Checker’s Use Only

Checker No.香港考試局　　保留版權

Hong Kong Examinations AuthorityAll Rights Reserved 2000 Total

2000-AL-PHY 1A–1

HONG KONG EXAMINATIONS AUTHORITY

HONG KONG ADVANCED LEVEL EXAMINATION 2000

PHYSICS A-LEVEL PAPER 1Question-Answer Book A

8.30 am – 11.30 am (3 hours)

This paper must be answered in English

INSTRUCTIONS

1. This paper consists of TWO sections, A and B.Answer ALL questions in BOTH sections.

2. Questions for sections A and B are printed intwo separate Question-Answer Books A and Brespectively.

3. Sections A and B each carries 60 marks. Youshould spend about 1 hour 30 minutesanswering each section.

4. Write your candidate Number, Centre Numberand Seat Number in the spaces provided on thecovers of Question-Answer Books A and B.

5. Question-Answer Books A and B must behanded in separately at the end of theexamination.

6. Supplementary answer sheets will be suppliedon request. Write your Candidate Number oneach sheet and fasten them with string insidethis book.

Candidate Number

Centre Number

Seat Number

Marker’sUse Only

Examiner’sUse Only

Marker No. Examiner No.

QuestionNo. Marks Marks

1

2

3

4

5

Total

2000-ALPHYPAPER 1(SECTION A)

A

2000-AL-PHY 1A–2 — 1 —

SECTION A

i Answer ALL questions in this section.ii Write your answers in the spaces provided in this question-answer book. In calculations you should show

all the main steps in your working.iii Assume : velocity of light in air = 3 x 108 m s-1

acceleration due to gravity = 10 m s-2

Question No. 1 2 3 4 5

Marks 11 13 12 11 13

1. In December 1998, a serious car accident happened on the Lantau Link. The car sped up the concrete rampand took off from the ramp. It then hit the top of a road sign of height 5 m above the road and 30 m awayfrom the ramp as shown in Figure 1.1.

Figure 1.1

(a) Sketch in Figure 1.1 the possible trajectories of the car in the air for a certain take-off speed.(2 marks)

(b) Assume that the car hit the road sign at the highest point in its trajectory. Estimate(i) the take-off speed of the car;

(ii) the projection angle of the car; and(iii) the time of flight before the car hit the road sign.

(You may neglect the air resistance and the size of the car.) (5 marks)

30 m

road sign

5 m ramp

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–3 — 2 — Go on to the next page

(c) Braking marks of 39 m long was found on the road in front of the ramp. Forensic measurementson the marks by the police indicated that the braking force was about 8000 N on the car of mass1000 kg. Estimate the speed of the car just before applying the brakes. (2 marks)

(d) A report on this accident appeared in a local newspaper in which the take-off speed of the car, u, isstated as

o2 5.9sin5102 ××>u

Referring to the relation, the angle of elevation of the road sign from the ramp is taken as the angle

of projection. Comment on the appropriateness of such an assumption. (2 marks)

30 m9.5o

5 m

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–4 — 3 —

2. Two identical pans, each of mass 150 g, are connected by a light string which passes over a light pulleysuspended from the ceiling. The pulley can rotate smoothly about a horizontal axis through its centre.Two identical weights m1 and m2, each of mass 10 g, are placed on the pans as shown in Figure 2.1.(Neglect air resistance.)

Figure 2.1

(a) In the space provided below, sketch and label all the forces acting on both m1 and the pansupporting it. Identify an action and reaction pair. (3 marks)

(b) Write down all the possible state(s) of motion that the system can take. (1 mark)

Initially the separation between the pans is 0.72 m. Now m2 is removed from the lower pan and the systemaccelerates from rest.

Figure 2.2

m1

panm2

m1p a n

O

x

0.72 m

m1

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–5 — 4 — Go on to the next page

(c) Show that the acceleration of m1 is given by Mm

mga2+

= where m and M are the masses of the

weight and the pan respectively. Calculate the tension in the string. (3 marks)

(d) Find the speed of the pans when they are at the same level. (2 marks)

(e) A light spring of force constant 4 N m-1 is fixed vertically below the descending pan as shown inFigure 2.2. A light plate is attached to the upper end of the spring. The descending pan comesinto contact with the plate when the two pans are at the same level. The motion of the systembecomes simple harmonic until it comes to rest momentarily. With the contact point taken as theorigin, find the equilibrium position and the angular frequency of the motion. (Assume that thepan moves together with the plate once they are in contact and the string does not slackthroughout.) (4 marks)

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–6 — 5 —

3. Figure 3.1 shows a circuit used for measuring the capacitance of a capacitor C.

Figure 3.1

Lead Z is first connected to X, which is the positive terminal of the battery. After about one minute, lead Zis disconnected from the battery and is then connected to Y. The stop watch is started when the currentthrough the microammeter drops to 50 µA. The variation of the current I with time t is recorded.

t/s I / ××××10-6 A

0 502 405 309 20

17 1022 626 434 2

(a) Explain why it is better to take readings of time for pre-selected current values (e.g. 50, 40, 30,…)rather than trying to read current values at pre-selected times (e.g. 0, 5, 10,…) ? (1 mark)

(b) State TWO uncertainties associated with the experiment. (2 marks)

(c) The experiment is repeated to measure the variation of current with time. Explain the advantageof doing so. (1 mark)

(d) Deduce whether the e.m.f. of the battery used is 3 V, 4.5 V or 6 V. (2 marks)

CLead Z

X

100 kΩ

Y A

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–7 — 6 — Go on to the next page

(e) A graph of ln I against t is plotted. The slope of the graph is –9.4 × 10-2 s-1.

(i) Write down the relation between I and t. Hence find the capacitance of C. (3 marks)

(ii) Explain why the capacitor is practically fully charged when lead Z has been connected tothe positive terminal of the battery for one minute. (2 marks)

(iii) If another 100 kΩ resistor is connected in parallel with the one in the circuit, state onepossible change on the graph. (No mathematical derivation is required.) (1 mark)

-9.0

-10.0

-11.0

-12.0

-13.0

-14.0

ln I 0 10 20 30 40 time/s

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–8 — 7 —

4. A metal cylinder of volume 0.5 m3 contains some compressed gas at an initial pressure of 16 × 105 Pa. Thegas is used to inflate identical non-elastic balloons, each to a volume of 1.2 m3 at atmospheric pressure of105 Pa. Assume that the balloons are inflated slowly so that the temperature of the gas does not change andthe pressure in the balloons is always equal to the atmospheric pressure. (You may assume the equation ofstate for an ideal gas in the calculation.)

(a) The density of the gas in the cylinder is 1.57 kg m-3 at room temperature. Estimate the r.m.s.speed of the gas molecules. (2 marks)

(b) Find the work done against atmospheric pressure in inflating one balloon. (2 marks)

(c) (i) Calculate the decrease in gas pressure in the cylinder after inflating one balloon. (3 marks)

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–9 — 8 — Go on to the next page

(ii) Find the number of balloons that can be inflated before the gas pressure in the cylinderdrops below 10 × 105 Pa. (2 marks)

(d) Briefly explain whether there is heat transfer between the cylinder and the surroundings when theballoons are being inflated in the way described in this question. (2 marks)

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–10 — 9 —

5. Figure 5.1 shows an ionization chamber that can be used to estimate the activity of a sample of uranium-238.The sample is placed inside a metal can held at a negative potential. Electrons produced inside the metalcan migrate to the sample while positive ions migrate to the wall of the can. The sample is connected to theground via a 109 Ω resistor. The potential difference across the 109 Ω resistor is measured by an op-ampcircuit.

Figure 5.1

(a) Name the op-amp circuit used in Figure 5.1. (1 mark)

(b) Figure 5.2 shows the variation of the voltmeter reading with the potential difference acrossthe metal can and the sample.

Explain the variation of the voltmeter reading. (3 marks)

Figure 5.2

109Ω

insulator

U-238 sample

ionization chamber(metal can)

power supply

V

+0 V

−

+

−+

60

40

20

05 10 15 20 25 30

80

100voltmeterreading/mV

p.d. across the metal canand the sample/V

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–11 — 10 —

(c) In the sample, uranium-238 decays into thorium-234 by emitting an α-particle. Thisnuclear reaction can be represented as :

He24

Th90234

U92238

+→

Given : Mass of one nuclide of U-238 = 238.0508 uMass of one nuclide of Th-234 = 234.0436 uMass of one nuclide of He-4 = 4.0026 u1 u (atomic mass unit) = 1.660 × 10-27 kg, which corresponds to 934 MeV

(i) Calculate the energy, in MeV, released in this nuclear reaction. (2 marks)

(ii) From the information provided in Figure 5.2, calculate the number of air particlesbeing ionized per second inside the metal can. Assume that each ionized airparticle carries one electronic charge. (electronic charge = 1.6 × 10-19 C) (2 marks)

(iii) If the energy required to produce an ion-electron pair is 30 eV, estimate theactivity, in disintegrations per second, of the U-238 sample. State theassumption(s) in your calculation. (3 marks)

(iv) Is this experimental method suitable for estimating the activity of a sampleemitting β-particles ? Give TWO reasons to support your answer. (2 marks)

END OF SECTION A

保留版權 All Rights Reserved 2000

2000-AL-PHY 1A–12

Useful Formulae in Advanced Level Physics

A1. ar

r= =υ ω2

2 centripetal acceleration C17. BNIl

=µ 0

magnetic field inside long solenoid

A2. a x= −ω 2simple harmonic motion C18. F

I Ir

=µ

π0 1 2

2force per unit length between longparallel straight current carryingconductors

A3. L I= ω angular momentum of a rigid body C19. T BANI= sin φ torque on a rectangular current carryingcoil in a uniform magnetic field

A4. T dLdt

= torque on a rotating body C20. E BAN t= ω ωsin simple generator e.m.f.

A5. E I= 12

2ω energy stored in a rotating body C21.VV

NN

s

p

s

p≈ ratio of secondary voltage to primary

voltage in a transformer

B1. υ = Tm

velocity of transverse wave motion in astretched string

C22. E LdI dt= − / e.m.f. induced in an inductor

B2. υρ

= E velocity of longitudinal wave motionin a solid

C23. E LI= 12

2energy stored in an inductor

B3. n p= tanθ refractive index and polarising angle C24. X LL = ω reactance of an inductor

B4. d Da

= λ fringe width in double-slit interference C25. XCC =1

ωreactance of a capacitor

B5. d nsinθ λ= diffraction grating equation C26. P IV= cosθ power in an a.c. circuit

B6. ′ =−−

f fuus

( )υυ

0 Doppler frequency C27. ∆ ∆V VRRout in

L

B/ = −β voltage gain of transistor amplifier in the

common emitter configuration

B7. 10 log ( )102

1

II

definition of the decibel C28. V A V V0 0= −+ −( ) output voltage of op amp (open-loop)

C1. FGm m

r= 1 2

2 Newton’s law of gravitation C29. ARR

f

i= − gain of inverting amplifier

C2. V GMr

= − gravitational potential C30. ARR

f

i= +1 gain of non-inverting amplifier

C3. r T3 2/ = constant Kepler’s third law D1. pV nRT NkT= = equation of state for an ideal gas

C4. EQ

r=

4 02πε

electric field due to a point charge D2. pV Nmc=13

2kinetic theory equation

C5. VQ

r=

4 0πεelectric potential due to a point charge D3. E RT

NkTk

A= =3

232

molecular kinetic energy

C6. E Vd

= electric field between parallel plates(numerically)

D4. E FA

xL

= macroscopic definition of Youngmodulus

C7. CQV

Ad

= =ε 0 capacitance of a parallel-plate

capacitorD5. E Fx= 1

2energy stored in stretching

C8. Q Q e t RC= −0

/ decay of charge with time when acapacitor discharges

D6. F dUdr

= − relationship between force and potentialenergy

C9. Q Q e t RC= − −0 1( )/ rise of charge with time when charging

a capacitorD7. E k r= / microscopic interpretation of Young

modulus

C10. E CV=12

2 energy stored in a capacitor D8. P gh+ +12

2ρυ ρ

= constant

Bernoulli’s equation

C11. I nA Q= υ general current flow equation D9. WQU +=∆ first law of thermodynamics

C12. Rl

A=

ρresistance and resistivity D10. E

nn = − 13 62.

eV energy level equation for hydrogen atom

C13. F BQ= υ θsin force on a moving charge in amagnetic field

D11. N N e kt= −0

law of radioactive decay

C14. F BIl= sinθ force on a moving conductor in amagnetic field

D12. tk

12

2= lnhalf-life and decay constant

C15. V BInQt

= Hall voltage D13.12

2m hvmυ = − Φ Einstein’s photoelectric equation

C16. BIr

=µ

π0

2magnetic field due to a long straightwire

D14. E mc= 2 mass-energy relationship

保留版權 All Rights Reserved 2000

NUMERICAL ANSWERS

1. (b) (i) 31.6 m s-1

(ii) 18.4o

(iii) 1 s

(c) 40.3 m s-1

2. (c) 1.55 N

(d) 0.48 m s-1

(e) 0.025 m below O3.6 rad s-1

3. (d) 6 V

(e) (i) 1.1 x 10-4 F

4. (a) 1750 m s-1

(b) 1.2 x 105 J

(c) (i) 2.4 x 105 Pa

(ii) 2

5. (c) (i) 4.30 MeV

(ii) 4.38 x 108

(iii) 3050

保留版權 All Rights Reserved 2000