Anglo-Chinese Junior College
Physics Preliminary Examination
Higher 2
CANDIDATE
NAME
CLASS
CENTRE
NUMBER
INDEX
NUMBER
PHYSICS
9745/01
Paper 1 Multiple Choice
2 Sep 2009
1 hour 15 minutes
Additional Materials: Multiple Choice Answer Sheet
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 circle 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.
This paper consists of 16 printed pages
2
DATA AND FORMULAE
Data
speed of light in free space,
c
= 3.00 × 108 m s−1
permeability of free space,
μo = 4π × 10−7 H m−1
permittivity of free space,
εo = 8.85 × 10−12 F m−1
(1/(36π)) × 10-9 F m-1
elementary charge,
e
= 1.60 × 10−19 C
the Planck constant,
h
= 6.63 × 10−34 J s
unified atomic mass constant,
u
= 1.66 × 10−27 kg
rest mass of electron,
me =
9.11 × 10−31 kg
rest mass of proton,
mp =
1.67 × 10−27 kg
molar gas constant,
R =
8.31 J K−1 mol−1
NA =
6.02 × 1023 mol−1
the Avogadro constant,
= 1.38 × 10−23 J K−1
the Boltzmann constant,
k
gravitational constant,
G =
acceleration of free fall,
g
6.67 × 10−11 N m2 kg−2
= 9.81 m s−2
Formulae
uniformly accelerated motion,
work done on/by a gas,
hydrostatic pressure,
=
2
v
=
W =
p =
s
ut +
1
2
at 2
u 2 + 2as
p ΔV
ρgh
gravitational potential,
φ = −
displacement of particle in s.h.m.,
velocity of particle in s.h.m.,
x
v
Gm
r
= xo sin ωt
= vo cos ωt
= ω xo2 − x 2
resistors in series,
resistors in parallel,
R =
1/R =
electric potential,
V
alternating current/voltage,
transmission coefficient,
x
T
where k
radioactive decay,
x
decay constant,
λ
R1 + R2 + …
1/R1 + 1/R2 + …
Q
4πε o r
= xo sin ωt
∝ exp(−2kd)
8 π 2 m (U − E )
=
h2
= xo exp(−λt)
0.693
=
t1
=
2
2009 H2 9745 Prelim Exam P1
3
1
A cylinder of length L has a circular cross-section of radius R.
The volume V of the cylinder is given by the expression V=π R2L
The volume and length of the cylinder are measured as
V = (15.0 ± 0.5) cm3
and
L = (20.0 ± 0.1) cm
What is the absolute uncertainty associated with the radius, R?
± 0.007 cm
A
2
± 0.009 cm
B
C
± 0.014 cm
± 0.019 cm
D
Fig 2 shows the variation of velocity v of a body with respect to time t.
v / m s−1
4
2
Fig 2
0
1
2
3
4
5
6
8
7
9 t/s
−2
The displacement of the body from t = 0 s to t = 8 s is
A
3
13.0 m
B
14.0 m
C
15.0 m
D
19.0 m
A motor-cycle shown in Fig 3 is taking off horizontally from a platform 1.25 m above the
ground and landing 10 m away. What is the take-off speed?
Fig 3
A
5 m s−1
2009 H2 9745 Prelim Exam P1
B
10 m s−1
C
15 m s−1
D
20 m s−1
4
4
Four forces are applied to a circular object, as shown in Fig 4. Which line in the table
correctly describes the resultant force and resultant torque on the object?
30 N
20 N
Fig 4
20 N
30 N
A
B
C
D
5
Resultant force
zero
non-zero
non-zero
zero
Resultant torque
zero
non-zero
zero
non-zero
Fig 5 shows a uniform beam of length L supported by two forces F1 and F2 at points of
1
1
L and
L from its ends.
8
4
distance
L
1 L
4
1 L
8
Fig 5
beam
F1
F2
The ratio of F1 : F2 is
A
6
B
2:5
3:2
C
D
3:5
When a mass of 4 kg is acted upon by a constant force of 8 N over a time of 4 s, its
rate of change of momentum is
A
7
2:3
2 kg m s−2
B
4 kg m s−2
8 kg m s−2
C
D
16 kg m s−2
Fig 7 shows that momentum of two trolleys, X and Y, just before they collide. The
collision reverses the direction of motion of both trolleys. Just after the collision, the
momentum of X is 4 N s.
24 N s
10 N s
Fig 7
X
Y
The magnitude of the corresponding momentum of Y is
A
10 N s
\
2009 H2 9745 Prelim Exam P1
B
18 N s
C
30 N s
D
38 N s
5
8
Which of the following situation is consistent with Hooke’s law?
A
B
C
D
9
Latent heat of vaporization is the energy required to
A
B
C
D
10
Change in Internal Energy
Increase
Decrease
Increase
No change
Heat is
added to gas
removed from gas
added to gas
removed from gas
Work is done
by gas
on gas
on gas
by gas
A sample of carbon-12 has a mass of 3.0 g.
Which expression gives the number of atoms in the sample?
(NA is the symbol for the Avogadro constant)
A
12
separate the molecules and to force back the atmosphere.
force back the atmosphere to make space for the vapour.
increase the average molecular speed in the gaseous phase compared to the
liquid phase.
separate the molecules of the liquid.
Which of the following is always true for the 1st law of thermodynamics?
A
B
C
D
11
Work done on stretching a metal rod is lost through internal energy in wire.
A spring does not return to its original length when the force applied is released.
A mass attached to a vertical spring is displaced downwards from its equilibrium
position and the spring−mass system performs simple harmonic motion when
mass is released.
A cantilever experiences a crack along its length after its free end is loaded with
a heavy mass.
0.0030 NA
B
0.25 NA
C
3.0 NA
D
4.0 NA
A trolley moves along a track from P to Q, as shown in Fig 12. The trolley has a kinetic
energy of 5 kJ at P. Its potential energy at Q is 40 kJ less than at P. The work it does
against friction from P to Q is 10 kJ.
trolley
P
Fig 12
Q
The kinetic energy of the trolley at Q is
A
13
30 kJ
B
35 kJ
C
45 kJ
D
55 kJ
What is the power required to give a body of mass m a forward acceleration a when it
is moving with velocity v up a frictionless track inclined at an angle θ to the horizontal.
A
C
mavg sin θ
mav + (mgv sin θ )
2009 H2 9745 Prelim Exam P1
B
D
(mav sin θ ) + mgv
(mav + mgv) sin θ
6
14
Which of the following is correct?
Scenario
Situation
A
Roller Coaster
Man at the top of a loop
B
Swinging a stone in vertical
plane with a rope
Swinging a simple pendulum
(mass at one end of string)
with hand
Car at roundabout
Stone is at the bottom
C
D
15
D
Weight of mass
Car making a right turn
Lateral frictional force
at the wheels
The gravitational potential is zero at a point nearer the earth.
The gravitational potential is zero at a point nearer the moon.
The gravitational potential is zero at a point equidistant from the earth and the
moon.
The gravitational potential is non-zero anywhere between the earth and the
moon.
Which of the following is always true about the geostationary satellite?
A
B
C
D
17
Pendulum makes 45o
angle to the vertical
Consider the earth and the moon. Which of the following is correct?
A
B
C
16
Centripetal Force
provided by
Normal Contact force
of seat on man
Tension in rope
It rotates from east to west.
Its period of rotation is one year.
It need not be directly above the equator.
Satellites in a geostationary orbit do not need to have the same mass.
A vertical spring is fixed onto the ground as shown in Fig 17. A sphere is released from
a height and starts to stick onto a top end of a spring of negligible mass at position X.
The spring undergoes maximum compression when the top end is at position Z. The
sphere oscillates with simple harmonic motion about Y with a period of 2.0 s.
Fig 17
X
3.0 cm
5.0 cm
Y
Z
The equation that most correctly describes the motion of the particle is
A
C
x = 3.0 sin π t
x = 3.0 sin 2π t
2009 H2 9745 Prelim Exam P1
B
D
x = 2.0 sin 2π t
x = 2.0 sin π t
7
18
A particle of mass m hung from a vertical spring of force constant k is oscillating with
simple harmonic motion. The maximum displacement above the equilibrium position
is x1, Take the acceleration due to gravity to be g.
The gravitational potential energy at the equilibrium position is U. Acceleration due to
gravity is assumed to be constant.
What are the values of its elastic potential energy and gravitational potential energy at
the maximum displacement below the equilibrium position?
elastic potential energy
gm ⎞
⎛
k ⎜ x1 +
⎟
2 ⎝
k ⎠
1
A
1
B
2
1
19
2
⎛
⎝
gm ⎞
⎛
⎝
gm ⎞
U − mg ⎜ x1 +
U − mg ⎜ x1 +
gm ⎞
⎛
k ⎜ x1 +
⎟
2 ⎝
k ⎠
D
2
2
k x1
1
C
gravitational potential energy
2
⎟
k ⎠
k
⎟
⎠
U − mgx 1
2
k x1
U − mgx 1
System P consist of a block of mass m fixed to a spring of force constant k. System Q
consists of an identical block as P, but is fixed to two identical spring connected in
series, each of force constant k. The lower ends of both springs are fastened to the
ground.
P
Q
P and Q are subjected to oscillating driving forces of the same magnitude and driving
frequency f. Which of the following graphs best represents the variation of amplitude of
oscillation A against driving force f for P and Q?
Given frequency, f =
1
k eff
2π
m
, where keff if the system's effective spring constant.
A
A
A
P
P
f
2009 H2 9745 Prelim Exam P1
P
P
f
f
B
Q
Q
Q
Q
A
A
C
f
D
8
20
At a particular instant, the wave profile of a surface wave on water is as indicated
below.
direction of
wave travel
air
Q
P
O
R
water
Which of the graphs below best represents the acceleration of the water molecules at
a quarter of the period later, taking upward acceleration as positive?
acceleration
A
O
P
Q
P
Q
P
Q
R
P
Q
R
R
acceleration
B
O
R
acceleration
C
O
acceleration
D
O
2009 H2 9745 Prelim Exam P1
9
21
In the figure below, P, Q, R, S, T, U, V are the respective mean positions of the air
molecules at various distances from the source O. The graph shows the
displacements of those air molecules at P, Q, R, S, T, U, V from their respective mean
positions in a longitudinal progressive wave at a particular instant of time. The wave is
moving towards the right and the displacement to the right is taken to be positive.
displacement
distance from O
O
Q
P
R
S
T
U
V
Which one of the following statements is correct?
At the instant shown above,
22
A
points marked P, R, T and V are rarefactions.
B
points marked Q, S and U are compressions.
C
points marked Q and U are rarefactions and the point S is a compression.
D
points marked Q and U are compressions and the point S is a rarefaction.
Visible light has wavelengths between 400 nm and 700 nm, and its speed in a vacuum
is 3.0 x 108 m s−1. What is the maximum frequency of visible light?
A
C
23
B
D
4.3 x 1011 Hz
7.5 x 1014 Hz
A narrow beam of monochromatic light falls at normal incidence on a diffraction grating.
Third-order diffracted beams are formed at angles 45o to the original direction.
What is the highest order of diffracted beam produced by this grating?
A
24
1.2 x 1011 Hz
4.3 x 1014 Hz
3rd
B
4th
C
5th
D
6th
A point charge of charge + Q is placed at X. A second charge of charge − 2Q is
placed at Y.
A
O
B
C
D
Y
X
+Q
− 2Q
What is an estimate of the direction of resultant electric field at O which lies along the
midpoint perpendicular dissector of the line joining XY?
2009 H2 9745 Prelim Exam P1
10
25
Two large parallel plates each at different constant potentials are as shown below.
An electron with kinetic energy 10.0 × 10 −19 J from plate A and moves
perpendicularly towards plate B. Given that the electric field strength between plate
A and B is 50.0 N C−1.
X
B
A
electron
− 5.0 V
+ 5.0 V
At X, which of the following are the values of its electric force F and kinetic energy
KE of the electron?
F
26
KE
A
8.0 × 10−18 N
6.00 × 10−19 J
B
1.6 × 10−18 N
6.00 × 10−19 J
C
8.0 × 10−18 N
16.0 × 10−19 J
D
1.6 × 10−18 N
16.0 × 10−19 J
Four point charges are fixed at the corners of a square of side length L.
+Q
− 2Q
− 4Q
+ 3Q
What is the electric potential at the centre of the square?
A
−Q
2 π ε 0L
2009 H2 9745 Prelim Exam P1
Q
B
8 π ε 0L
Q
C
8 π ε 0 L2
D
− Q2
2 π ε 0L
11
27
The filament lamp L is connected to a battery of e.m.f. E and internal resistance r.
The lamp has a resistance R when working. What fraction of the power supplied by
the battery goes to the lamp?
L
R
E, r
A
28
R
r
B
R+r
r
C
R2
R
R+r
D
(R + r )
2
The resistance of cylinder 10.0 cm long and having a cross-sectional area of
2.00 x 10−4 m2 is 1.41 x 10−5 Ω.
A list of material and its resistivity is given below. The material of the cylinder
could be
A
B
C
D
29
Material
Resistivity / 10− Ωm
Silver
Copper
Gold
Aluminium
1.59
1.70
2.44
2.82
8
A circuit containing four resistors is connected across a 12 V supply with negligible
resistance as shown.
What are the resistances R1 and R2?
A
B
C
D
R1 / Ω
1.5
R2 / Ω
4.5
2.0
2.0
4.5
2.0
6.0
4.5
2009 H2 9745 Prelim Exam P1
12
30
A sinusoidal current of peak value IO dissipates power in a resistor at a mean rate P.
What are the values of the root mean square current in the resistor and the maximum
instantaneous power dissipated?
A
B
C
D
31
root mean square current
0
0
I0
2
I0
2
maximum power
2P
2P
2P
2P
The diagram below shows a mass spectrometer in which positive ions of different
masses and charges pass through slits S1, S2 and S3 before entering the main
chamber. Between S2 and S3 they pass through a region with both magnetic and
electric fields, the intensity of which may be varied. In the main chamber, only a
constant magnetic field is applied.
Which is of the following statements is incorrect?
A
the magnetic and electric fields between S2 and S3 are mutually perpendicular.
B
ions arriving at point P have the same charge per unit mass.
C
the trajectories of the ions in the main chamber all have the same radii.
D
all ions from slit S3 enter the main chamber with the same velocity.
2009 H2 9745 Prelim Exam P1
13
32
A triangular loop of wire is rotating at a constant angular speed about an axis in a
uniform magnetic field. The magnetic field is directed out of the plane of the page. At
time t = 0 s, the plane of the loop is perpendicular to the magnetic field and side LM is
moving into the page.
L
M
Which graph best represents the variation of the magnetic flux through the loop with
time?
φ
φ
t
0
t
0
A
B
φ
φ
t
0
C
2009 H2 9745 Prelim Exam P1
t
0
D
14
33
A square coil of cross sectional area A and N turns is placed with its plane
perpendicular to a magnetic field of flux density B as shown below. The coil is rotated
180° about axis XY in a time of 2 seconds, so that its plane is once again
perpendicular to the magnetic field. The average induced e.m.f. in the coil is given by
X
B
Y
A
34
NBA
B
2NBA
C
NBA
2
D
0
During a science practical assessment (SPA) task to investigate a mini-transformer, a
student used the circuit shown below to take measurements. Two of the original entries
in the student’s results are missing as shown:
Vp / V
I p / mA
N p turns
Vs / V
I s / mA
Ns turns
120
1.0
?
?
25
25
Assuming the transformer was 100% efficient, what are the missing results?
A
B
C
D
35
N p turns
Vs / V
625
1
625
1
3000
3000
4.8
4.8
A metal surface in an evacuated tube is illuminated with monochromatic light causing
the emission of photoelectrons which are collected at an adjacent electrode.
If the experiment were to be repeated with light of half the intensity but the same
wavelength, how would the photocurrent I and stopping potential V be affected?
A
B
C
D
I halved, V doubled
I halved, V unchanged
I unchanged, V halved
I halved, V halved
2009 H2 9745 Prelim Exam P1
15
36
Arrange the following in the order of increasing wavelengths:
1.
2.
3.
4.
A
37
An electron moving through a potential difference of 60.0 V
A proton with a kinetic energy of 500 eV
An electron moving with a speed of 107 m s−1
A photon with an energy of 3.0 eV
4, 1, 2, 3
B
4, 3, 2, 1
C
2, 3, 1, 4
D
3, 2, 4, 1
In a He-Ne laser, when a metastable helium atom and neon atom in ground state
collides, the excitation energy of the helium atom is often transferred to the neon atom.
This excites the neon atoms and produces a population inversion.
Which neon energy level diagram correctly shows the excitation of the neon atoms by
the helium atoms, and the subsequent production of red laser light?
spontaneous emission
stimulated
emission
excitation
spontaneous emission
stimulated
emission
excitation
A
B
stimulated emission
spontaneous emission
stimulated
emission
excitation
C
2009 H2 9745 Prelim Exam P1
spontaneous
emission
excitation
D
16
38
39
Which is the following statement is incorrect?
A
in an intrinsic semiconductor, the size of the band gap is about 0.8 eV.
B
when not placed in contact, both p-type and n-type semiconductors have no net
charges on them.
C
in an n-type semiconductor, doping with donor atoms introduces an additional
donor level just right above the valence band.
D
the depletion region widens when a p-n junction diode is reverse biased.
A deuteron, the nucleus of a deuterium atom, consists of a proton and a neutron.
Given the following information:
1 u = 931 MeV
Mass of deuteron
= 2.013553 u
Mass of proton
= 1.007276 u
Mass of neutron
= 1.008665 u
The binding energy of the deuteron in MeV is
A
40
1.876
B
2.223
C
2.388
D
4.029
A scientist wanted to find out the age of a sample of rock.
The isotope Potassium-40, present in many rocks, slowly undergoes radioactive decay
to form Argon-40. When the rock was formed the Potassium-40 isotope was trapped in
the rock and there was no Argon-40. All the Argon-40 formed by the Potassium-40
decay also stayed trapped in the rock.
The scientist found that the rock contained 3 times more Argon-40 than Potassium-40.
What fraction of the original Potassium-40 is left in the rock?
A
1
4
B
1
3
C
End of paper
2009 H2 9745 Prelim Exam P1
1
2
D
3
4
Anglo-Chinese Junior College
Physics Preliminary Examination
Higher 2
CANDIDATE
NAME
CLASS
CENTRE
NUMBER
INDEX
NUMBER
PHYSICS
9745/02
Paper 2 Structured Questions
26 Aug 2009
1 hour 15 minutes
Candidates answer on the Question Paper.
No Additional Materials are required
READ THESE INSTRUCTIONS FIRST
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.
This paper consists of 14 printed pages
For Examiners’ use
only
1
/ 6
2
/ 9
3
/ 8
4
/ 7
5
/ 8
6
/ 7
7
/ 15
Total
/ 60
2
DATA AND FORMULAE
Data
speed of light in free space,
c =
3.00 × 108 m s−1
permeability of free space,
μo = 4π × 10−7 H m−1
permittivity of free space,
εo = 8.85 × 10−12 F m−1
(1/(36π)) × 10−9 F m−1
elementary charge,
e
= 1.60 × 10−19 C
the Planck constant,
h
= 6.63 × 10−34 J s
unified atomic mass constant,
u
= 1.66 × 10−27 kg
rest mass of electron,
me =
9.11 × 10−31 kg
rest mass of proton,
mp =
1.67 × 10−27 kg
molar gas constant,
R =
8.31 J K−1 mol−1
NA =
6.02 × 1023 mol−1
the Avogadro constant,
= 1.38 × 10−23 J K−1
the Boltzmann constant,
k
gravitational constant,
G =
acceleration of free fall,
g
6.67 × 10−11 N m2 kg−2
= 9.81 m s−2
Formulae
uniformly accelerated motion,
work done on/by a gas,
hydrostatic pressure,
=
2
v
=
W =
p =
s
ut +
1
2
at 2
u 2 + 2as
p ΔV
ρgh
gravitational potential,
φ = −
displacement of particle in s.h.m.,
velocity of particle in s.h.m.,
x
v
Gm
r
= xo sin ωt
= vo cos ωt
= ω xo2 − x 2
resistors in series,
resistors in parallel,
R =
1/R =
electric potential,
V
alternating current/voltage,
transmission coefficient,
x
T
where k
radioactive decay,
x
decay constant,
λ
R1 + R2 + …
1/R1 + 1/R2 + …
Q
4πε o r
= xo sin ωt
∝ exp(−2kd)
8 π 2 m (U − E )
=
h2
= xo exp(−λt)
0.693
=
t1
=
2
2009 H2 9745 Prelim Exam P2
3
For
Examiner’s
Use
Answer all the questions in the spaces provided.
1 (a)
Define acceleration.
[1]
(b)
A child is jumping on the trampoline as shown in Fig 1.1. The variation of the
velocity v of the child with time t is shown in Fig 1.2. The downward direction is taken
to be the positive displacement.
v / m s−
1
O
A
B
D
t/s
C
Fig 1.1
Fig 1.2
State the child’s position and direction of motion at points O, A, B, C and D in the
table below.
Points
Child’s position
Child’s direction of motion
O
A
B
C
D
[5]
2009 H2 9745 Prelim Exam P2
For
Examiner’s
Use
4
2
Fig. 2.1 shows a section of an atmosphere which contains doubly charged positive ions
at their respective equilibrium positions. An electromagnetic wave is travelling through
from right to left, causes the ions to oscillate with simple harmonic motion. At an instant
of time t1, the wave profile in that region is as shown.
wave profile at instant time t1
5.0 μm
P
distance from O/cm
Q
O
0
1
Fig 2.1
(a)
2
3
4
5
6
7
The wave profile in the region at an instant of time t1
Are the positive ions undergoing free oscillations or forced oscillations? Give your
reasoning.
[2]
(b)(i)
What is the velocity of the wave?
[1]
(ii) At instant of time t1, what is the velocity of the positive ions at P?
(c)
magnitude of velocity =
m s−1
direction of velocity =
[3]
Due to the electric force on the ions by electromagnetic waves, the amplitude of each
positive ion is 5.0 μm.
What is the acceleration of an ion when it is displaced upwards by 3.0 μm?
2009 H2 9745 Prelim Exam P2
magnitude of acceleration =
m s−2
direction of acceleration =
[3]
5
3 (a)
For
Examiner’s
Use
Write down the equation that defines magnetic flux density in terms of the force on a
current carrying conductor. State the meaning of each term used.
[2]
(b)
Fig 3.1 shows two-current carrying conductor X and Y.
Fig 3.1
The current in each wire is 18 A. The wires are parallel to each other and are 3.0 cm
away from each other.
(i)
State the direction of the magnetic field at Y due to the current in wire X.
Direction is
[1]
(ii) Draw an arrow on Fig 3.1 to show the direction of the magnetic force experienced
by wire Y. Label this force F.
[1]
2009 H2 9745 Prelim Exam P2
For
Examiner’s
Use
6
(iii) Fig 3.2 shows how the magnetic flux density B, due to the current carrying wire X
varies with distance r from the centre of the wire.
Fig 3.2
Using information provided from Fig 3.2,
1.
show that the magnetic flux density B is inversely proportional to the distance
d from the centre of the wire.
[2]
2.
determine the force acting on a 0.25 m length of the wire Y when the wires are
3.0 cm apart.
force =
2009 H2 9745 Prelim Exam P2
N [2]
7
4
Fig 4.1 below shows some of the energy levels (measured in electron-volts) of the
hydrogen atom.
Energy/ eV
4
−0.85
3
−1.52
2
−3.41
1
−13.64
Fig 4.1
(a)
State and explain which transitions would be observed if cool hydrogen vapour is
bombarded with
(i) electrons of kinetic energy 12.2 eV
(ii) photons of energy 12.2 eV
[3]
A metal plate with a work function of 2.70 eV is illuminated with photons of the
electromagnetic radiation emitted when a hydrogen atom (with energy levels of
Fig 4.1) undergoes a transition from its first excited level to its lowest level.
(b)
(i)
Determine the maximum speed with which a photoelectron leaves the surface of
the plate.
Maximum speed =
m s−1 [2]
(ii) Hence calculated the minimum de Broglie wavelength associated with the
photoelectrons that leave the surface of the plate.
Minimum de Broglie wavelength =
2009 H2 9745 Prelim Exam P2
m [2]
For
Examiner’s
Use
For
Examiner’s
Use
8
5
Heisenberg’s position-momentum uncertainty principle can be expressed in the form
Δx Δp ≥
h
2
where Δx and Δp are the uncertainty in position and momentum respectively.
(a)
A neutron is confined within an atomic nucleus of size 1.0 x 10−14 m. Taking the
uncertainty in the position of the neutron to be equal to the size of the nucleus,
calculate the minimum uncertainty with which the velocity of the neutron can be
simultaneously measured.
m s−1 [3]
minimum uncertainty in velocity =
(b)
In quantum mechanics, the wavefunction ψ ( x ) of an electron describes its wavelike
properties at the subatomic scale. State the physical significance of the expression
⏐ψ(x)⏐ for region Δx
2
[1]
(c)
Explain what is meant by quantum tunneling.
[2]
(d)
Fig 5.1(a) shows a thin potential barrier and Fig 5.2(b) shows a thick potential barrier.
incident
beam
incident
beam
Fig 5.1(a)
Fig 5.1(b)
On the diagrams in Fig 5.1 sketch clearly the wavefunction of an electron as it
tunnels through the thin barrier in Fig 5.1(a) and the thick barrier in Fig 5.1(b).
Assume that the electron travels from left to right.
[2]
2009 H2 9745 Prelim Exam P2
9
6 (a)
(i)
For
Examiner’s
Use
Outline briefly the experimental evidence provided by the α−particle scattering
experiment that an atom
has a very small nucleus,
[1]
(ii) has a charged nucleus.
[1]
An α−particle of initial energy 9.6 x 10−13 J approaches a gold ( 197
79 Au) nucleus such
O
that its angle of deviation is 180 .
(b)
(i)
Describe the energy change that takes places as the α−particle approaches the
gold nucleus.
[1]
(ii) The gold nucleus and the α−particle may be assumed to behave as point charges.
Determine the distance of closest approach of the α−particle to the nucleus.
distance =
(c)
m [2]
A Greenpeace article includes the following statement.
‘Existing British nuclear power stations will leave a legacy of half a million tonnes of
nuclear waste that the government has no idea how to dispose of safely. This waste
will remain a threat to our health and the environment for a million years.’
Explain why nuclear waste is hazardous.
[2]
2009 H2 9745 Prelim Exam P2
10
7
A compact disc (CD) is made from a small piece of clear polycarbonate plastic of
1.2 mm thick and a radius of 68 mm.
During manufacturing, the plastic is impressed with microscopic long and short bumps
arranged in a single, continuous and long spiral track from inside of the disc to outside.
The spiral track occupies the surface of the aluminium disc between 23 mm and
60 mm from the centre.
A thin, highly reflective aluminium layer is sputtered onto the disc. Then a thin acrylic
layer is sprayed over the aluminium. The label is then printed onto the acrylic. The
bumps in the track are approximately 500 nm wide, average length of 830 nm, 125 nm
high with 1600 nm separating one track from the next.
Large amount of digital data which is represented by binary code in combinations of 0’s
and 1’s are encoded along the track. Surrounding the bumps, the flat aluminium
surface is called land.
label
acrylic
aluminium
125 nm
polycarbonate
plastic
2 lands between
a bump
2 bumps
Fig. 7.1 Side view of cross-section of a part of a track
lands between bumps (along a track)
track
lands
between
tracks
track
bumps along a track
Fig. 7. 2
Plan view of lands and bumps as seen from playing side
2009 H2 9745 Prelim Exam P2
11
1600 nm
diffraction
grating
laser
125 nm
500 nm
830 nm
Fig. 7.3 Dimensions of tracks and bumps
Fig. 7.4 CD player tracking
One of the hardest job of a CD player is to keep the laser beam centered on the spiral
track. One method is to split the beam using a diffraction grating into say 3 beams. The
central maximum is centered on the track and the first-order maximas are tracking
beams. Normally, the reflected intensity from the lands on either side is given a ‘1’, if
one of the tracking beams encounters the bumps in an adjacent track, the change in
intensity will cause the position of the laser to be corrected.
direction of
motion of laser
tracking motor
drive motor rotates
the disc
laser beam
and pickup
Fig. 7.5
Reading the CD
When data is read, the laser moves from the centre to the outer edge of the disc. The
motor spins the CD at very high angular speeds of between 200 to 500 rpm. As the
laser moves outward at a very low speed from the center of the disc, the bumps move
past the laser at high linear speeds.
2009 H2 9745 Prelim Exam P2
12
As the laser is tracking the spiral of data using the bumps, hence there cannot be
extended gaps where there is no bump. To read the CD, the laser beam passes
through the plastic layer, reflects off the aluminium layer and hits an opto-electronic
device that detects changes in reflected light. The laser beam is wide enough that
when it reflects from a pit, part of it also reflects off the land on either side of the track.
The height of the bumps must be made so that the light reflected from the bump
interferes destructively with the light that reflected from the land (between the tracks) to
produce a minimum intensity and thus a ‘0’. On the other hand, when the laser beam
that hits a land (along the track) interferes constructively with the light reflected from
the land (between the tracks) a maximum intensity is produced, and thus a ‘1’. The
changes between the two intensity levels represent the binary digits, 0’s and 1’s.
(a)(i)
What is the purpose of the aluminium layer?
[1]
(ii) What is the purpose of the acrylic layer?
[1]
(b)
A laser beam falls on a small part of the playing surface of the CD. Beams are
reflected at 29.20 and 74.50 to the normal, as well as in the normal direction itself.
playing side
of the CD
0
74.5
29.20
Fig. 7.6 Laser beam at normal incidence
(i)
Show that the wavelength of the laser beam is 780 nm.
wavelength =
2009 H2 9745 Prelim Exam P2
[2]
13
(ii) The spiral track only occupies a certain area of the disc. Show that the length of
the spiral track is about 4.6 km.
length =
km [2]
(iii) If the average spacing of the ‘bumps’ along the spiral is 830 nm, estimate the
total number of ‘bumps’ on the disc.
number of ‘bumps’ =
(iv)
[1]
If the laser beam is replaced by a beam of white light, why are coloured
spectrum observed?
[1]
(v)
Fig. 7.7 is a copy of the disc in Fig. 7.6. On Fig. 7.7 in sectors P and Q on the
disc, sketch and label the components of colours. You can mark the red end
with ‘R’ and the blue with ‘V’.
sector Q
sector P
white light
[1]
Fig. 7.7
2009 H2 9745 Prelim Exam P2
14
(c)
As the laser pickup moves outwards, the angular speed of the disc decreases.
What is the reason for this?
[2]
(d)
(i)
In the case of a standard digital versatile disc (SD DVD), there can be singlelayer as well as double-layer and single-side and double side. For double-layer,
the outer layer is made of semi-reflective gold layer, to allow the laser beam to
penetrate to reach the inner layer which is made of reflective aluminium layer.
The laser used to read a compact disc (CD) has a wavelength of 780 nm, while
the laser used to read a DVD has a wavelength of 650 nm. How does this make
it possible for a DVD to hold more information than a CD?
[1]
(ii)
Why is the capacity of the DVD not doubled when a whole second layer is
added?
[1]
(e)
A Blu-ray disc uses a laser of wavelength 405 nm. What is a possible height of
the bump for data to be read correctly?
height of ‘bumps’ =
End of paper
2009 H2 9745 Prelim Exam P2
nm [2]
Anglo-Chinese Junior College
Physics Preliminary Examination
Higher 2
CANDIDATE
NAME
CLASS
CENTRE
NUMBER
INDEX
NUMBER
PHYSICS
9745/03
Paper 3 Longer Structured Questions
28 Aug 2009
2 hours
Candidates answer on the Question Paper.
No Additional Materials are required
READ THESE INSTRUCTIONS FIRST
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
/ 9
2
/ 12
3
/ 8
4
/ 11
Section B
This paper consists of 19 printed pages
5
/ 20
6
/ 20
7
/ 20
Total
/ 80
2
DATA AND FORMULAE
Data
speed of light in free space,
c
= 3.00 × 108 m s−1
permeability of free space,
μo = 4π × 10−7 H m−1
permittivity of free space,
εo = 8.85 × 10−12 F m−1
(1/(36π)) × 10−9 F m−1
elementary charge,
e
= 1.60 × 10−19 C
the Planck constant,
h
= 6.63 × 10−34 J s
unified atomic mass constant,
u
= 1.66 × 10−27 kg
rest mass of electron,
me =
9.11 × 10−31 kg
rest mass of proton,
mp =
1.67 × 10−27 kg
molar gas constant,
R =
8.31 J K−1 mol−1
NA =
6.02 × 1023 mol−1
the Avogadro constant,
= 1.38 × 10−23 J K−1
the Boltzmann constant,
k
gravitational constant,
G =
acceleration of free fall,
g
6.67 × 10−11 N m2 kg−2
= 9.81 m s−2
Formulae
uniformly accelerated motion,
work done on/by a gas,
hydrostatic pressure,
=
2
v
=
W =
p =
s
ut +
1
2
at 2
u 2 + 2as
p ΔV
ρgh
gravitational potential,
φ = −
displacement of particle in s.h.m.,
velocity of particle in s.h.m.,
x
v
Gm
r
= xo sin ωt
= vo cos ωt
= ω xo2 − x 2
resistors in series,
resistors in parallel,
R =
1/R =
electric potential,
V
alternating current/voltage,
transmission coefficient,
x
T
where k
radioactive decay,
x
decay constant,
λ
R1 + R2 + …
1/R1 + 1/R2 + …
Q
4πε o r
= xo sin ωt
∝ exp(−2kd)
8 π 2 m (U − E )
=
h2
= xo exp(−λt)
0.693
=
t1
=
2
2009 H2 9745 Prelim Exam P3
3
For
Examiner’s
Use
Section A
Answer all the questions in this section.
It is recommended that you spend about one hour on this section.
1(a)
Fig 1.1 shows two charged parallel plates Y and Z which are 15 mm apart and
each having a length of 30 mm.
Plate Y
+1000 V
P
7.5 mm
B
15 mm
Fig 1.1
Plate Z
Q
−400 V
30 mm
(i) In Fig 1.2 draw lines to show the electric field between the plates.
+1000 V
Plate Y
Fig 1.2
Plate Z
−400 V
[1]
(ii) Sketch in Fig 1.3, the variation of the electric potential V along PQ. Label on the
graph the position of zero electric potential as A.
V
Fig 1.3
0
P
X
Q
State the value of electric potential corresponding to position B.
electric potential at B =
2009 H2 9745 Prelim Exam P3
V
[3]
4
An electron traveling at a speed of 3.2 × 107 m s−1 in a horizontal path enters the
electric field between the two parallel plates. You may assume that the plates are
in a vacuum and there is no electric field outside the plates.
(b)
(i)
Show that the magnitude of the electric field strength between the plates is
9.33 x 104 V m−1.
[1]
(ii) Show that the acceleration of the electron whilst in the field is 1.64 × 1016 m s−2
and state the direction of the acceleration.
[2]
(iii) Calculate the time taken by the electron to pass through the electric field hence
or otherwise, explain whether the electron would leave the parallel plates.
time taken =
s
[2]
2009 H2 9745 Prelim Exam P3
For
Examiner’s
Use
5
2 (a)
For
Examiner’s
Use
A balloon contains 0.40 mol of ideal gas A at 27 OC. The average kinetic energy of
a molecule of an ideal gas is given by
(i)
3
2
kT.
Compute N, the number of molecules of gas A in the balloon,
number of molecules =
[2]
(ii) Calculate the average kinetic energy of a molecule of gas A in the balloon,
average kinetic energy =
J [2]
(iii) Show that the total internal energy of the molecules of gas A in the balloon is
1500 J (to 2 significant figures).
[1]
(b)
The temperature of the molecules of gas A in the balloon is increased. Assume
that the volume of the balloon remains constant.
(i) Explain how this increase in temperature affects the speed of the molecules
of gas A.
[3]
(ii) State and explain using the kinetic theory, the effect this increase in
temperature has on the pressure of the gas A.
[4]
2009 H2 9745 Prelim Exam P3
6
3
Long gas steel pipeline needs regular checks for corrosion and this could be done
using an intelligent inspection device.
The device has magnetic field detectors (the inductive coil sensors) placed between
two sets of very powerful magnets. The magnets have steel brushes to make sure
they have very good contact with the steel wall of the pipeline. The magnetic flux, φ,
remains within the pipe unless there is a crack or an open gap in the wall of pipe.
Where there is damage to the wall of the pipeline, magnetic flux 'leaks out', as
shown in Fig 3.1.
gap
magnetic
field lines
pipe walls
Fig 3.1
The graph in Fig 3.2 shows the variation of magnetic flux leakage with distance from
the centre of an open gap in the pipe wall.
Magnetic flux leakage, φ / x 10− Wb
6
2.0
1.5
1.0
0.5
0.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
Distance / mm
horizontal centre position of gap
Fig 3.2
(a)(i)
The inspection device is moving at a speed of 3.0 m s−1. Calculate the time
taken for the device to move 2.0 mm along the pipe.
time taken =
2009 H2 9745 Prelim Exam P3
s [1]
For
Examiner’s
Use
7
(ii) The coil in the magnetic detector has 5000 turns and a cross sectional area of
5 x 10−6 m2. Use the graph in Fig 3.2 to calculate the EMF induced across the
coil of the detector at the position –2 mm from the centre of the open gap.
induced EMF =
(iii)
V [3]
Explain what the induced EMF at the instant the detector is directly over the
centre of the crack is (i.e. at position 0 mm).
[1]
(b)
In Fig 3.3, sketch a graph showing how the induced EMF across the detector coil
changes as it moves past the crack from position – 3.5 mm to + 3.5 mm.
induced EMF / V
−4
−3
−2
−1
0
1
2
3
4
distance /mm
[3]
Fig 3.3
2009 H2 9745 Prelim Exam P3
For
Examiner’s
Use
8
4
In scientific research, spectroscopists often use the emission line spectrum of gases
to uniquely identify the elements that constitute the gases. The emission line
spectrum of hydrogen gas is shown in Fig 4.1.
Fig. 4.1
(a)
Using the concept of electron energy levels in atoms, explain how an emission
line spectrum is formed.
[2]
(b)
Fig 4.2 below represents the lowest energy levels of the electron in a hydrogen
atom, with the principle quantum number n and the corresponding values of
energy associated with each level shown.
− 0.54 eV
− 0.85 eV
− 1.51 eV
n=5
n=4
n=3
− 3.40 eV
n=2
n =1
− 13.6 eV
Fig. 4.2
(i)
Calculate the longest possible wavelength of the spectral line observed when
an electron undergoes a transition from the energy levels shown in Fig 4.2 to
the ground state (n = 1).
wavelength =
2009 H2 9745 Prelim Exam P3
m [3]
For
Examiner’s
Use
9
(ii) State what happens when an electron in the ground state of a hydrogen atom
absorbs 13.6 eV of energy.
[1]
(c)
The electronic transition in part (b)(i) is an example of spontaneous emission.
In contrast, in lasers the dominant process that leads to that formation of a
well-collimated intense beam is stimulated emission. The word LASER is an
acronym for Light Amplification by Stimulated Emission of Radiation.
By drawing a suitable energy level diagram, explain the process of stimulated
emission.
[3]
(d)
A typical X-ray spectrum is shown in Fig 4.3.
Fig. 4.3
Region Y
Explain how the continuous region indicated by Y in Fig 4.3 is formed.
[2]
2009 H2 9745 Prelim Exam P3
For
Examiner’s
Use
10
For
Examiner’s
Use
Section B
Answer two questions from this section.
5
The diagram below shows a cylinder of mass m and uniform cross-sectional area A,
immersed in a fluid of density ρ. In Fig. 5.1, the cylinder is floating in equilibrium with
length l immersed in the fluid.
Fig. 5.1
(a) (i)
State Archimedes’ principle.
[1]
(ii) By using the principle of floatation, express the weight mg of the cylinder in
terms of l, A, ρ and g. State your reason/s clearly.
[3]
(b)
Fig 5.1 shows the cylinder being depressed vertically downwards an additional
distance x from its equilibrium position so that its new length immersed in the fluid
is now (l + x). The cylinder is then released and is observed to oscillate vertically.
(i)
Show that the new upthrust acting on the cylinder when it is depressed by an
addition distance x is given by the expression (l + x)Aρg. State your reason/s
clearly.
[1]
2009 H2 9745 Prelim Exam P3
11
For
Examiner’s
Use
(ii) By taking the net force on the cylinder to be acting vertically downwards, write
down the appropriate equation relating net force to the mass and acceleration
of the cylinder, and show that its acceleration, a, is related to the displacement
from equilibrium position, x, by the equation
Aρ g
a = −(
)x
m
[3]
(iii) By using the result of part (b)(ii) or otherwise, explain why the cylinder
oscillates with simple harmonic motion.
[2]
(c)
The following graph shows the variation with time t of the displacement x of the
cylinder as measured from its equilibrium position.
Fig 5.2
A student claims that the curve may be described by the equation
x = x0 sin ωt
Identify two features of Fig. 5.2 which show that the student’s claim is incorrect.
1.
2.
[2]
2009 H2 9745 Prelim Exam P3
12
(d)
For
Examiner’s
Use
Calculate, using the data from Fig. 5.2,
(i) the angular frequency of the oscillations,
angular frequency =
rad s−1 [2]
(ii) the magnitude of the acceleration of the cylinder at t = 1.5 s.
acceleration =
(e)(i)
m s−2 [2]
Explain what is meant by damping.
[2]
(ii) Suggest two ways in which the damping of the cylinder’s oscillations can be
reduced.
[2]
2009 H2 9745 Prelim Exam P3
13
6 (a)
For
Examiner’s
Use
In the circuit shown in Fig 6.1, the potential difference of the battery is 5 V.
Assume that the battery has no internal resistance.
Fig 6.1
R1 is a Light Dependent Resistor (LDR) that varies from 0 Ω in bright light to
1000 Ω in the dark. R2 is a fixed resistor of 1.0 kΩ.
(i)
What would voltmeter V1 read when LDR is covered over so that no light
reaches it?
[2]
(ii) State the maximum and minimum of the readings of voltmeter V2.
[1]
(b)
The circuit in Fig 6.1 can be modified to become a type of electric thermometer.
The LDR is replaced by a thermistor, RT, which is used as a temperature probe as
shown in Fig 6.2.
A high resistance voltmeter can be used to indicate the temperature. We need to
calibrate the voltmeter so that it can be read directly as a thermometer.
Fig 6.2
The variation of the resistance of the thermistor, RT, as a function of its
temperature is shown in Fig 6.3. The value of the fixed resistor RR is 1.0 kΩ.
2009 H2 9745 Prelim Exam P3
14
Fig 6.3
(i)
Write down the expression relating the reading on the voltmeter, V, and
resistance of the thermistor, RT.
[1]
(ii) Hence use the information from the graph to show that the reading on the
voltmeter when the temperature is 25 oC is 2.5 V.
[1]
(iii) The process is repeated to find the relationship between the voltmeter
reading and the temperature. The graph is shown in Fig 6.4.
Fig 6.4
2009 H2 9745 Prelim Exam P3
15
For the range 10 oC to 90 oC, comment on the usability of the voltmeter as a
thermometer.
[2]
(c)
A conductor AB carries a current of 3.0 A from A to B. Sketch the magnetic field
patterns around the conductor in a plane perpendicular to the conductor seen
from the end A in the space to the right for each of the following situations:
(i)
Conductor on its own.
[2]
Fig 6.5(i)
(ii) Conductor within a uniform magnetic field the direction of which is show by
the arrow marked BE.
[2]
Fig 6.5(ii)
(iii) Draw an arrow on the conductor in Fig 6.5(ii) to show the direction of the
force exerted by the uniform field on the conductor.
[1]
(iv) Define magnetic flux density.
[1]
(v) Given that the flux density of the Earth’s magnetic field, BE = 50 x 10−6 T,
calculate the magnitude of this force per metre length of the conductor in
Fig 6.5(ii).
force per metre =
2009 H2 9745 Prelim Exam P3
[2]
16
(d)
Fig 6.6 shows a uniform magnetic flux density B in the plane of the paper. Q and
R mark the points where two long, straight parallel wires carry the same current, I,
in the same direction and perpendicular to the paper. The line through QR is at
right angles to the direction of B.
Fig 6.6
P is a point where the resultant magnetic flux density is zero, i.e. it is a neutral
point. P is closer to R than to Q.
(i)
Explain whether the direction of the current I is into or out of the paper.
[3]
(ii) There is a second neutral point on the line through QR. State, giving reasons,
whether it is to the left of Q, between Q and R or to the right of R.
[2]
2009 H2 9745 Prelim Exam P3
17
7 (a)
For
Examiner’s
Use
Explain using band theory why the electrical resistivity of a semiconductor
decreases as the temperature increases.
[3]
(b)
Introducing certain impurities into semiconducting material also decreases its
electrical resistivity. Describe briefly how this occurs for a n-type semiconductor.
[3]
2009 H2 9745 Prelim Exam P3
18
(c)(i)
Fig 7.1 shows two kinds of semiconductors, p-type and n-type, in contact. State
and explain the important characteristic which distinguishes the depletion
region from the rest of the material.
Depletion layer
X
p
n
Y
Fig 7.1
[3]
(ii)
Explain the effect on the depletion layer of applying a small potential difference
across XY if
1.
X becomes negative with respect to Y
[2]
2.
X becomes positive with respect to Y.
[2]
(iii)
Hence explain how the p-n junction could be use as a rectifier.
[2]
2009 H2 9745 Prelim Exam P3
For
Examiner’s
Use
19
(d)
The circuit in Fig 7.2 shows four diodes and a resistor R connected to a
sinusoidally alternating supply of peak voltage VO. Fig 7.3 shows the variation of
the potential difference across DB with time over two periods.
Fig 7.2
(i)
Sketch graphs on the axes given in Fig 7.3, showing the variation with time over
two periods of
1.
the potential of C with respect to A, label as P
2.
the potential of B with respect to A, label as Q
3.
the potential of B with respect to D, label as R
[3]
Fig 7.3
(ii) State the r.m.s. voltage in terms of VO for
1. the alternating supply
r.m.s. voltage =
2.
[1]
the potential difference across resistor R.
r.m.s. voltage =
End of paper
2009 H2 9745 Prelim Exam P3
[1]
For
Examiner’s
Use