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香港考試局 保留版權 Hong Kong Examinations Authority All Rights Reserved 2002 Total

2002-AL-PHY 1A–1

HONG KONG EXAMINATIONS AUTHORITY

HONG KONG ADVANCED LEVEL EXAMINATION 2002

PHYSICS A-LEVEL PAPER 1 Question-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, and each section carries 60 marks. Answer ALL the question in each section.

2. Question for sections A and B are printed in two separate Question-Answer Books, A and B respectively.

3. Write your Candidate Number, Centre Number and Seat Number in the spaces provided on the covers of Question-Answer Books A and B.

4. Question-Answer Books A and B must be handed in separately at the end of the examination.

5. Supplementary answer sheets will be supplied on request. Write your Candidate Number on each sheet and fasten them with string inside

Candidate Number

Centre Number

Seat Number

Marker’s Use Only

Examiner’s Use Only

Marker No. Examiner No.

Question No. Marks Marks

6

7

8

9

Total

2002-AL PHY PAPER 1 (SECTION A)

A

2002-AL-PHY 1A–2 – 1 – 保留版權 All Rights Reserved 2002

SECTION A

i . Answer ALL questions. 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: speed of light in air = 3 × 108 m s−1 acceleration due to gravity = 10 m s−2

Question No. 1 2 3 4 5

Marks 13 13 10 12 12

1. A light spring is suspended from a fixed point and a vertical metre rule is placed nearby as shown in Figure 1.1. A pointer adhered to the lower end of the spring indicates a reading of 10.0 cm. A pan is now attached to the spring. The reading x indicated by the pointer is recorded for different masses m added to the pan. The result is tabulated as follows:

m / g 0 20 40 60 80 100 120

x / c m 14.9 20.1 25.2 29.9 34.9 40.0 45.2

(a) ( i ) Plot a graph of m against x on the graph paper printed on page 2. (3 marks )

( i i ) What is the physical significance of the slope of the graph? Use the graph, or otherwise, to find the force constant of the spring, in Nm-1, and the mass of the pan. (4 marks )

(b) All the masses are removed from the pan and a piece of plasticine of mass 80g is dropped from rest at a small distance above the pan. The plasticine sticks to the pan and the system then oscillates with simple harmonic motion.

( i) Find the motion’s period and its equilibrium position indicated by the pointer. (Assume that the air resistance is negligible.) (4 marks )

10.0 cm

Metre rule

x

pan m

Figure 1.1

2002-AL-PHY 1A–3 – 2 – 保留版權 All Rights Reserved 2002

(b) ( i i ) If,instead,the air resistance is significant,sketch the variation of the displacement

of the system from the equilibrium position with time for a few oscillation cycles. (No need to draw the scales.) (2 marks)

t ime

displacement

0

Go on to the next page

2002-AL-PHY 1A–4 – 3 – 保留版權 All Rights Reserved 2002

wall

2 . (a) A piece of string is fixed at one end to a wall. A wave pulse travels along the string at string at a speed of 0.5 ms-1 towards the fixed end ,its shape at time t=0s is shown in Figure 2.1.

( i ) Draw on the above diagram the wave pulse at t=1s and t=2s. (3mrks ) ( i i ) Skerch a graph of the displacement of a point Pon the string at a distance of 0.1m from

the wall during the period of t=0st to t=1s (2marks )

At t = 2 s

At t = 1 s

Figure 2 .1

At t = 0 s

0.2 0.4 0.6 0.8 1.0

displace

t/

0 time/s

0.02

− 0.02

displacement/m

wall

2002-AL-PHY 1A–5 – 4– 保留版權 All Rights Reserved 2002

(b)

The string is now replaced by a piece of wire and its free end is attached to a weight. The wire

passes over a fixed smooth pulley and is set into vibration at a frequency of 100 Hz with the stationary wave pattern shown in Figure 2.2. At the same time, a sound wave is also generated by the vibrating wire.

( i ) Describe the energy transfer in the production of sound from the wire. State THREE

differences between the wave on the wire and the sound wave emitted from it. (4 marks)

( i i ) I t is known that the speed v of the wire has the fol lowing rela t ion:

wirethe of length unit per mass wirethe in tensionv ∝

(I) What is the lowest possible frequency of vibration for station for stationary waves on the

wire if the vibrating length remains unchanged? Explain your answer with the aid of a diagram. (2 marks)

( I I ) If the weight is doubled while keeping the wave pattern in Figure 2.2 unchanged, find the

frequency of the frequency of the sound emitted from the wire. (2 marks)

Smooth pulley

weight Figure 2.2

Go on to the next page

2002-AL-PHY 1A–6 – 5 – 保留版權 All Rights Reserved 2002

2. A metal sphere has centre fixed at O as shown in Figure 3.1. The radius of the sphere is r0 and it carries a negative charge –Q. The electric potential at infinity is taken to be zero. (Given:permittivity = 8.85 × 10 –1 2 C2 N− 1 m− 2 )

Figure 3.1 (a) ( i ) Write an expression for the electric potential V0 on the surface of the sphere. (1 mark)

( i i ) If Q = 2.2 × 10–11 C andVo = –10 V，findro。 (2marks )

( i i i ) Let B be a point at a distance rB from O。Sketch the variation of the potential VB at B for

all values of rB . (2 marks)

Meta l sphere ca r ry ing a charge–Q

ro

BrB

O

VB /V

rB/m 0 ro

2002-AL-PHY 1A–7 – 6 – 保留版權 All Rights Reserved 2002

Go on to the next page

(b) ( i ) A particle of small positive charge q is held stationary by an external force at B where Br = 5 cm. Find the magnitude of the force required in terms of q and state its direction. (3 marks)

(ii) If the particle at B is projected with speed v such that it can escape from the electric field

of the sphere, find the minimum value of v, The charge-to-mass ratio of the particle is 1.76 × 1011C kg –1. (Hint : Consider the energy possessed by the particle.) (2 marks)

2002-AL-PHY 1A–8 – 7 – 保留版權 All Rights Reserved 2002

4. A metal cylinder of volume 0.02 m3 is on the sea surface where the temperature is 27oC. It contains a

compressed gas with pressure 18.0 atm (1 atm represents the standard atmospheric pressure). A diver carries the cylinder and dives 20m down to the seabed where the temperature is 21 oC. (Assume the gas is

ideal and the volume change of the cylinder due to temperature variation is negligible.)

(a) It is known that the pressure due to sea water increases by 1 atm every 10 m further down that one dives in the sea. What is the total pressure, in atm, at the seabed? (2 marks)

(b) After the diver has been on the seabed for some time, he inflates a balloon to a volume of 0.01 m3 by using the cylinder of compressed gas. Assume that the balloon is inflated slowly so that the temperature of the gas does not change and the final pressure in the balloon is equal to that at the seabed. (i) Find the gas pressure, in atm, in the cylinder just before the diver inflates the balloon.

(2 marks)

(ii) Calculate the gas pressure, in atm, in the cylinder after the balloon has been inflated.

(3 marks)

(iii) What fraction of the gas originally in the cylinder has been used to inflate the balloon?

(2 marks)

2002-AL-PHY 1A–9 – 8 – 保留版權 All Rights Reserved 2002

(c) The balloon is then released and it rises from the seabed to the sea surface. Assume that the volume of the balloon remains unchanged and the subsequent variation of its speed with time is shown in figure 4.1 Sketch the corresponding variation of the net force acting on the balloon with time in the spaces provided. Explain briefly. (3 marks)

Figure 4.1

0 time

net force

0 time

speed

Go on to the next page

2002-AL-PHY 1A–10 – 9 – 保留版權 All Rights Reserved 2002

5 . A student has constructed a refracting telescope as shown in Figure 5.1 The focal lengths of the objective and the eyepiece are 60 cm and 20 cm respectively.

(a) With the telescope in normal adjustment, find ( i ) the separation between the two lenses,and

(ii) the angular magnification when viewing a distant building.

(2 marks)

(b) The student now uses the telescope to view a small piece of newspaper, 3cm ╳ 3 cm , fixed to a

notice-board 1.5m away from the objective. He then adjusts the position of the eyepiece such that the final image is formed at infinity.

Figure5.1

(i) On the attached graph paper, complete the ray paths p and Q as they pass through the telescope, showing how the final image is formed at infinity. The piece of newspaper, represented by AB. and the objective are already drawn on the graph paper. Label the positions of the first image of the piece of newspaper and the eyepiece clearly on the diagram. (Horizontal scale: 1 to 20; Vertical scale: 1 to 1) (3 marks)

3 cm

3 cm

1.5 m

Objective

eyepiece

2002-AL-PHY 1A–11 –10– 保留版權 All Rights Reserved 2002

(ii) Find the height of the first image and the separation of the objective and the eyepiece. (2 marks)

( i i i ) What is the angular magnification in this case ? (Assume that when the piece of newspaper

is observed with an unaided eye, the distance between the piece of newspaper and the eye remains unchanged.) (2 marks)

(iii) If the eyepiece is adjusted so that the final image is at the least distance of distinct vision

(which is taken to be 25 cm ) of the student’s eye, briefly explain the change in the angular magnification. State the effect on the eye of prolonged use of the telescope in this way.

(3 marks)

E N D O F S E C T I O N A

2002-AL-PHY 1A–12 – 11 – 保留版權 All Rights Reserved 2002

高級程度會考常用公式

A1. rr

va 22

ω== 向心加速度 C17. lNI

B 0µ= 螺線管中的磁場

A2. xa 2ω−= 簡諧運動 C18.rII

Fπ

µ2

210= 帶電長直平行導線每單位長度之作用力

A3. ωIL = 剛體的角動量 C19. Φ= sinBANIT 載電流的矩形線圈在勻強磁場中的轉矩

A4. dtdLT = 轉動物體的轉矩 C20. tBANE ωω sin= 簡單發電機的電動勢

A5. 2

21 ωIE = 轉動體所儲存的能量 C21.

p

s

p

s

NN

VV

≈ 變壓器次級電壓和初級電壓

之比

B1. mTv = 橫波在緊張弦線上的速度 C22. dtLdIE −= 電感器的感生電動勢

B2. ρEv = 縱波在固體中的速度 C23. 2

21 LIE = 電感器儲存的能量

B3. pn θtan= 折射率和偏振角 C24. LX L ω= 感抗

B4. aDd λ

= 雙縫干涉實驗中條紋的寬度 C25. C

X C ω1

= 容抗

B5. λθ nd =sin 衍射光柵方程 C26. θcosIVP = 交流電路的功率

B6.

−−

=′suv

uvff 0 多普勒效應頻率方程 C27.

B

Linout R

RVV β−=∆∆ 共發射極組態之晶體管放大器電壓增益

B7.

1

210log10

II 分貝的定義 C28. ( )−+ −= VVAV 00 運算放大器的輸出電壓(開

環)

C1. 221

rmGmF = 牛頓萬有引力定律 C29.

i

f

RR

A −= 反相放大器的增益

C2. r

GMV −= 重力勢 C30. i

f

RR

A += 1 非反相放大器的增益

C3. 23 Tr =常數 開普勒第三定律 D1. NkTnRTpV == 理想氣體物態方程

C4. 2

04 rQE

πε= 點電荷的電場強度 D2. 2

31 cNmpV = 分子運動論方程

C5. r

QV04πε

= 點電荷的電勢 D3. kTNRTE

Ak 2

323

== 氣體分子動能

C6. dVE = 平行板間的電場(數值) D4.

Lx

AFE = 楊氏模量的宏觀定義

C7. d

AVQC 0ε== 平行板電容器的電容 D5. FxE

21

= 伸長物體儲存之能量

C8. RCteQQ −= 0 電容器放電時，電量隨時間

的衰減 D6.

drdUF −= 力與勢能的關係

C9. ( )RCteQQ −−= 10 電容器放電時，電量隨時間

的增加 D7. rkE = 楊氏模量的微觀詮釋

C10. 2

21 CVE = 電容器儲存的能量 D8. =++ ghvp ρρ 2

21

常數 伯努利方程

C11. nAvQI = 普適電流方程 D9. WQU +=∆ 熱力學第一定律

C12. A

lR ρ= 電阻和電阻率 D10. eV

nE n 2

6.13−= 氫原子的能級方程

C13. θsinBQvF = 磁場對運動電荷的作用力 D11. kteNN −= 0 放射衰變定律

C14. θsinBIlF = 磁場對載流導體的作用力 D12. k

t 2ln

21 = 半衰期和衰變常數

C15. nQtBIV = 霍耳電壓 D13. Φ−= hvmvm

2

21 愛因斯坦光電效應方程

C16. rI

Bπ

µ2

0= 長直導線所產生的磁場 D14. 2mcE = 質能關係式

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2002 A Physics 1A 1. (a) (ii) 4 N m–1, 20 g

(b) (i) 0.35 m, 0.99 s

2. (b) (ii) 25 Hz

(iii) 141 Hz

3. (a) (ii) 0.02 m

(b) (i) 79 q

(ii) 1.2 × 106 m s–1

4. (a) 3 atm

(b) (i) 17.6 atm

(ii) 16.1 atm

(iii) 0.085

5. (a) (i) 80 cm

(ii) 3

(b) (ii) 2.0 cm, 1.2 m

(iii) 9