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This paper consists of 20 printed pages

Anglo-Chinese Junior College Physics Preliminary Examination Higher 2

PHYSICS Paper 1 Multiple Choice Additional Materials: Multiple Choice Answer Sheet

9646/01 01 September 2015

1 hour 15 minutes

READ THESE INSTRUCTIONS FIRST

Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your Name and Index number in the answer sheet provided.

There are forty questions in this section. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate

Answer Sheet.

Read the instructions on the Answer sheet very carefully.

Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this Question Paper.

2

Anglo-Chinese Junior College 2015 J2 H2 9646 Preliminary Examinations

DATA AND FORMULAE Data speed of light in free space, c = 3.00 108 m s1

permeability of free space, o = 4 107 H m1

permittivity of free space, o = 8.85 1012 F m1

(1/(36)) 10-9 F m-1

elementary charge, e = 1.60 1019 C the Planck constant, h = 6.63 1034 J s

unified atomic mass constant, u = 1.66 1027 kg rest mass of electron, me = 9.11 1031 kg

rest mass of proton, mp = 1.67 1027 kg molar gas constant, R = 8.31 J K1 mol1

the Avogadro constant, NA = 6.02 1023 mol1 the Boltzmann constant, k = 1.38 1023 J K1

gravitational constant, G = 6.67 1011 N m2 kg2 acceleration of free fall, g = 9.81 m s2

Formulae

uniformly accelerated motion, s = ut + 21 at 2

v 2 = u 2 + 2as

work done on/by a gas, W = p V

hydrostatic pressure, p = g h

gravitational potential, = r

Gm

displacement of particle in s.h.m., x = xo sin t

velocity of particle in s.h.m., v = vo cos t

= 2 2

0x x

mean kinetic energy of a molecule of an ideal gas

E = 3

2kT

resistors in series, R = R1 + R2 +

resistors in parallel, 1/R = 1/R1 + 1/R2 +

electric potential, V = r

Q

o4

alternating current/voltage, x = xo sin t

transmission coefficient, T exp(2kd)

where k = 2

2

8 ( )m U E

h

radioactive decay, x = xo exp(t)

decay constant, = 1

2

0.693

t

3

[Turn over Anglo-Chinese Junior College 2015 J2 H2 9646 Preliminary Examinations

1 A thermometer is used to measure the temperature of the room.

What is the most appropriate reading on the thermometer and the uncertainty in this reading?

reading / o C uncertainty in reading / o C

A 24 0.5

B 24 0.2

C 24.0 1.0

D 24.0

0.5

2 The molar mass of water is 18 g.

The approximate number of water molecules in a glass of water is

A 2210 B

2510 C 2810 D

3110

3 The variation of the acceleration a with time t of a body moving in a straight line is shown

in the graph below.

The shaded area represents

A the velocity at t1.

B the velocity at t2.

C the change in velocity from t1 to t2.

D the average velocity between t1 and t2.

4


4 The minimum time T required for a car to safely overtake a lorry on the motorway is

measured from the time the front of the car is level with the rear of the lorry, until the rear

of the passing car is a full car-length ahead of the lorry.

The car is 3.5 m long and the lorry is 17.0 m long. The graph shows the variation with

time t of the speeds v of the car and the lorry.

What is the value of T?

A 0.86 s B 1.2 s C 2.6 s D 3.0 s 5 A ball is thrown with kinetic energy K from ground level at an angle of 45º to the

horizontal.

Which statement is not correct?

A The kinetic energy of the ball is 2

Kat maximum height.

B The potential energy of the ball is 2

Kat the maximum height.

C The kinetic energy of the ball is 2

Kwhen the ball reaches a height equal to half the

maximum height.

D The potential energy of the ball is

4

Kwhen the ball reaches a height equal to half the

maximum height.

5


6 A typical lift of mass 1100 kg is powered by a motor and assisted by a counterweight of

mass 1000 kg. The motor is turned off and allowed to turn freely. The lift then

accelerates downwards.

If a 60 kg person is standing on a light weighing scale, the reading on the scale is

A 545 N B 561 N C 589 N D 633 N 7 Two spheres of masses 1 kg and 2 kg, are travelling on a smooth horizontal surface with

speeds 2 m s-1 and 3 m s-1. They collide elastically, and their respective speeds after the

collision are v1 and v2 respectively.

Which of the following are possible quantities for the spheres after the collision?

magnitude and direction of v1 magnitude and direction of v2

A

14

3 m s-1 to the left

1

3 m s-1 to the right

B

1

3m s-1 to the left

14

3m s-1 to the right

C

2

3 m s-1 to the left

5

3 m s-1 to the left

D

5

3 m s-1 to the right

2

3m s-1 to the left

motor

counterweight

after collision

1 kg 2 kg

v1 v2

before collision

1 kg 2 kg

2 m s-1 3 m s-1

6


8 A ball is suspended vertically in air from a spring and slowly lowered to equilibrium

position. The ball has density 600 kg m-3. The force constant of the spring is 500 N m-1

and its extension is 10 cm.

The ball is then completely immersed in water. The density of water is 1000 kg m-3, and

the volume of the coils is negligible.

What is the change in the length of the spring from its unextended length?

A 0.33 cm B 5.0 cm C 6.0 cm D 6.7 cm 9 A rigid sphere P is rolling with a constant angular velocity on a hard horizontal surface in

the direction shown. A second rigid sphere Q is sliding with a constant velocity on a hard

horizontal surface in the direction shown.

If air resistance is negligible, which of the following best represent the forces exerted by

the surface on P and Q?

force on P by surface force on Q by surface

A

B

C

D

P Q

7


10 A uniform horizontal scaffold has a mass 30 kg and length 6 d. Two painters of masses

50 kg and 80 kg are standing on the scaffold while holding on to the ends of the ropes.

The tensions in the ropes are T1 and T2. Both pulleys are assumed to be frictionless.

What is the value of T1?

A 343 N B 348 N C 712 N D 722 N 11 A container of gas undergoes thermodynamics changes. The process is shown below.

State A to B State B to C State C to A

constant pressure

decrease in temperature

constant volume

increase in temperature

increase in volume

no change in temperature

What is the work done on the gas?

State A to B State B to C State C to A

A positive zero positive

B negative zero positive

C positive zero negative

D negative positive zero

50 kg

T1 T

2

80 kg

d

1.5 d 1.5 d

d

8


12 A mass is attached to one end of a spring as shown in Fig. 12 (a) and is slowly lowered

to its equilibrium position as shown in Fig. 12 (b). (Diagram may not be to scale)

What are the possible changes in elastic potential energy (EPE) and gravitational

potential energy (GPE)?

change in EPE / J change in GPE / J

A 0.20 0.20

B 0.10 0.20

C 0.15 0.05

D 0.05 0.15

13 A tow-truck produces constant power and pulls a car on a level ground.

The car experiences a constant frictional force of 6000 N. The table shows the velocity of the car, v, corresponding to its acceleration, a.

a / m s-2 v / m s-1

2.0 11.1

0.8 13.9

What is the mass of the car?

A 7500 kg B 3000 kg C 1500 kg D 1200 kg

Fig. 12 (a) Fig. 12 (b)

9


14 A military aircraft makes a loop in a vertical circular plane at constant angular speed. Which of the following is possible?

position of aircraft

contact force of seat on pilot / N

centripetal force on pilot / N

A

top (upside down) bottom

6540 4980

5760

B


4980 6540

5760

C


5760 6540

4980

D


6540 5760

4980

15 A small point mass is in a gravitational field setup by a massive perfect sphere of uniform

density. The graphs below show the variation of gravitational force F on the small point

mass and gravitational potential energy U which distance between the centres of both

masses r. Both graphs are not drawn to scale.

When the two masses are separated by a distance r0, which of the following is correct?

A The U of two masses is given by the gradient of the tangent at r

0 in the F-r graph.

B The magnitude of F on the massive perfect sphere is given by the ratio of U to r

0 in

the U-r graph.

C The U of two masses is given by the area under the F-r graph from 0 to r

0.

D The magnitude of F on the massive perfect sphere is given by the gradient of the

tangent at r0 in the U-r graph.

U

r 0 0

F

r 0 0

r0 r

0

10


16 An Earth-orbiting satellite experiences a continuous resistance from external influences. Which of the following correctly describes the changes in the kinetic energy and the

gravitational potential energy of the satellite?

kinetic energy gravitational potential

A increase increase

B increase decrease

C decrease increase

D decrease decrease

17 The graph shows how the kinetic energy of a 50 g particle moving with simple harmonic

motion varies with time.

What is the maximum acceleration of the particle?

A 0.14 m s-2 B 0.20 m s-2 C 0.40 m s-2 D 1.0 m s-2

kinetic energy / J

time / s

11


18 A block of mass M, at rest on a frictionless horizontal surface, is attached to a spring.

The spring is compressed initially and released to allow the mass to move in a simple

harmonic motion.

Which of the following can correctly represent the variation of displacement x and

acceleration a of M with respect to time t?

displacement against time acceleration against time

A

B

C

D

M

x

x

t 0

a

t 0

x

t 0

a

t 0

x

t 0

a

t 0

x

t 0

a

t 0

12


19 Which of the following statements is correct for an object undergoing a very lightly

damped oscillation?

A The period of oscillation increases over time.

B The total energy of object decrease exponentially with time.

C The amplitude of the oscillation is proportional to the frequency.

D The damping force is always pointing towards the equilibrium point. 20 Two identical masses are connected to two separate springs. Mass P is connected to a

spring with spring constant k while mass Q connects to a spring with spring constant 2k.

Both systems are attached to an oscillator. Air resistance is not negligible.

Which of the following graphs correctly shows the variation of amplitude x0 as the

oscillator frequency f varies?

A B

C D

P

Oscillator

k

2k

Q

f

x0

P

Q f

x0

P

Q

f

x0

Q

P

f

x0

P & Q

13


21 Oxygen molecules in the Earth’s atmosphere have a root mean square speed of about

500 m s-1. The mean translational kinetic energy of the oxygen molecules is E.

The relative molecular mass of oxygen and helium are 32 and 4 respectively. What are the best approximation of the root mean square speed and the average

translational kinetic energy of a helium molecule in the atmosphere?

Root mean square speed of helium molecules

Average translational kinetic energy of the helium molecules

A 180 E

B 180 8E

C 1400 E

D 1400 8E

22 A sample of an ideal gas initially having internal energy U1 is allowed to expand

adiabatically performing external work W. Heat Q is then supplied to it, keeping the

volume constant at its new value, until the pressure rises to its original value.

The internal energy of the sample is then U2.

The increase in internal energy, U2 – U1, is equal to

A W B Q – W C Q D W – Q

23 A student wants to determine the specific latent heat of vaporisation of an unknown

liquid. He used two different heaters, one at 50 W and the other at 100 W, to vaporize

the liquid. The liquid is found to vaporize at a rate of 0.0429 kg s-1 and 0.0875 kg s-1

respectively.

What is the best estimate of the specific latent heat of vaporisation of the liquid?

A 3 -11.12 10 J kg

B 3 -11.14 10 J kg

C 3 -11.15 10 J kg

D 3 -11.17 10 J kg

pressure

volume

U1 U

2

14


24 The displacement-distance graphs of two sound waves are shown below. Wave X is

traveling to the right and wave Y is traveling to the left. Both waves are traveling at the

same speed of 5 cm s-1.

What is the phase difference of the two waves after 3 s at 30 cm from the origin?

A 3

B

2

C D

3

2

25 A ringing 444 Hz tuning fork is brought near the D string of a guitar. This causes the

string to vibrate at the 3rd harmonic frequency such that 3 loops are formed on the string.

If the length of the D string is 650 mm, what is the speed of the wave on the string?

A 63.9 m s-1 B 95.9 m s-1 C 192 m s-1 D 575 m s-1

26 A laser is shined through a diffraction grating of 300 lines per mm. The second order

fringe falls onto a screen 75 cm away from the diffraction grating and 20 cm away from

the central fringe.

What is the wavelength of the laser beam?

A 429 nm B 444 nm C 858 nm D 888 nm

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 10 20 30 40 50 60Distance / cm

Displacement / μm

X Y

75 cm

20 cm

Laser

Diffraction grating

Screen

15


27 A negatively charged oil drop is balanced above the midpoint of two large horizontal

plates in vacuum. A potential difference of V is applied between the plates.

Which of the following statements is correct?

A Decreasing V causes the oil drop to move towards the top plate.

B Increasing V increases the electric field strength between the plates, but increases

the electric potential energy of the particle.

C When vacuum is replaced by air, both the electric field strength between the plates

and the electric potential energy of the particle will increase.

D When a thin horizontal conductor of the same cross-sectional area as the plates is

placed along XX’, the electric field strength experienced by the oil drop increases,

but its electric potential energy decreases.

28 Two point charges of charged - 2Q and +Q are arranged at two corners of an equilateral

triangle of side r in vacuum.

What can be deduced about the electric potential V, and the magnitude and direction of

electric field strength E at point X?

V magnitude of E direction of E

A

0

4

Q

r

2 2

0 0

3

4 4

Q QE

r r

B 0

2 4

Q

r

2

0

3

4

QE

r

C

0

4

Q

r 2

0

4

QE

r

D

0

4

Q

r

2

0

4

QE

r

+Q

- 2Q

r

X

r

r

16


29

A 10 Ω resistor and a thermistor are connected in series to a battery of e.m.f. 3.0 V and

negligible internal resistance. The table shows the voltage of both thermistor and resistor

corresponding to the current flowing in them.

If the resistance of the resistor is doubled, what is the e.m.f. of the new battery assuming

negligible internal resistance required for current flowing in the circuit to remain the

same?

A 4.0 V B 4.5 V C 5.0 V D 6.0 V

30 The diagram shows a potentiometer setup with four resistors in place.

The jockey is at the null point. Which of the following statements is not true?

A Increasing the resistance of resistor 4 will increase the balance length l.

B Increasing the resistance of resistor 3 will decrease the balance length l.

C Decreasing the resistance of resistor 2 will increase the balance length l.

D Increasing the resistance of resistor 1 will decrease the fractional uncertainty of the

balance length l.

2 3

4

G

1

l

0.1

0.2

0.3

0.4

0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

I / A

V / V

17


31 Three equally spaced unit length wires, X, Y and Z are placed along a straight line as

shown below. Wire Y carries a current always pointing into the paper while wire X and Z

each carries a current always pointing out of the paper. The current flowing through

wires X, Y and Z are I, 2I and 3I respectively.

Which of the following is incorrect?

A Increasing the current in X can cause a change in the direction of the net force

experienced by Y.

B Increasing the current in Z can cause a change in the direction of the net force

experienced by Y.

C Increasing the current in X can cause a change in the direction of the net force

experienced by Z.

D Decreasing the current in Y can cause a change in the direction of the net force

experienced by Z.

32 A particle X, with charge +q, is accelerated from rest across a uniform electric field. It

enters a magnetic field with a speed v and moves in a circular path of radius r.

A heavier particle Y, with the same charge +q, is now accelerated from rest across the

same uniform electric field.

Which of the following describe the speed and radius of particle Y’s circular path as it

enters the magnetic field?

speed radius of circular path

A v Smaller than r

B v Larger than r

C Less than v Smaller than r

D Less than v Larger than r

I I 2I 2I . . x x W X Y Z

I 2I 3I

18


33 A resistor of resistance R dissipates heat at a certain rate when a steady current I

passes through it.

The resistance is now doubled and a sinusoidal current is used such that the resistor

dissipates heat at the same rate.

What is the peak value of the alternating current?

A 2

I B

2

I C I D 2I

34 A student sets up a circuit using 5 identical ideal diodes and a resistor as shown below.

Which diagram shows the variation of the voltage across the points AB?

A B

C D

35 A monochromatic light source emits a narrow, parallel beam of light of wavelength

546 nm, the power in the beam being 0.080 W.

If the beam falls on the cathode of a photocell, what is the photocell current, assuming

that 1.5% of the photons incident on the cathode liberate electrons?

A 0.30 mA B 0.53 mA C 10.0 mA D 35.0 mA

19


36 An x-ray emission spectrum shows the characteristic x-ray spectrum.

The emission lines which represent transitions between discrete energy levels are not

perfectly sharp but display a finite linewidths.

Which of the following best accounts for this phenomenon?

A Quantum tunnelling of electrons

B Wave-particle duality of photons

C Energy-time uncertainty principle

D Diffraction of electrons in the target of the X-ray tube 37 An electron is confined in the central cylinder (from x = 0 to x = L). The central cylinder

has a zero potential and lies between two semi-infinitely long end cylinders which are

given infinitely great negative potential. The wave functions for the electron may be

given by the wave equation

( ) sin( )n

x A xL

where n is a positive integer representing the quantum state of the electron. A, B and C

define equally spaced interval along the central cylinder.

When n = 2, which of the following statements correctly describes the locations of the

electron?

A The electron may be found at A, B and C.

B The electron is likely to be found beyond x = L.

C The electron is most likely to be found at A or C.

D The electron is most likely to be found at only B.

intensity

wavelength

characteristics x-ray spectrum

linewidth

x = 0 x = L

A B C

20


38 Which of the following statement about a p-n junction is false?

A The depletion layer consists of immobile charged impurity atoms.

B Recombination of electron-hole pairs contributes to the current in a photodiode cell.

C The lattice site in the p-type semiconductor within an unbiased p-n junction consists

of negatively charged ions.

D A light emitting diode operates when free electrons moving across the p-n junction

fall into empty holes in the p-type layer.

39 Which of the following statements about X-ray and electron beam is false?

A Electron beam has a wave speed equal to the speed of the electrons.

B X-ray is an electromagnetic radiation and travels at the speed of light.

C X-ray can be used to provide information about atomic spacing in a crystalline

material.

D Electron beam can be used to provide information about atomic spacing in a

crystalline material.

40 The 14C:12C ratio of living material has a constant value during life but the ratio

decreases after death because 14C is not replaced. The half-life of 14C is 5700 years.

The 14C content of 5 g sample of living wood has a radioactive count rate of about

80 per minute. The count rate of 10 g sample of ancient wood is 50 counts per minute.

If the measurement when no sample is present is 20 counts per minute, what is the

approximate age of the ancient wood?

A 4 000 years

B 6 000 years

C 11 000 years

D 20 000 years

H2 Physics P1

Qn Ans Key

1 D

2 B

3 C

4 D

5 C

6 A

7 A

8 D

9 D

10 A

11 C

12 B

13 C

14 B

15 D

16 B

17 B

18 C

19 B

20 B

21 C

22 B

23 A

24 B

25 C

26 A

27 D

28 A

29 A

30 B

31 B

32 D

33 C

34 D

35 B

36 C

37 C

38 B

39 A

40 C

This paper consists of 20 printed pages.

Anglo-Chinese Junior College JC 2 Physics Preliminary Examination Higher 2

CANDIDATE NAME

CLASS

CENTRE NUMBER

S 3 0 0 4 INDEX NUMBER

PHYSICS Paper 2 Structured Questions Candidates answer on the Question Paper. No Additional Materials are required

9646 25 August 2015

1 h 45 minutes


Write your Name and Index number in the spaces on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiners’ use only

1 / 8

2 / 8

3 / 8

4 / 7

5 / 7

6 / 7

7 / 15

8 / 12

Total / 72

2

Anglo-Chinese Junior College 2015 J2 H2 9646 Preliminary Examination

For Examiner’s Use




(1/(36)) 10-9 F m-1



rest mass of proton, mp = 1.67 1027 kg molar gas constant, R = 8.31 J K1 mol1 the Avogadro constant, NA = 6.02 1023 mol1

the Boltzmann constant, k = 1.38 1023 J K1 gravitational constant, G = 6.67 1011 N m2 kg2

acceleration of free fall, g = 9.81 m s2 Formulae


v 2 = u 2 + 2as

work done on/by a gas, W = p V hydrostatic pressure, p = g h


Gm



= 22 xxo

mean kinetic energy of a molecule of an ideal gas,

E = 3

2kT




Q

o4



where k = 2

2 )(8

h

EUm


decay constant, = 2

1

6930

t

.

3

[Turn over



Answer all the questions in the spaces provided.

1 (a) For a spring undergoing elastic change, the force per unit extension of the spring is

known as the force constant k.

Show that the energy stored E in the spring for an extension x of the spring is given

by the expression E = 2

1k x2.

[2]

(b) Fig. 1.1 shows a diagram of a man doing a bungee jump.

Fig. 1.1

The man has a mass of 60 kg and falls a distance of 30 m before the elastic rope attached to him starts to exert any force on him. The force constant of the elastic rope is 90 N m-1. The gravitational potential energy at the bottom of his fall is taken to be zero.

Calculate,

(i) how far the man has fallen from the top when he has maximum kinetic energy,

Distance = ………………… m [2]

4



(ii) the extension of the elastic rope when the man come to an instantaneous rest for the first time.

Extension = ………………… m [2]

(iii) Hence, sketch 2 fully labelled graphs on Fig. 1.2 showing how the kinetic

energy and elastic potential energy vary with the distance fallen. Label your graphs clearly.

Fig. 1.2

[2]

5

[Turn over



2 (a) (i) List all the quantities that determine the state of an ideal gas.

……………………………………………………………………………………….… ……………………………………………………………………………………….… ……………………………………………………………………………………….[1]

(ii) State what is meant by an ideal gas.

……………………………………………………………………………………….… ……………………………………………………………………………………….… ……………………………………………………………………………………….[1]

(b) A rigid storage cylinder contains 6.1 moles of an ideal gas. The gas is at a temperature of 23 °C and a pressure of 5.0 x 107 Pa.

(i) Show that the number of gas atoms in the storage cylinder is 3.67 x 1024.

[1]

(ii) The gas leaks slowly from the cylinder such that, after a time of 35 days, the pressure has reduced by 3.0%. The temperature remains constant.

1. Determine the number of gas atoms that remains in the cylinder.

Number of gas atoms = ………………… [2]

6



2. Calculate the average rate, in atom per second, at which the gas atoms escape from the cylinder.

Average rate of escape = ………………… s-1 [2]

3. Explain why the rate of escape obtained in (b)(ii)2. is an average rate.

……………………………………………………………………………………….… ……………………………………………………………………………………….… …..………..………………………………………………………………………….[1]

3 Fig. 3.1 shows the top view of a current balance where a uniform wire is bent into a

rectangular frame ABCD (50 cm by 10 cm) and placed inside a solenoid. The wire is in

series with a battery of mass 40 g and length h, pivoted at XY such that it is in equilibrium.

The wire is made from a copper wire of mass of 10 g.

(a) For the rectangular frame to be in equilibrium, state the direction of the current in the

solenoid with respect to point P and Q.

………………………………………………………….….……………………………….[1]

(b) The magnetic flux density in the solenoid is 2.0 T and the current flowing through the

wire is 0.5 A.

(i) Calculate the magnitude of the magnetic force experience by the side AD of

the rectangular frame.

Magnetic force = ………………… N [1]

Fig. 3.1

7

[Turn over



(ii) Assuming that the length of the battery h to be negligible, determine the length

l for the rectangular frame to be in equilibrium.

l = ………………… m [2]

(iii) The battery is replaced another identical one such that the current in the frame

increased from 0.5 A to 0.9 A. The mass of the new battery is 50 g. Determine

if the rectangular frame will remain in equilibrium at the pivot point calculated

in (b)(ii).

……………………………………………………………………………………….… ……………………………………………………………………………………….… …..………………………………………………………………………………….[2]

(c) After the rectangular frame achieves equilibrium, the frame is observed to always

topple after some time. State and explain a possible cause for the phenomenon.

……………………………………………………….………………………………………… …………………………………………………………………………………….…………… …………………………………………………………………………………….…………… ………………………………………………………………………………………….……… …………………………………………………….….…………………………………….[2]

8



4 A early model of an atom as illustrated in Fig. 4.1, consists of a uniform distribution of

charge -Q within a sphere of radius R and a point charge of +Q at the centre.

(a) Show that the electric field strength due to the -Q charge at a radius r < R, as shown

in Fig 4.2, can be given by

r

o

rE

3, where ρ is the charge density due to the -Q

charge.

[1]

[2]

(b) State the relation between electric field strength E and potential V.

……………………………………………………….………………………………………… …………………………………………………….….……………………………………..[1]

[2]

(c) Hence or otherwise, sketch a well labelled graph for the variation of the following

quantities with distance r from the centre of the atom,

(i) on Fig. 4.3 (a) : electric potential VN for the +Q point charge [1]

(ii) on Fig. 4.3 (b) : electric potential VC for the -Q spherical charge [2]

(iii) on Fig. 4.3 (c) : electric potential V for the atom [2]

Fig. 4.1

uniform distribution

of charge -Q

uniform distribution of charge -Q

Fig. 4.2

R

r

point charge of

charge Q

9

[Turn over



R R

r

V

0

VC

r

0

Fig. 4.3 (b)

VN

r

0

Fig. 4.3 (a)

Fig. 4.3 (c)

N

10



5 (a) Explain what is meant by

(i) stimulated emission,

………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………….….…………………………….[1]

(ii) and population inversion.

………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………….….…………………………….[1]

(b) “The lower of the two energy levels involved in lasing must be a metastable state”.

Explain the validity of this statement.

……………………………………………………….………………………………………… …………………………………………………………………………………….…………… …………………………………………………………………………………….…………… ………………………………………………………………………………………….……… …………………………………………………….….…………………………………….[2]

(c) By making reference to mobile charge carriers, state and explain the change in

resistivity of the p-n junction when it is changed from unbiased bias to forward bias.

……………………………………………………….………………………………………… …………………………………………………………………………………….…………… …………………………………………………………………………………….…………… …………………………………………………………………………………….…………… …………………………………………………………………………………….…………… ………………………………………………………………………………………….……… …………………………………………………….….…………………………………….[3]

11

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6 The source of electromagnetic radiation of our sun is a nuclear fusion that happens in the core of the sun. The first step of the fusion reaction is to fuse two hydrogen nuclei to form a deuterium nucleus.

2

1 0.42 MeV ep p H e

(The neutrino ( e) has negligible rest mass and a positron (

e ) has the same rest mass

as the electron.)

(a) Explain what is meant by the term nuclear fusion.

………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………….….…………………………………….[1]

(b) (i) Express the binding energy of deuterium in terms of the mass of proton, pm ,

the mass of neutron, nm , and the mass of deuterium,

dm .

…………………………………………….….…………………………………….[1]

(ii) By applying the law of conservation of mass-energy to the above fusion

reaction, determine the binding energy of deuterium. ( 1.00728pm u and

1.00867nm u )

Binding Energy of deuterium = ………………… J [3]

12



(iii) The positron that is produced in the above reaction almost immediately collides with a nearby electron and annihilates, producing two identical photons.

e+ + e- ® 2g

Calculate the frequency of the photons produced.

Frequency = ………………… Hz [2]

13

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7 Carbon dating is a method of determining the age of an organic sample by using the

properties of radiocarbon (14C ), a radioactive isotope of carbon.

Cosmic rays in the upper atmosphere cause nuclear reactions that create 14C . The ratio of

14C to 12C in the carbon dioxide molecules in our atmosphere is currently about

111:7.69 10 . The carbon atoms in all living organisms have this same 14C to

12C ratio

because the organisms continuously exchange carbon dioxide with their surroundings.

When an organism dies, this exchange of carbon dioxide stops and the radioactive 14C that

is in its body decay with a half-life, 12

t , of 5,730 years. Therefore, by measuring the amount

of 14C activity in a material, it is possible to measure its age. Using such technique,

scientists have been able to identify sample of wood, bone and shell as having lived 1,000 to 25,000 years ago. At equilibrium with the atmosphere, 1.0 g of carbon shows an activity of about 13.56 decays

per minute. By comparing the activity rate of a sample, A, we can then determine its

estimated age, t. The activity rate of a sample is given by

12

ln2 t

oA A et

where

(a) Fig. 7.1 shows a list of samples and their estimated age.

Sample Activity / decay per minute Estimated age / years

Sample A 11.51 1,300

Sample B 9.07 3,500

Sample C 5.16 7,500

Sample D 4.35 9,400

Sample E 11,800

Sample F 2.75 13,200

Sample G 1.88 16,800

Fig. 7.1

(i) Complete Fig. 7.1 for Sample E. [1]

14



(ii) Fig. 7.2 shows the value of ln (A / decay per minute) plotted against the

corresponding values of t / number of years.

Fig. 7.2

Complete Fig. 7.2 using your answer obtained from (a)(i) and draw the best fit

line.

[2]

(iii) Using Fig. 7.2, determine the estimated age of a sample that has an activity rate

of 2.10 decay per minute.

Estimated age = ………………… years [2]

15

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(b) An archaeologist recently unearthed a bone sample said to date back to the Yuan

dynasty (1271 – 1368 AD). To determine its authenticity, he measured the rate of decay

of a 1.0 g of processed carbon from the bone sample over five 1-minute intervals during

the day and the result is shown in Fig. 7.3. (Assume that background count has been

accounted for.)

Reading 1 2 3 4 5

Activity / decay per minute 12 13 13 12 11

Fig. 7.3

(i) State a characteristic in Fig 7.3 that shows the decay is a random process.

…………………………………………………………………………………………… …………………………………………………….….……………………………….[1]

(ii) Determine the estimated age of the bone.

Estimated age = ………………… years [3]

(iii) Suggest a possible reason for the estimate in (b)(ii) to be unreliable.

…………………………………………………………………………………………… …………………………………………………….….……………………………….[1]

(iv) If the archaeologist would like to make a conservative estimate of the age of the

bone sample using Fig. 7.3, state and explain qualitatively what should be

done.

…………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………….….……………………………….[2]

16



(c) The mean amount of carbon dioxide in the atmosphere does not stay constant.

Fig. 7.4 shows the variation of monthly mean carbon dioxide measured at Mauna Loa

Observatory, Hawaii, USA (Northern hemisphere). Monthly mean CO2 concentrations

are determined from daily averages for the number of CO2 molecules in every one

million molecules of dried air.

Fig. 7.4

*Moving average values are the average of seven adjacent seasonal cycles centered on the

month to be corrected.

It is observed that the monthly CO2 level varies in a predictable pattern annually: the

CO2 level will reach a maximum around May before declining steadily to a minimum

near October.

Induced emf = ……………. V [1]

(i) State a possible reason for the fluctuation and explain clearly why this has an

impact on the CO2 concentration in the atmosphere.

…………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………….….……………………………….[2]

(ii) Explain how the increase of non-radioactive carbon dioxide in the atmosphere

affects the activity rate of carbon in the atmosphere.

…………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………….….……………………………….[1]

Monthly value

Monthly value

(moving average*)

17

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8 A competition diving board is made of an aluminum extrusion, a single piece of

aluminium that has been heated and pressed. Two hinges connect the board to the

stand, allowing small extensions and the board can form a larger arc. The rubber fulcrum

position can be adjusted via a wheel by the diver.

To achieve a higher trajectory off the board, besides the board material and the relative

distance between the hinges and fulcrum, the diver must “ride the board” by pressing

down on the board with his weight at the precise moment the board flexes down.

Photo: Steve Voellmecke

Design a laboratory experiment to determine the relationship between the maximum

height of a load projected and the distance between the hinges and fulcrum.

The equipment available includes the following:

A 1m diving board model with hinges and movable fulcrum mounted on a stand

Motion sensor, force sensor and data logger

Loads of various masses

Several G-clamps

A vernier calliper

You should draw diagrams to show the arrangement of your apparatus. In your account

you should pay attention to

(a) the equipment you would use for the investigation,

(b) the procedure to be followed,

(c) the control of variables,

(d) any safety precautions,

(e) any precautions that you would take to improve the accuracy of the experiment.

[12]

stand

movable

fulcrum

hinges board

18



Diagram

.…………………...…….…………..……………………………………………………...……………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

19

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.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

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.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

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20



.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

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.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

.…………………...…….…………..……………………………………………………...……………

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.…………………...…….…………..……………………………………………………...……………

……………………………………........…………………………………………..……………………

End of paper

1

2015 JC2 H2 P2 Prelim Exam Mark Scheme

Qn Suggested MS

1 (a) Show linear graph of F vs x and work done = force x displacement

=

2

1F x =

2

1(kx) x

= 2

1k x2

(b)(i) kx – mg = 0 90x=(60)(9.81) x = 6.54 m

Hence distance is 30 + 6.54 = 36.5 m

(ii)

2

1k x2 = m g (30 + x )

2

1(90) x2 = 60 (9.81) (x + 30)

x = 27.4 m

(iii)

2(a)(i) Amount of gas; temperature; pressure and volume

(ii) No intermolecular forces or obeys the equation P V = n R T

(b)(i) n =

AN

N N = (6.1) ( 6.02x1023) = 3.67x1024

(ii)1. 1 2

1 2

P P

n n

Nf = 0.97 ( 3.67x1024 ) = 3.56 x 1024

2. Average rate of escape =

231.1 x 10

35 x 24 x 3600

30 36.5 57.4

2

= 3.64 x 1016 s-1

3. Pressure is higher initially therefore molecules escapes faster initially

3(a) P to Q

(b)(i)

2(0.5)(0.1)

0.1

F BIL

N

(ii) Taking moment about XY,

0.1( ) (0.01)(9.81)( 0.25) (0.04)(9.81)(0.5 )

ACCM CCM

l l l

0.1981 0.024525 0.1962 0.3924

0.5905 0.220725

0.374

l l

l

l m

(iii) increase in ACCM increase in CCM

(0.08)(0.374) (0.01)(9.81)(0.5 0.374)

Frame will not be in equilibrium.

(c) After some time, the wire in the solenoid heats up, thereby increasing its resistance

This result in a reduction of the magnetic force experienced by AD due to a smaller B/(I flowing in the rectangular wire) reducing the anticlockwise moment

4(a)

rr 2

o

3

2

o

o

QE

4 r

4r

3

4 r

r

3

(b) Negative electric potential gradient

(c)(i)

Q

1V

r

(ii) Outside cloud Q

1V

r

Within cloud : Minimum curve with min at centre of cloud

3

(iii) Scalar sum of V+Q and V-Q

Within atom: V increase at an increasing rate towards the centre Beyond radius of atom: 0

5(a)(i) Incident photon interact with the excited atom to bring it to a lower energy state, emitting a coherent photon

(ii) More atoms at excited state than lower energy state/ground state

(b) Upper energy level is metastable to enable population inversion

in order to facilitate stimulated emission for lasing to take place

Lower energy level is usually fast decay to prevent reabsorption of the photons. Therefore the statement is not valid

(c) Mobile electrons in the n-side are repelled by the negative terminal, electrons in the p-side move toward the positive terminal.

The movement causes the depletion region to narrow.

The resistance of the diode decreases, and current flows through the diode.

6(a) Nuclear fusion is the combining of two (or more) light nuclei to produce a heavier nucleus with a large amount of energy released as the nucleus formed has a lower total mass than that of the parent nuclei.

(b) (i) 21

2. p n dHB E m m m c ----------------------------------------- (1)

(ii) By conservation of mass-energy, (in units of J)

2 2 6 19

2 14

2 2 14

0.42 10 1.60 10

6.72 10

2 6.72 10

p p d e

d e

d p e

m m c m m c

m m c

m c m m c

--- (2)

21

2

2 14

.

6.72 10

p n dH

e n p

B E m m m c

m m m c

= 3.57 ´10-13 J (c) 2mec

2 = 2hf

f =9.11´10-31 ´ 3.0 ´108( )

2

6.63´10-34

=1.24 ´1020 Hz

7a)(i)

ln 2( )(11,800)5730

13.56

3.25

t

oA A e

e

(ii) ln(A) ln(3.25) 1.180

Good best fit

(iii) ln(A) ln(2.1) 0.742

15,400 years

4

(b)(i) Activity count is not constant

(ii) Average count = (11+12+12+13+13) / 5 = 12.2

ln 2( )( )5730

12.2 13.56

t

o

t

A A e

e

874t years

(iii) Too few data points

The activity rate at that time may not be the same as the current activity rate

Any other reasonable answer

(iv) He should use the largest activity count to predict the age of the sample

As this will give the sample the youngest possible age

(c)(i) Acknowledge the presence of seasonality

The fluctuations are the result of photosynthetic activity by plants.

(ii) Activity rate will decrease as the proportion of radioactive C will be reduced

5

b

squash ball

hinge movable fulcrum

diving board model

stand

table top

G-clamp

h

A set of measuring tapes mounted against a white wall

fixed load

of 300g G-clamp

6

Basic procedure

Vary b (by changing the movable fulcrum), and measure corresponding h. B1

Diving board can be displaced by either a fixed force (more accurate) or displacement (less accurate)

B1 [2]

Diagram

Reasonable setup where b can be varied and h can be measured D1 [1]

Measurements / Measuring Instruments

1. Measure b using measuring tape/metre rule. M1

2. Measure h using a video camera to take videos, and replay in slow motion to

determine the maximum height using the measuring tapes ( M1 [2]

Control of variables

Same projectile to be used all the time C1

Point of launch of projectile must be constant C1

Keep force to displace the free end of diving board constant C1 [max

2]

Analysis

Establish equation h = k b n and tabulate ln (b) and ln (have) A1

Plot ln (have / m) vs ln (b / m) to determine k (vertical intercept) and n (gradient) A1 [2]

Further details to improve accuracy (include 1m max for safety)

[safety] As the load may drop off accidentally, a small foam mattress is placed below the free end.

S1 [max 1m]

[safety] Look out for the path projected squash ball so as not to be struck S1

Take repeated reading and calculate average max height have, as reading likely to

vary F1

[max 2m]

Carry out preliminary experiment to determine the appropriate projectile to be used F1

Carry our preliminary experiments to estimate the vertical height to mount the measuring tapes, ensure the variation in distance b causes significant maximum

height h, and if not significant to change the choice of b. F1

This paper consists of 27 printed pages

Anglo-Chinese Junior College Physics Preliminary Examination Higher 2

CANDIDATE NAME

CLASS

CENTRE NUMBER

S 3 0 0 4 INDEX

NUMBER

PHYSICS Paper 3 Longer Structured Questions Candidates answer on the Question Paper. No Additional Materials are required

9646/03 28 August 2015

2 hours


Write your Name and Index number in the spaces on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions.

Section B Answer any two questions. You are advised to spend about one hour on each section At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiners’ use only

Section A

1 / 7

2 / 8

3 / 6

4 / 8

5 / 6

6 / 5

Total / 40

Section B

7 / 20

8 / 20

9 / 20

Total / 40

Grand Total / 80

2


For

Examiner’s Use




(1/(36)) 10 F m



rest mass of proton, mp = 1.67 1027 kg molar gas constant, R = 8.31 J K1 mol1

the Avogadro constant, NA = 6.02 1023 mol1 the Boltzmann constant, k = 1.38 1023 J K1

gravitational constant, G = 6.67 1011 N m2 kg2 acceleration of free fall, g = 9.81 m s2

Formulae


v 2 = u 2 + 2as

work done on/by a gas, W = p V

hydrostatic pressure, p = g h


Gm



= 22 xxo

mean kinetic energy of a molecule of an ideal gas

E = 3

2kT




Q

o4



where k = 2

2 )(8

h

EUm


decay constant, = 2

1

6930

t

.

3

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For Examiner’s

Use

Section A

Answer all the questions in the section.

1 A golf ball is hit from a point A on the ground and moves through the air to point B. The

path of the ball is illustrated in Fig.1.1.

Fig. 1.1

The ground slopes downhill with constant gradient. The ball has an initial velocity of

63 m s-1 at an angle of 14° to the horizontal. The ball hits the ground at B after 4.9 s.

Take downwards and to the right directions as positive.

(a) Ignoring air resistance, calculate

(i) the horizontal displacement from A to B,

horizontal displacement = ……………….. m [1]

(ii)

the vertical displacement from A to B,

vertical displacement = ……………….. m [2]

4


For

Examiner’s Use

(iii) the angle of the slope to the horizontal,

= ……………….. ° [1]

(b) In real situation, air resistance provides a force on the ball in opposite direction to its motion.

(i) On Fig. 1.2, sketch a likely path of the ball hit from A when air resistance is

taken into account.

Fig. 1.2

[1]

(ii) Give reason for the shape you have drawn for b(i) for

1.

the position of the highest point, ……………………………………………………………………………………... ……………………………………………………………………………………... …………………………..………………………..………..……………………[1]

2.

2.

The angle at which the ball hits the ground ……………………………………………………………………………………... ……………………………………………………………………………………... ……………………..………………………………..…..………………………[1]

5

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For Examiner’s

Use

2 A 200 kg satellite is orbiting around the Sun with a period of 1 year. The distances

between the satellite, the Earth and the Sun are kept constant as shown in Fig. 2.1. The

distances between the centres of the satellite and Earth, rE is 1.51 x 109 m, and between

the centres of the satellite and Sun, rS is 1.48 x 1011 m. The mass of the Sun, Ms, is

1.99 x 1030 kg.

(a) Given that 1 year has 365.25 days, show that the speed of the satellite is about

2.95 x 104 m s-1.

[1]

Sun

satellite

Earth

Fig. 2.1

6


For

Examiner’s Use

(b) Determine the mass of the Earth, ME.

Mass of Earth, ME = ……………….. kg [4]

(c) If the mass of the satellite was 400 kg instead, by considering the forces acting on

the satellite or otherwise, state and explain changes, if any, to its

(i) orbital radius, and …………………………………………………………………………..………………. ………………………………..………………………………..………………………[2]

[2]

(ii) speed. …………………………………………………………………………..………………. ………………………………..………………………………..………………………[1]

[2]

7

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For Examiner’s

Use

3 A variable resistor of resistance R is connected between the terminals of a battery of emf

E and internal resistance r as shown in Fig. 3.1.

Fig. 3.1

(a)

(i) Show that the current I in the circuit is given by I = E

R + r

[1]

(ii) According to the Maximum Power Theorem, the power dissipated in the variable

resistor reaches a maximum value of 2E

4 r.

Determine the value of R in terms of r when this occurs.

R = ……………….. [2]

8


For

Examiner’s Use

(b) (i) Write down an expression of the efficiency of the transfer of power from the

battery to the variable resistor in terms of R and r.

…………………………..………………………………..……………………………[1]

(ii)

The resistance of the variable resistor is varied such that the energy is

transferred to it at maximum efficiency.

State and explain the choice of R compared to r.

………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. …………………………..………………………………..……………………………[2]

9

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For Examiner’s

Use

4 (a) A 2.0 cm square copper coil is moving on a smooth surface with a constant speed of

1.0 cm s-1 towards 2 uniform magnetic fields as shown in Fig. 4.1. An external force F

is applied on the coil to ensure that the coil moves at a constant speed. The position

of the coil in Fig. 4.1 is taken to be at t = 0.0 s.

The magnetic field in Region A is pointing out of the paper while the magnetic field in

Region B is pointing into the paper. The magnetic flux density of both fields is 1.0 T.

The resistance of the coil is 2.0 x 10-4 Ω.

A short instant later, the side WX of the coil enters Region A.

(i) Calculate the magnitude of the induced emf across WX of the coil.

Induced emf = ……………….. V [1]

(ii) Hence or otherwise, determine the heat dissipated by the coil in one second.

Heat dissipated = ……………….. J [1]

(iii) Determine the magnitude of the force F at this instant.

F = ……………….. N [1]

Fig. 4.1

10


For

Examiner’s Use

(b) Subsequently, the side WX of the coil enters Region B while the side YZ of the coil

remains in Region A. State and explain the magnitude of the induced emf within the

coil at this instance.

………………………………………………………………………………………….……… ………………………………………………………………………………………….……… ……………………………………………..…………….………………………..……..….[2]

(c) Hence or otherwise, plot on, Fig. 4.2, a fully labelled graph of the variation of F with

respect to time from t = 0.0 s till the coil completely emerged from Region B.

[3]

Fig. 4.2

11

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For Examiner’s

Use

5 A small spherical ball bearing of mass m rest at a point P on a smooth curved track, as

shown in Fig. 5.1. The radius of curvature of the track is r.

Fig. 5.1

The ball bearing is moved a small distance to one side and is then released.

(a) Indicate and label in Fig. 5.1 all the forces acting on the ball bearing when it is at the displacement x. [1]

(b) When the ball is at a horizontal displacement x, show that the acceleration of the ball

bearing towards P can be given by

a gx

r

where g is the acceleration due to free fall. State clearly any assumption that you made.

[3]

curved track,

radius r x

12


For

Examiner’s Use

(c) Hence or otherwise, explain why the ball will undergo linear simple harmonic motion. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. …………………………………………………………………………………………………. …………………………………………………………………………………………….…[2]

6 An auto-transformer is a transformer with only one winding in which the primary and

secondary terminals are connected to this shared coil. Fig. 6.1 shows one such example

with three terminals, T1, T2 and T3.

Fig. 6.1

Between terminal T1 and T2, there are 400 turns, and between T2 and T3, there are 250

turns. Any two terminals can be chosen as the terminals for the primary coil or the

secondary coils.

(a) If the auto-transformer is to be used as a step up transformer, list down all the

possible values of s

p

V

V, where pV is the potential difference across the primary coil

and sV is the potential difference across the secondary coil.

Possible values: …………………………………………..[2]

T2 T

1 T

3

13

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For Examiner’s

Use

(b) A 240 V sinusoidal source is connected to terminals T1 and T2. Determine the peak

potential difference across terminals T1 and T3

Peak potential difference across T1 and T3 = ……………….. V [2]

(c) State one advantage of using an auto-transformer over a conventional transformer

that has two separate windings for the secondary and primary coils.

...................................................................................................................................... ………………………………………………………………………………………………… ………………………………………………………………………………………………[1]

14


For

Examiner’s Use

Section B Answer two questions for this section.

7 (a) A smooth sphere A of mass M1 moves along a frictionless floor with speed u1. It

makes a head-on collision with smooth sphere B of mass M2 moving towards A

from the opposite direction with speed u2 as shown in Fig. 7.1.

After collision, A and B move apart in opposite direction with speeds v1 and v2

respectively.

Total momentum of the system is assumed to be conserved.

(i) Apply Newton’s laws of motion to show that expression for the principle of

conservation of momentum for A and B is

1 1 2 2 1 1 2 2M u M u M v M v

[2]

(ii) If the collision in (a) is elastic, and M1 = 9.0 kg, M2 = 1.0 kg, u1 = 300 m s -1,

u2 = 300 m s-1, and the impulse occurs within 0.50 s.

1. Determine the final momenta of A and B.

final momentum of A = ……………….. N s

final momentum of B = ……………….. N s [3]

u1 u2 Fig. 7.1

15

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For Examiner’s

Use 2. Using your answer in (a)(ii)1. or otherwise, explain why, in practice, it is

not possible for the collision in (a)(ii) to be elastic.

................................................................................................................... ………………………………………………………………..………………… …………………………………………………………………..……………[1]

3. On Fig. 7.2 below, sketch well-labelled graphs for the momenta of A

and B before, during and after collision. [1]

(b) For an elastic collision, total momentum and total kinetic energy are conserved and

their numerical values are p and E respectively.

Complete Fig. 7.3 in terms of p and E. [1]

Quantities before

collision during

collision after

collision

Total momentum p p

Total kinetic energy E E

Explain the reasoning for your answers for

(i) Total momentum ........................................................................................................................... ………………………………………………………………………..…………..…… …………………………………………………………………………..……..……[1]

time / s

momentum / Ns

before collision

after collision

during collision

Fig. 7.2

Fig. 7.3

16


For

Examiner’s Use (ii) Total kinetic energy

........................................................................................................................... ………………………………………………………………..…………………..…… …………………………………………………………………..……………..……[1]

(c) A four-engine jet plane of mass 9.0 x 105 kg is flying at 300 m s-1. In each second,

each engine sucks in 220 kg cold still air which combusts with 1.0 kg of liquid fuel,

and the 1600 K exhaust gas exits the nozzle at 450 m s-1. Fig. 7.4 shows one of

the jet engines.

Photo courtesy of Wikipedia

(i) Determine the acceleration of the jet plane.

acceleration = ……………….. m s-2 [4]

(ii) The turbine blades spins to turn the fan (to suck in cold air) and the

compressor (to increase the air pressure). Explain how the hot expanding

gasesin the combustor is able to spin the turbine blades.

…………………………………………………………………………………………. …………………………………………………………………………………………. ………………………………………………………………………………………[1]

direction of motion of plane

Fig. 7.4 A jet engine

compressor turbine

nozzle

mixer

combustor

fan

17

[Turn over


For Examiner’s

Use

(iii) Explain why the exhaust gas must be ejected above a mimimum speed. …………………………………………………………………………………………. …………………………………………………………………………………………. ………………………………………………………………………………………[1]

(d)

A can of soda is on the floor of a jet plane. Fig. 7.5 (a) shows the can of soda when

the jet plane is flying at uniform velocity at a fixed altitude.

Subsequently, the jet plane decelerates uniformly while maintaining its altitude and

path.

(i) 1. Draw the water level in the can on Fig. 7.5 (b). [1]

2. Explain the effect of the deceleration on the water surface.

…………………………………………………………………………………... …………………………………………………………………………………... ..………………………………………………………………………………[1]

(ii) The soda water contains air bubbles rising to the water surface.

1. Explain where the bubbles will collect. …………………………………………………………………………………... …………………………………………………………………………………... ………………………………………………………………………………..[1]

2. Draw the bubbles on Fig. 7.5 (b). [1]

Fig. 7.5 (a)

soda water

direction of motion of plane direction of motion of plane

Fig. 7.5 (b)

18


For

Examiner’s Use

8 (a) In a photoelectric experiment, electrons are emitted from a metal surface when it is

illuminated with suitable electromagnetic radiation. The graph in Fig. 8.1 shows the

stopping potential as a function of the frequency of the incident light falling on a

metal surface.

(i) Determine the photoelectric work function for this metal.

Work function = ……………….. J [2]

(ii) Deduce the Planck’s constant from the graph.

Planck’s constant = ……………….. J s [2]

0.5

0

0 1.0 1.5 2.0 2.5

2.0

4.0

6.0

8.0

0

7.0

5.0

3.0

1.0

Stopping potential / V

frequency / x1015

Hz Fig. 8.1

19

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For Examiner’s

Use

(iii) Explain why the graph does not extend below the x-axis. …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… ………………………..…………………………………………………..................[1]

(b) Fig. 8.2 shows the possible energy levels for an electron in a hydrogen atom. (i) Cool hydrogen gas is irradiated with electromagnetic radiation of wavelength

85.5 nm, and electrons are emitted from the gas. Determine the maximum

kinetic energy of these electrons.

Maximum kinetic energy = ……………….. e V [2]

n = 1

n = 2

n = 3 n = 4 n = 5 n = ∞

energy / eV

-0.85 -1.50

-3.40

-13.60

-0.53 0

Fig. 8.2

20


For

Examiner’s Use

(ii) Instead of irradiating with electromagnetic radiation, the cool hydrogen gas is

now bombarded by a stream of electrons.

The Hα spectral line in the Balmer series is due to the emission of photon as the

electron transits from level n = 3 to the level n = 2.

1.

Determine the minimum potential difference that the bombarding electron

must be accelerated in order for the hydrogen atom to emit the Hα line.

Minimum potential difference = ……………….. V [2]

2. Other than the Hα spectral line, state the number of other possible

transitions.

…………………………………………………………………………………….[1]

3. Calculate the shortest wavelength of the electromagnetic radiation

produced and suggest the type of electromagnetic radiation.

Shortest wavelength = ……………….. m

Type of electromagnetic radiation = ………………………….. [3]

21

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For Examiner’s

Use

(c) An X-rays are produced when electrons hits a gold foil. A plot of the intensity of

emitted X-rays versus their wavelength gives a smooth continuous curve starting

at a minimum wavelength and exhibiting some sharp peaks as shown in Fig. 8.3.

(i) Explain the origin of the smooth continuous curve and the existence of a

minimum wavelength, λmin.

…………………………………………………………………………..…………… …………………………………………………………………………..…………… …………………………………………………………………………..…………… ……………………………………………………………………………..………… ……………………………………………………………………………..………… ……………………………………………………………………………..………… …………………………………………………………………………...……….. [3]

(ii) Given that the minimum wavelength is 5.0 x 10-11 m, calculate the minimum

momentum of the electrons striking the gold foil.

Minimum momentum = ……………….. N s [2]

Relative intensity

λ / pm Fig. 8.3

λmin

22


For

Examiner’s Use

(iii) With increasing wavelengths above this minimum wavelength, a first group

of sharp peaks is seen in the plot of X-ray intensity versus wavelength.

These are known as the characteristics X-rays.

Explain the formation of these characteristics X-rays.

……………………………………………………………………………………….. ……………………………………………………………………………………….. ………………………………………………………………………..……………… ………………………………………………………………………………..……[2]

23

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For Examiner’s

Use 9 (a) State the principle of superposition for waves.

…………………………………………………………………………..……………..………… …………………………………..……………………………………………………..………… …………………………………..……………………………………………………..………… ………………………………………………………………..…………………………...…. [2]

(b) Two identical coherent microwave sources, S1 and S2, are positioned in front of a

screen as shown in Fig. 9.1. They both emit unpolarised microwaves of wavelength

0.26 cm. A microwave detector is used to determine the intensity of the microwave

along the line AB.

S1 and S2 are positioned such that a is 2.50 cm and D is 10.00 cm. In this

configuration, point P is a point of maximum intensity.

Fig. 9.1

(i) State the conditions for S1 and S2 that need to be met in order for the intensity at

point P to be a maximum.

…………………………………………………………………………………..………… …………………………………………………………………………………..………… …………………………………………………………………………………..………… ………………………………………………………………..…………………...…. [2]

S2

S1

P

a

D

Microwave detector

A B Screen

C

24


For

Examiner’s Use (ii) Source S1 is moved further away from the screen (along the dotted line PS1) at

a constant speed of 30 mm s-1.

Determine the frequency at which the intensity detected at P toggles between

high and low intensity.

Frequency = ……………….. [2]

(iii) Source S1 finally stops at point C as shown in Fig. 9.1, which is line with S2.

State why the equation ax

D should not be used to determine the distance

between two successive maxima along AB in such a setup.

…………………………………………………………………………………..………… …………………………………………………………………………………..………… ………………………………………………………………..…………………...…. [1]

25

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For Examiner’s

Use (c) Jane sets up a siren to project a 130 Hz sound wave towards a wall 100.0 m away. A

microphone attached to a data-logger is placed at a distance 5.5 m away from the

siren to detect the sound as shown in Fig. 9.2.

When the siren is first switched on, the amplitude of the sound waves is recorded on

the data-logger. The amplitude of the sound wave is observed to suddenly decrease

after a short time interval of 564 ms.

Fig. 9.2

(i) Determine the wavelength, l , of the sound wave.

l = ……………………….. m [3]

(ii) Explain why the amplitude of the sound wave does not decrease to zero.

……………………………………………….……………………………..…………… ……………………………………………….……………………………..…………… ……………………………………………….……………………………..…………… ……………………………………………….……………………………..…………… ……………………………………………….……………………………..…………… ………………………………………………………………….…………………… [3]

100.0 m

5.5 m

microphone

data-logger siren

(not to scale)

26


For

Examiner’s Use (iii) Calculate the period T of the sound wave.

T = ……………………….. ms [1]

(iv) The data-logger is now replaced with a C.R.O. The maximum voltage of the

sinusoidal wave formed on it is 0.7 mV.

Sketch on Fig. 9.3(a) the expected trace on the C.R.O. screen. The vertical

scale is 0.5 mV cm-1 and the time base is set to 1 ms cm-1.

[2]

(v) The microphone is now moved towards the screen until the next stable

sinusoidal wave is observed on the C.R.O. screen.

Sketch on Fig. 9.3(b) the expected trace on the C.R.O. screen.

[1]

1 cm

1 cm

1 cm

1 cm Fig. 9.3(b)

Fig. 9.3(a)

27

[Turn over


For Examiner’s

Use (d) A parallel beam of white light that consists of wavelengths 400 nm to 700 nm is

incident normally on a diffraction grating. The grating has 300 lines per millimetre.

Deduce, by calculation, whether the second order diffracted beams will overlap with

the third order diffracted beams.

[3]

2015 Prelims H2 P3 (Section A)

1 (a) (i) Horizontal displacement x = 63 cos 14° (4.9) =299.5 m = 300 m

(ii) Vertical displacement

y = -63 sin 14° (4.9) + 2

1(9.81) (4.9)

2

= 43.07 m = 43.1 m (iii)

= tan-1

43.07

299.5= 8.18° above the horizontal

b(i)

(ii) 1 As the ball rises, it experiences a net deceleration greater than g because air resistance is acting in

the same direction as the gravitational force.

2 Angle is smaller with respective to the vertical axis because forward / horizontal velocity is much reduced

2(a)

S

S

11

v r

2r

T

2(1.481 10 )

365.25(24)(60 60)

4 1v 2.95 10 ms

(b) S Em a F F

S E2

S 2 2

S E

S E2

S 2 2

S E

1111 3011 7 2 E

11 2 9 2

G M m G M mm r

r r

G M G Mr

r r

6.67 10 M6.67 10 (1.99 10 )(1.48 0 )(1.99 10 )

(1.48 0 ) (1.51 10 )

11

E

9 2

114E

9 2

6.67 10 M0.00586 0.00606

(1.51 10 )

6.67 10 M1.8 10

(1.51 10 )

24

EM 6.15 10 kg

24 24

EM 6.80 10 kg,6.59 10 kg

(c)1.

S E2

S 2 2

S E

S E2

S 2 2

S E

G M m G M mm r

r r

G M G Mr

r r

Since the force equation is independent of the mass of satellite and only dependent on its period, rS and rE and hence position remain the same

2.

S

2v r

T

From 1, rS remains the same, and T is the same, then v remains the same

3 (a) (i) EI =I2R + I

2r

V=I(R+r)

I = r R

E

(ii)

Power dissipated in R PR= I 2 R = ( r R

E

)2 R

Let ( PR )max =

r 4

E 2

occurs when R = R1

(

r R

E

1)2 R1 =

r 4

E 2

Solving R1 = r (b) (i)

Efficiency = inputpower

outputpower =

T

R

p

P=

E I

RI2

= r R

R

(ii) =

r R

R

=

R

r 1

1

when R is at its maximum. The higher the external load’s resistance

compared to the internal resistance r, the lower the % of power wasted in the internal resistance and hence the higher efficiency.

4(a)(i)

4

(1)(0.02)(0.01)

2 10

Induced emf Blv

V

(ii) 2

4 2

4

4

(1)

(2 10 )(1)

2 10

2 10

VHeat dissipated

R

J

(iii)

4

4

2

2 10(1)( )(0.02)

2 10

2 10

F BIL

N

(b) There is an induced emf of equal magnitude at both WX and ZY but now in opposite polarity, therefore the voltage is doubled. V = 4 x 10

-4 V.

(c)

5(i) Normal contact force N drawn perpendicular to surface of track Force of earth on ball bearing, weight of ball bearing – vertically downwards

(ii) By Newton 2

nd law,

Horizontal net force towards equilibrium (vertical line) F = mg sin

m a = mg sin

a = g sin When is very small, OR When (x/r) is very small

sin , = x

r

a = g sin

= g = - g r

x(-ve sign as x is in opp direction as a)

(iii) Since g and r are constants, hence a is proportional x

The negative sign indicate that a is always directed towards the equilibrium position

6(a)

400

250 OR

8

5 OR 1.6

650

400 OR

13

8 OR 1.625

650

250 OR

13

5 OR 2.6

(b)

Vs

Vp=

650

400

Vs =650

400240( )

= 390 V

Vpeak = 2 Vs( ) = 2 390( )

= 552 V

(c) Less eddy current, shorter core The auto-transformer is physically smaller than the conventional transformer for the same turns

ratio

(Section B)

7. (a) (i) 1 2F F

1 1 1 1 2 2 2 2( M v ) M u M v ( M u )

t t

1 1 2 2 1 1 2 2M u M u M v M v

(ii)

1.

1 2

1 2

(9.0) (300) (1.0) (300) (9.0) v (1.0) v

2700 300 9v v (1)

As collision is elastic,

1 1 2 2

2 1

1 2

relative speed of approach relative speed of separation

u v v u

300 ( 300) v ( v )

600 v v (2)

Solving,

1

1

1

2

v 180 ms ( ve : opp dirn to initial assumed dirn)

v 780 ms

final momentum of A = 1620 Ns

final momentum of B = 780 Ns

2. Loss of energy due to heat/sound

3.

Quantities before

collision during

collision after

collision

Total momentum p p p

Total kinetic energy E < E E

(b)

(i)

No external resultant force throughout, hence total momentum is

conserved throughout.

(ii) During collision, there are internal forces which converts part of the KE

into EPE, and after collision the gain in EPE is converted back into KE.

(c) (i)

Force on air,

airair

air

dmF v u

dt

220 (450 300)

33000 N

Force on fuel,

fuelfuel

fuel

dmF v 0

dt

1.00 (450 0)

450 N

time / s

momentum / Ns

2700

1620

780

300

A

B

0.5 s

By N3L, resultant force on plane,

plane

5

F 4 450 33000

M a 133800

(9.0 10 ) a 133800

2a 0.148 ms

(ii) When fuel combust it becomes high pressure gas, result in high force/high

pressure per unit area on the turbine blades

(iii) Exhaust gas must experience a change in momentum (backwards) so that

the plane can experience the same change in momentum (forward)

(c) (i) 1.

2. Due to its inertia, water moves with a greater velocity than the can, and

hence pushes against the front of the can.

(ii) 1. As water is more massive (denser), it requires a larger pressure

difference to decelerate, thus water pushes against the left wall, and the

air bubbles move to the right wall.

2.

8 (a)(i) 34 15

0 6.63 10 1.25 10hf eV

= 8.3 x 10-19

J (or 5.2 eV)

(ii)

Gradient = 15

15

4.04 10

1.00 10

h = 4 x 10

-15 x 1.6 x10

-19

v

a

v

a

= 6.4 x 10-34

J s

(iii) There is no electron emitted below the work function of the metal and hence zero stopping potential required.

(b)(i)

Energy of incident light = hf = hc

=

34 818

9

6.63 10 3 102.33 10

85.5 10J

= 14.54 eV Maximum KE of electrons = 14.5 eV – 13.6 eV

= 0.94 eV (ii) 1. Energy required for transition from n=1 to n = 3

(-1.50)-(-13.6) eV = 12.1 eV Potential Difference = 12.1 V

(ii) 2. 2 (ii) 3. 34 8

19

6.63 10 3 10

12.1 1.6 10

hc

E

= 103 nm

Ultraviolet

(c)(i) When an electron collides with an atom, it will lose a certain amount of kinetic energy and scattered off at angle. This loss of KE manifests itself as a photon of X-ray that is emitted.

Large numbers of electrons colliding with the atoms lose different amounts of KE that leads to a large number of wavelengths being emitted, resulting in the smooth curve (continuous spectrum).

When the electron loses all its energy upon the first collision, only one wavelength is emitted and that gives the minimum wavelength of the photon emitted

(c)(ii)

2

31 34 8

11

2

2

2 9.11 10 6.63 10 3.0 10

5 10

e

e

p hc

m

m hcp

= 8.5 x 10-23

Ns (c)(iii) The bombarding electron with sufficient energy knocks a deep-lying electron out of the inner shell

of the target atom creating a hole. Electron from a higher energy shell falls to occupy the hole and emits a characteristic X-ray photon.

9(a) The principle of superposition states that the net displacement at a given place and time caused by 2 or more waves which traverse the same space and meet is

the vector sum of the displacement which would have been produced by the individual waves separately at that position and instant of time.

(b)(i) The path difference (S1P – S2P) must be equal to an integer multiple of wavelength, and The two sources must be in phase. (ii) 1 cycle refers to the fringe going from high and low intensity and to high intensity again. For this, S1

will travel one wavelength.

1

2

Distance S travels to go through 1 cycle

0.260 10 m2

3

2

0.260 10Time taken for 1 cycle

30 10

8.67 10 s

d

v

11 28.67 10

11.5 Hz

f T

(Note that the speed of the EM wave is 3 x108 ms

-1, therefore the time taken for the wave to travel

the addition distance is assumed to be negligible) (iii) D, the distance from the source to the screen (or S1P), is not much greater than a, the distance

between the two sources.

( 4D

a => both are same order of magnitude)

(c) (i)

1

Total dist. travelled by waveSpeed of sound,

time

2 100 5.5

0.564

335.1m s

v

335.1

130

v

f

2.58 m

(ii) When the siren sounds, the sound waves is radiated at at angle outwards (not unidirectional), therefore intensity decreases as the sound travlels farther away from the siren.

The sound wave reflects off the wall and returns to Jane’s position. The reflected wave and the wave from the loudspeaker interfere destructively and thus Jane hears a softer sound.

The interference is not completely destructive because the reflected sound wave has a lower intensity than incoming wave due to the waves spreading out.

(iii)

1 1

3

130

7.69 10 s

7.69 ms

T f

(iv)

Fig. 9.4a

Sinusoidal AND correct period (~7.5 boxes). Correct amplitude (~1.4 boxes)

1 cm

1 cm

Fig 9.4b

Period same as Fig 9.4a AND larger amplitude. (any position near the destructive interference point will have a larger amplitude than the minimum.)

(d) (For each order, max and min angle can be determined by max maxsind n or

min minsind n respectively.)

For the second order,

3

9

2,max

2,max

10sin 2 700 10

300

24.8

For the third order,

3

9

3,min

3,min

10sin 3 400 10

300

21.1

Since 2,max 3,min , the two orders overlap.

1 cm

1 cm

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