y 1 .6 x l 0a Pa sf lowi r rg p ls t i ln ob jcc t o f s i rn i la r shapc and o1 'u , id th 5 tnnr ' l

Nl l l l / l 3 (trart)

26 (b) ( i) IJolv do you check a forrnula fbl cl inrensionalcor ts is ter tcy ' / Why r locs th is mcthod o1 'c l rcck i r tgt to t g ive t lc l ' i l t i tc con l ' i r t r ta t io t l t l ta t an ec lu l l t ion isco|rcet ?

(i i ) Express the unit of furce and o1' charge in ternrso l ' the S l base un i ts k i logram, metre , secot rd andlmpere. I- lence, by re{ 'erence to Cotr lomh's law

I Q , Q zr,- =

4^u ,t

exp ress t he un i t o f e11 t l r e pe r rn i t t i v i t y o f avacuurn, in terms o1 ' thesc base t tn i ts .

A unit ol ' fk,, t l ic perrreabi l i ty of i l vacul lrn, is kg ln s-2 A-2.Use thc ur r i t , and your un i t o f , , , to dec ide which one of theIbl lowing r.elat ions between ., [4, and c, the speed of l ight inr l vacuurn, is dirnensional ly consistent:

oflo = r:2; 11f!y = c, olto = c*l; of\r = c-?.J82/ l /13 (par t )

27 Explain tlre meaning ol'the terms (a) base unit,I Iow do you check a lbrmula lbr d i rnens ional cons is ter rcy?S(ate r r ro wi rys in which an ec luat ion that is d imensional lyconsistent nray nevertheless be physicit l ly incorrect.' tThc current density . / in a therrr ionic diode with paral lel,plane electrodes separated by a cl istance r/ depends on thepotentinl r l i l ' l 'erence V bctwccn anode and cathode. Use t l ted i rncns ions or base un i l .s o l ' thc re levant quant i t ics to l ' rndlvhclhcr thc ccpatiorrs:

. l =A l t t ; t k / r r t . 1 - ' / . v ' t t d -2 . . . . . , . . . . . . . . . . . , . . . . . . . . , , . . . . . . ( i )

. l = Beo(e/ r r r " l ' ih r / -2 . . . . . . . . . . . , . . . . . . . ( i i )are d imensional ly cons is tent . ( ln these eqt ta t ions, p t , and e, ,are thc permeabil i ty and pernri t t iv i ty 01' vacutttn, and e/tn"is thc spec i t ' i c c l rarge o l ' the e lect ror t ; A and /J ared i rnens ion less constants . )

N84/ l /13 (parr )

' r2 t l An cquat ion lor t l re specd v o l ' Io t tg i t t rc l in l t l wz lvcs in a th inrod o l ' r tn e le ts t ic so l id o f Yourrg tnoc lu lus I and dens i ty p ist , = 1E/p) l i2 . Us ing the base un i ts or c l imens ions of ther luant i t ics i r rvo lved, shorv that th is eqt ra t io t l i t l d i t t tens ional ly

[3]N87/ I/13(part)

/\Physics TOpical Papcr

29

3 0 n ) tItas tu

S- ' r t

ABC

D

31rfJ

a

321 (

1c)rc

Avo

A n

/ic( is

A (

33A p

an {

as s

he

1P s

24 (a)

(h)

( c )

Long Questiorts15 -t ' tre cri t ical I ' low spccd v" is

obstac le , thc dens i ty p o f thcone of - the equr t ions:

(a) vr= AnrlP, (b) r, .

re l i l tec l to t l rcl i qu id , and i t s .

width a o l ' t l rev i scos i t y 4 by

= [Jt]/np, (

O Irc.s s

{ i l \ /

) l .n,\ - I ,

oI '

' l

rr t)

r i t ll1 (). ' 5

r i s

ltsnd

D 40 1`N97/I/l

30 Argon ancl ncon are moltzttontic gases. One lnole o1' argonhas mass 40 g and one mole of neon has rnass 20 g.

What is the rat io number of atoms in I mole of argon 2

Avogadro Constant

29 n sarnp le o f carbon- l2 has a n . )ass o i 3 .0 g .Which expression gives the nurnber of atorns in the Sarrrnle?(l /a is.the synrbol lbr the Avogadro constant.)A 0.O030 A B O25 A C30

MF;:{Jf`lIla;:rr

200N at a dircction30 to orand B Own a1orcc0f4O0N at

60 tO0 ,as shO `n il11he diagrall bc|Ov(Fig,2)

Which one of the l 'ol lorving sketches correctly represents thernagnitude and direct ion of t l , te snnl lesr lorce that Jonesshould exert such that the resultant of al l three lbrccs actsalons 0x?

N80/II/7

35 n par t ic le has an in i t ia l ve loc i ty o f l5 rn s- r in the 0 ; rdirecl. ion, as .sho',vn in Fig. 3. At a later t i rne i ts velocity i .s15 rn s-r at an angle of 60" to 0.r (Fig, 4). (Direct ions areind icated by rneasur ing angles ant ic l .ockvy ise f rom thedirect ion 0r.)

?

?

?

nurnber of atoms ina lways Ialways 2l, only i f both gases are at thepressure2, only if both gases are at thepressu re

I rnole of neon

same temperature and

same temperature and

FigI

force acting on thc body is

D cOs e+mg sin E F+mg tan9

J77/H/4

D

31rrJ

33

N2000/t/l

Tl ie value of the Avogadro constant is (r.02 x 1023 permole.

( i) Dcf ine t lre rnole.( i i ) Calcu la te the rnass of an atonr o f r2C, us ing the

above value of the Avogadro constant.

A so l i d i r on cube o1 ' s i de 20 rn rn l r as a mass o f6.3 x 101 kg. One rnole of iron atolns has a mirss o1'5 .6 x l0- t kg.

( i) How many irou atoms are there in the cube?( i i ) Hence f ind the maximum vo lume that an i ron

atom could occr.rDV in the sol id state.

( i i i ) U^sc your an.swer lo (c) ( i i ) above to esti lnate thediameter of an iron atom.

N82/l /17 (part)

Scalars & Vectors

Forces of 5N, 4N and 3N are in equi l ibr iunr. As.suming thatsin 37o = 0.6, the angle l tetween the 5N force and the 3Nlbrce is

A37 B53 C90 D 127 E I43J76/I /5

A

C

D

E

,

C

)

)

32

A h o r i z o n t a l f o r c e F i sapplied to a body of rnass mon a smooth p lane inc l inec l a tan angle 0 to t lre lrorizontal,as shown in Fig. L

The rnagnitude of the resultant

A F cos 0 - r ng s i n 0B F s i n 9 + m g c o s 0C F s i n 0 - t n g c o s 0

0

15ms l

Fig3 Fig4

The change of vclocity that has takcn place in this intcrvalis

zero26 rn s-r at an angle o1'30' to 0.r.l 5 r n s - r a t an ang le o l ' 120 " t o 0x .26 nr s- r t r t an angle o1 '210 ' to 0 . r .l5 m s- r a t an anqle o l -300 ' to 0r .

?

?

??

N85/I/I

Srn i t h

l 5 n r s - t

I Phys ica l Quant i t ies & Uni ts 17 'A' Physics Topical Paper

36 I ro r -ces o l ' 4N anc l 6N rc t r t t n po i r t t . \ \ / h i c l r o i t s o l - t l t clo l l o rv ing coLr l r l no t be the rnagn i tudc o f ' t hc i r resL r l t an t ' J

41 \ \ /h ich l inc i r i the t r tb lc cor rc t : t lye l te l ' !v l tnc l t t tor t tcntunt i ts sca l i t r or

ic icnt i f ics 1 'orcc , k inet icvcctor qr l i i r l t i t i es ' i

i l t0n t (n lun tsc l t l i i t 'V c c t o r

scal arvecIorve (: t0r N92/l / |

vertical lineF i g , 5

-fhe lr

( t

J86/I/l

37 Three coplanar forces, of rnagniturle 70 N, 40 N and 50 N,lcr or.r a body at P in t lre dircct iorts sl. to"vtt in thc. cl i l tcr i l rnbe Iorv.

NB 4NC 6N

D 8NE K)N

frt rt 'c, \ sc l t l l t rI ] sca l a rC vcc to rD vector 'E vcc to r

k i t rct i r : ( r t ( t '9 . \ 'sc: a la rvectot 'sca l a r.scalart,cctt) r

Which one of the fbl lowing is the approximate bearir ig of theaddit ional lbrce required to maintain equi l ibr iurr ' l

A 3 7 " D z l J "B 127" tr 233'c t43' N86/t/ l

38 Wnicn pa i r inc luc les a vector quant i ty lnc l l scr lar c luur t i ty?

z\ d i .sp lacerr rent ;acce lerat ionB lbrr- 'c; kinct ic energyC power; speedD work; potential energy N87/l /3; J9411/l : J2000/Ul

39 Wtrictr I isl corrtain.s only scalar quanti t ies'/

A rni lss, accelerat ion, temperature, kinetic energyB tnass, volume, electr ic potential, kinetic enefgyC accelerat ion, ternperature, volunre, electr ic chargeD rnorrent, electr ic f ield, dcnsity, magnetic I ' l t rxR k inct ic energy, ve loc i ty , Iength, e lcc t r ic potcnt iu l

N90/ r / t

40 Two lbrccs act on a circular cl isc as shown in thc cl iagrnni.

3 N

Which i l n0wlbrce?

best s l rows the l ine o l ' ac t ion o1 ' thc resu l tant

Pl iysical Quanti t ies & Units

42 'Ve loc i ty is a vcctor c luant i ty , and thc k inc t ic energy o l ' abody rs equal to l ra l f i t .s rnass t i rnes t l tc square o f i ts ve loc i ty ,so k inet ic cnergy must a lso be a vector . 'Cotntnent on thecorrectr iess oi ' this arsurneltt . N7l l l l l

43 n trol lcy ol ' rnnss 0.ttO kg runs l i 'ccly, lvi t l tout accelerat i l tg,clown an incl ined plane wlten the plane ttrakes an angle of5.0' with the horizontal. Find the lorce paral lel to the planeres is t ing the mot ion. t3 l

. N&7l l / l

44 Gt) Wlrat is rneant by t\ t ,ector qtnnti t l ,? tzl(b) A bal l is thrown into the air and, at one

in.stant, i t is rnoving uprvards rvith a speedof 5 .0 rn s- l a t an anqle o f ( r0o to thcver t icn l .

( i ) U s i n g a s c a l e s u c h r h l t 1 . 0 c r n 0represents a .speed of 1.0 rn s-l , draw al i n e , s t a r t i n g a t 0 o n F i g . 5 , t orepresent thc velocity ol ' the bal l atthat ins tant .

Vest

(bCa11ng270)East(bear ing.90")

46s )q ni

47 nd :s1bt1

aIrl t

48rrI

49((

( i i ) On Fig. 5, construct l i rres to representthe vertical and the horizontal com-ponents o f the ve loc i ty o f t l ie ba l l .I-lencc, li 'om your druwing, deterrnine

18

L t lre vert ical conrponent o1'thc velocity,

2 . thc l ror izonta l cornponent o l ' the ve loc i ty . [5 ]J95/II l l (part)

45 nrc str ing t l [ ' i r part icular bow is pul lcr. l back so t lrat, jLtstbelbre tltc arrow is I'ired, tlie archer exerts a force ol' 260 Non the str ing, as showrr in Fig. 6.

string

2

Fig6

' l 'hc l ine of act ion ol ' the 260 N l i ;rce ntakes i tn iursle of -50"lvi th each scc:t ion ol ' t l re str inq.

1Ph C

(bca l i ng 0 " )

A

-

N90/I/2

'A ' Phys ics Topica l Paper

i l tc l l c Tl re tens ion in the s t r ing is Z.(a) ( i ) On F ig . 6 , i 'd icatc t l re d i rect io 's o l . thc ten.s ion in

t l te two .scct ions o l ' the s t r ing a t po in t p .

( i i ) By ca lcu la t ion or sc :a le drawing, dctcr r r r inc t l rcmagni tude of the tens ion T in the s t r inq.

r _ . . . . . . . . . . . , . . . , . . , . . N t3 lN2000/lll2 (parr)

Lortg Questiorts

46 s l r o l v by rneans o l ' a l abe l l ec j ske t ch l r ow two vec ro rquanti t ies, act ing at r ight anglcs, ar.e atJdcd.

N 80/l/ I -1 r'nr 't \

47 a'a'cJ B are two vectors acr. ing at r ight arrgles. Dralv label lecldiagrarns to show the vector aclcl i t ion (A + B) ancl the vecrorsubtraction (A - B). State the magnitude.s of the resultantsand the i r d i rec t ions wi th respect to vector A.

J83lI l13 (part)48 @ Some phys icar quant i t ie .s are or len pa i red toget r rer ,

one of the pair being a vector ancr trre other a scarar,Ident i ry the vector quant i ty in each o1. the tb l lowinspairs.

( i) ve Iocity and spcccl( i i ) weight ancl ma.ss(i i i ) energy and mornentum( iv) grav i ta t ionar | ie rcr s r rength and grav i ta t iona l

porenrial t4l(b) Two vectors A and I| are at right angres to each other.

Draw a vector diagrarn to srrow how the surn o1' thevectors could be fbund. el

(c) A car changes i ts verocity rtom 30 rn s-r cruc East to25 m s- r due South.( i ) Draw a vector d iagram ro show rhe in i t ia l anc l

f lna l ve loc i t ies and t l re changc in vc loc i ty .( i i ) Calculate the change in speecl.( i i i ) Calcu la te t l ie change in ve loc i ty . t6l

J89/l l /8 (paLt)

2/I / l

c l l ' a' ' i r r ,the

1 l l / |

i ng ,) o l ', 11 / r

I . JJtu l

t2)

; l)tI

,l

49 (d Distinguisrr between tr-re cri.rtrtrtce ttnvecrby an objectand its clisplacenrenr fi.om a iixecl point. t}l

N95/l t t /2 (part)

?

?

?

???

?

??

?

I Phys ica l Quant i t ies & Uni ts 19 'A' Physics Topical Paper