# Carmel Holy Word Secondary School

```HKAL Laboratory report writing exercise
Assessing area
A.
Objective : State the objective of the experiment.
Exercise : A_1
You are asked to perform an experimental for measuring the rate of diffusion of bromine. Tube is
first evacuated by connecting via rubber tube to pump. With capsule attached as shown, tap closed,
end of capsule broken. Tap opened and time t taken for ‘half-brown’ level to move a certain distance
S up tube is measured.
Question :What is the objective of this experiment?
(1 mark)
Objective : Measuring the rate of diffusion of bromine.
1A
Exercise : A_2
Glass tube is lowered slowly into the beaker of water until the air inside the tube is heard to vibrate
loudly (with the frequency of the tuning fork). Then a stationary wave motion of the air in the tube
is produced form the superposition of the incident and reflected waves from the air/ water surface.
Resonant frequency, f0 = v/4l, where l is the air column length and v velocity of sound. By
measuring f0 and l, the velocity of sound in air is found.
Question : What is the objective of this experiment?
(1 mark)
Objective : Measuring the velocity of sound in air.
1A
Exercise : A_3
With the following setup, an experiment demonstrating the interference of a 3 cm microwave using
one microwave transmitter is performed.
6 cm
Transmitter
3 cm
3 cm
Probe
Metal
plates
Arrange the metal plates such that two slots of approximately 3 cm wide are formed with a
separation of about 6 cm. Interference occurs between the two wave-trains diffracted from the two
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slots that act as two coherent sources. The receiver detects the maxima and minima of the
interference pattern as it is moved around. Constructive and destructive interference occur
1
whenever the path difference of the microwaves from the slots is nλ and ( n  ) respectively.
2
Question : What is the objective of this experiment?
Objective : Demonstration of the interference of a 3 cm microwave.
(1 mark)
1A
Exercise : A_4
You are asked to measure the wavelength of red light using a diffraction grating. The following
diagram is the set-up.
Place two metre rules perpendicular to each other as shown. Hold a diffraction grating against one
end of a metre rule. View through the grating the vertical filament of the ray-box lamp placed about
1 m from the metre rules. Ask your partner to move a pencil along the second metre rule until it is
in line with the middle of the red colour of the first order spectrum. Measure the distance x and
hence find sinθ.
Question : What is the objective of this experiment?
Objective : Measurement of the wavelength of red light.
(1 mark)
1A
Exercise : A_5
The following is the set-up for measuring the capacitance of a parallel-plate air capacitor using a
reed switch.
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Coil
Reed switch
400 Hz from low impedance
output of signal generator
12 V
100 k
V
Light-beam
galvanometer
Diode (to rectify a.c.)
Capacitor
Question : What is the objective of this experiment?
(1 mark)
Objective : Measuring the capacitance of a parallel-plate air capacitor.
1A
Exercise : A_6
a.c. supply
L, R
C
a.c. supply
mA
L
R
C
mA
or
Set up the above circuit, set the signal generator output to a value, say 3 V, with a measurable
current, and increase the frequency stepwise from a low value, say 10 Hz, check whether the output
is constant at the previous setting, 3 V, then record the corresponding current readings on the a.c.
milliammeter, when frequency increases, the current reading rises and then drops.
Question : What is the objective of this experiment?
(1 mark)
Objective :
Investigating the current in an LRC series circuit for different frequencies of an a.c.
supply.
1A
Exercise : A_7
The diagram below illustrates the basic features of the laboratory apparatus for investigating
photoelectricity. It contains a vacuum photoelectric cell P with a photosensitive metal C of large
area and a collector of electrons D.
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P
C
incident monochromatic
D
A
ammeter
V
voltmeter
battery
Question : What is the objective of this experiment?
Objective : Investigation of photoelectricity.
(1 mark)
1A
Exercise : A_8
You are given some isotopes of a certain element. The isotopes are ionized so that they carry the
same charge Q, and enter a speed selector as shown. Only those isotopes with a definite speed can
pass straight through the mutually perpendicular uniform electric and magnetic fields in the speed
selector. The whole set-up is in a vacuum environment.
speed selector
+
a beam
of ionized
isotopes
-
When entering the magnetic field, all ions describe circular arcs and strike the photographic plate P.
For particles of mass M, the radius r of the path is given by
Q v B1 =
Mv 2
,
r
r =
Mv
.
B1Q
If B1 is constant, r is directly proportional to M (assuming Q is the same for all ions). When ions
with different masses are present each set produces a definite line and from their positions the
(relative) masses can be found.
Question : What is the objective of this experiment?
(1 mark)
Objective : Determination of the relative mass of the isotopes.
1A
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Assessing area
B. Apparatus : The list of apparatus and materials used.
Exercise : B_1
The diagram shows a set-up used to measure the speed of a bullet in the laboratory.

L
m
v
M
The bullet (of mass m, in the form of a small metal ball) is ‘fired’ horizontally towards a block of
wood (of mass M, in which a hole has been drilled) suspended from two vertical inextensible strings
(each of length L). On striking the block, the bullet is embedded and the block rises by swinging
through an angle θ as shown.
Question : List out all the apparatus of this experiment.
Apparatus : 1 bullet, 1 block of wood, 2 inextensible strings.
(2 marks)
Half correct 1A, all correct 2A.
Exercise : B_2
Use a thermocouple - small thermal capacity, and can react rapidly (establishing thermal
equilibrium) so as to follow varying temperatures.
to potentiometer
R
R1
R2
A
C
G
B
Pt-Rh
Pt
G
ice
water
E1
0 OC
 OC
Question : List out all the apparatus of this experiment.
Apparatus :
Cu
Cu
ice
water
unknown
temperature t
(2 marks)
2 cells, 1 beaker with ice, 1 beaker with water, 2 resistors, 2 cupper wires, 1 Pt-Rh
wire, 1 Pt wire.
Half correct 1A, all correct 2A.
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Exercise : B_3
The following set-up is an experiment for measuring the rate of diffusion of bromine into air and
hence estimating the mean free path of bromine molecules.
T
A
R = 0.1m
in
t = 500s
Question : List out all the apparatus of this experiment.
(2 marks)
Apparatus : Bromine liquid, 1 glass tube, 1 bromine capsule, 1rubber tubing, 1 V-shaped tube.
Half correct 1A, all correct 2A.
Exercise : B_4
For measuring the surface tension of water using the rise of water in a glass capillary tube, we first
set up the apparatus as shown below.
Travelling
microscope
Capillary tube
h
Pin
Liquid
Question : List out all the apparatus of this experiment.
(2 marks)
Apparatus : 1 travelling microscope, 1 capillary tube, 1 pin, 1 beaker with liquid.
Half correct 1A, all correct 2A.
Exercise : B_5
An experiment showing the phase change of the particle oscillations with distance from a sound
wave source.
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double beam
oscilloscope
loudspeaker
L
optical bench
y1
microphone
M
y2
Y2
Y1
a.f.
oscillator
scale
Question : List out all the apparatus of this experiment.
Apparatus :
(2 marks)
1 a.f. oscillator, 1 loudspeaker, 1 optical bench, 1 microphone, 1 double beam
oscilloscope.
Half correct 1A, all correct 2A.
Exercise : B_6
A prism spectrometer experiment.
Question : List out all the apparatus of this experiment.
Apparatus : 1 collimator, 1 telescope, 1 prism.
C - collimator, T – Telescope
(2 marks)
Half correct 1A, all correct 2A.
Exercise : B_7
The set-up shown below is used to investigate the potential around a charged sphere.
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Question : List out all the apparatus of this experiment.
Apparatus :
(2 marks)
1 e.h.t. power supply, 1 nylon fishing line, 1 plastic football coated with aquedag, 1
flame probe, 1 gold-leaf electroscope with lamp behind, 1 protractor.
Half correct 1A, all correct 2A.
Exercise : B_8
The following diagram shows an arrangement for investigating the factors which determine the
charge stored in a parallel-plate capacitor.
Reed switch coil
Potential divider
d.c.
supply
A
V
Parallel
plates
Question : List out all the apparatus of this experiment.
Apparatus :
(2 marks)
1 d.c. supply, 1 potential divider, 1 voltmeter, 1 microammeter, 1 reed switch coil, 1
parallel plates.
Half correct 1A, all correct 2A.
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Exercise : B_9
The circuit of a d.c. power pack used for generating a variable d.c. voltage from the a.c. mains is
shown below.
Np
Vp
240 V
50 Hz
Vs
350 V
4
A
Ns
2
1
20 H
+
3 32 F
25 k
50 W
+
+
400 V d.c.
100 mA
32 F
B
Question : List out all the apparatus of this experiment.
(2 marks)
Apparatus :
1 a.c. supply (240 V 50 Hz), 1 transformer, 4 diodes, 2 capacitors (32 F), 1 inductor
(20 H), 1 potential divider.
Half correct 1A, all correct 2A.
Exercise : B_10
Set-up :
+ 5.0 V
Rc
amplifier
input
Rb
Ri
100 
V
Vin
10 k
Ib
Vbe
2 k
Ic
output
Vout
Question : List out all the apparatus of this experiment.
Apparatus :
V
(2 marks)
1 battery, 1 potential divider, 2 voltmeters, 2 resistors (10 kΩ and 2 kΩ), 1
transistor, 1 d.c. supply (5.0 V).
Half correct 1A, all correct 2A.
Exercise : B_11
Experiment for observing the absorption spectrum of iodine using a diffraction grating.
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straight
filament lamp
grating
iodine
vapour
Vaporize some iodine crystals in a test tube by warming. View a straight filament lamp through
iodine vapour with a diffraction grating, the grating should be set with its lines parallel to the
filament of the lamp.
Question : List out all the apparatus of this experiment.
(2 marks)
Apparatus : 1 straight filament lamp, 1 test tube with iodine vapour, 1 diffraction grating.
Half correct 1A, all correct 2A.
Exercise : B_12
As shown below, in a gravitational analogue simulation of α-particle scattering by a thin metal
sheet, balls are allowed to roll down a ramp chute on to a model ‘hill’ where they experience
deflection.
B
r
ball
3-dimensional
model 'hill'
(symmetric in
horizontal plane)
A
ramp chute
Question : List out all the apparatus of this experiment.
Apparatus : 1 ramp chute, 1 ball, 1 model ‘hill’ (3-dimensional).
HKAL Laboratory report writing exercise
possible path of
deflected ball
(2 marks)
Half correct 1A, all correct 2A.
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Assessing area
C. Setup : Diagram showing the setup with labels.
Exercise : C_1
A long spiral spring of force constant k hangs vertically from a fixed support with a weight of mass
m attached to its bottom end. If the weight is pulled downwards and then released show that the
subsequent motion is s.h.m., with the displacement from the equilibrium position at any time t given
by x = a cosω0t, where a is a constant and ω0 the natural angular frequency of oscillation.
Question : Draw a labeled set-up diagram in the spaces provided below.
(2 marks)
Diagram 1A, labels 1A.
Unstretched
position
Equilibrium
position
l
P
x
F = k ( l + x)
mg
Exercise : C_2
A light spring of force constant k is connected to a block of mass m on a frictionless surface inclined
at an angle θ to the horizontal. The block is displaced from its equilibrium position O and then
released. Suppose at a certain instant the displacement of the block from the equilibrium position is
x as shown.
Question : Draw a labeled set-up diagram in the spaces provided below.
(2 marks)
Diagram 1A, labels 1A.
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
Exercise : C_3
A spring is held vertically with a weight, attached to its lower end. It is made to oscillate vertically
by a periodic up-and-down motion of the hand. On increasing the frequency of motion of the hand,
it is observed that the amplitude of motion of the weight increases, becoming a maximum at a
certain frequency.
Question : Draw a labeled set-up diagram in the spaces provided below.
(2 marks)
Diagram 1A, labels 1A.
Exercise : C_4
In an experiment, we use a moving-coil meter. The moving-coil meter has many parts : pointer, coil,
permanent horseshoe magnet, concave pole piece, pivot, hair spring, jeweled bearing, fixed soft iron
cylinder.
Question : Draw a labeled set-up diagram of the moving-coil meter in the spaces provided below.
(2 marks)
Diagram 1A, labels 1A.
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Exercise : C_5
In an experiment, we use a simple d.c. motor using permanent magnets, coil, brushes and
commutator.
Question : Draw a labeled set-up diagram of the d.c. motor in the spaces provided below. (2 marks)
Diagram 1A, labels 1A.
Axle
Coil
N
-
Carbon
brush
S
Commutator +
Exercise : C_6
As part of a musical instrument, a uniform wire is held taut but unstretched between a fixed point
and a smooth cylindrical peg of radius 1 cm. The tension in the wire can be increased by rotating
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the peg about its fixed axis so that some wire is wound onto the peg. Two knife edges, A and B, are
placed 0.36 m apart under the wire and push the wire stretched upward. The final shape of the wire
is like a bridge.
Question : Draw a labeled set-up diagram in the spaces provided below.
(2 marks)
Diagram 1A, labels 1A.
A
wire
B
0.36 m
peg
Exercise : C_7
The viscosity of a liquid can be measured by using Stokes’ law. Ball-bearings are dropped into a
long vertical glass tube containing the liquid and their respective terminal velocities are measured
for calculating the coefficient of viscosity of the liquid. Two markers A and B are stickled on the top
and the bottom of the glass tube respectively.
Question : Draw a labeled set-up diagram in the spaces provided below.
(2 marks)
Diagram 1A, labels 1A.
Marker A
long glass
tube
containing
liquid
falling ballbearing
Marker B
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Exercise : C_8
A cart is accelerated from rest across a horizontal table. The cart is connected with a mass A by
a string through a pulley at the corner of the table. The cart has a vertical post at one side, on
which a ball is held by an electromagnet at a height of 0.50 m above the cart. When the mass A
is released, it falls vertically and pulls the cart to move horizontally on the table.
Question : Draw a labeled set-up diagram in the spaces provided below.
(2 marks)
Diagram 1A, labels 1A.
ball
0.5 m
cart
A
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Assessing area
D. Theory (optional) : Using physics’ theory to explain the experiment and derive the equation.
Exercise : D_1
In a laboratory a small weight is attached by a piece of string of length l to a fixed point and set into
circular motion in a horizontal plane. The set-up is shown below.
P
length l

T
F

Question :
mg
Derive an expression for the angle of inclination of the string with the vertical  in
terms of g, l and ω.
(4 marks)
T is tension in string, F centripetal force.
Resolving (1) vertically, mg = T cos, Forces (2) horizontally F = T sin .
As F = ml sin 2 , hence, cos =
g
l 2
1A+1A
.
1A+1A
Exercise : D_2
To study a circular motion, a small rubber bung of mass m is attached to one end of a piece of string
passing through a thin glass tube, which has a weight W hanging at its other end. The rubber bung is
set into a horizontal circular motion by a student holding the glass tube.
L
A
glass
tube
paper
marker
W
Question :
rubber
bung

T=W

mg
Show that the weight W equals mω2L in theory, where ω is the angular speed and
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L is the length of the string beyond the upper opening of the glass tube.
(3 marks)
The string dips so that the vertical component of the tension balances the weight of the rubber bung.
W cosθ = mω2 r
(as T = W)
1A
2
 W cosθ = mω (L cosθ)
1A
W = mω2 L
1A
Exercise : D_3
The diagram shows a set-up used to measure the speed of a bullet in the laboratory.

L
m
v
M
The bullet (of mass m, in the form of a small metal ball) is ‘fired’ horizontally towards a block of
wood (of mass M, in which a hole has been drilled) suspended from two vertical inextensible strings
(each of length L). On striking the block, the bullet is embedded and the block rises by swinging
through an angle θ as shown.
Question :
By applying conservation laws, show that the speed of the bullet is given by the
mM 
relation v  
 2 gL1  cos   where g is the acceleration due to gravity.
 m 
(4 marks)
1. The horizontal momentum of the system is conserved, therefore mv = (m + M)V where V is the
common velocity just after impact.
1A
2. After the collision, the only forces acting on the system (block + bullet) are the weight and the
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3.
string tensions (which do no work), therefore the mechanical energy is conserved.
From energy conservation, 1 2 (m + M)V2 = (m + M)gh .
1A
1A
mM 
As h = L(1 – cosθ), by eliminating V, we hav v  
 2 gL1  cos   .
 m 
1A
Exercise : D_4
m
. In order
k
to plot a linear graph, we plot T x against m. Find the value of x and the meaning of the slope of this
graph.
(2 marks)
For an experiment of a vertical mass-spring oscillating system, we know that T = 2
x = 2 and slope =
4 2
.
k
1A+1A
Exercise : D_5
For an experiment of a simple pendulum, we know that T = 2
l
. In order to plot a linear graph,
g
we plot T y against l. Find the value of y and the meaning of the slope of this graph.
(2 marks)
y = 2 and slope =
4 2
.
g
1A+1A
Exercise : D_6
A block of mass m moves freely on a horizontal ground with a dynamic coefficient of friction μ. If
the initial speed of the block is u, derive a expression for the stopping distance of the block in terms
of u, μ and g, where g is the gravitational acceleration constant.
(4 marks)
As friction f = –μN = –μmg
So F = ma, –μmg = ma, a = –μg.
1A
1A
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Also
v2 = u2 + 2as
0 = u2 + 2(–μg)s
s =
1A
u2
2 g
1A
Exercise : D_7
Figure below shows an experiment of a man of mass m standing against the wall of a cylindrical
compartment called a ‘rotor’. The level of the rotor’s floor can be adjusted. The diameter of the
rotor is d.
wall
FA
FB
weight
floor
d
The rotor is spun at a certain speed about its central vertical axis so that, at this angular speed, the
man remains ‘pinned’ against the wall even if the floor of the rotor is pulled downwards. FA is the
friction and FB is the normal reaction by the wall. It is known that the maximum value of FA equals
μFB. Derive an expression of the minimum angular speed ω, of the rotor needed to keep the
‘pinned’ against the wall in terms of d,μ and the gravitational acceleration constant g.
FA = mg
max FA =μFB
mg ≦μmω2r
ω2 ≧
g
0.5  d
ω ≧
2g
d
(4 marks)
1A
1A
1A
1A
Exercise : D_8
In an experiment, two identical pans, each of mass m, are connected by a light string which passes
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over a light pulley suspended from the ceiling. The pulley can rotate smoothly about a horizontal
axis through its centre. Two different weights m1 and m2 (m2 > m1) are placed on the pans as shown
below.
m1
pan
m2
Neglecting the air resistance, derive an expression for the vertical acceleration a of the weight m1 in
terms of g, m, m1 and m2.
(3 marks)
Net downward force = (m + m2) g – (m + m1) g = (m2 – m1) g.
m2  m1
Downward acceleration a =
g.
2m  m1  m2
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1A
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Assessing area
E. Procedures : The procedures showing a logical ordering of steps. You may write them in points
form.
Exercise : E_1
Experiment investigating the dependence of the stopping distance of a vehicle on its initial kinetic
energy under the action of a constant resistive force.
light
gate
h
Set up the tilting runway as shown. Arrange a light gate for measuring the speed of the trolley near
the lower end of the tilting runway. The speed of the trolley is calculated from the time taken for the
card to pass the light gate. Measure the stopping distance of the trolley, which is from the light gate
up to the place where it stops. Repeat the experiment by releasing the trolley at different heights.
Plot a graph of stopping distance against the square of the speed recorded (representing the kinetic
energy of the trolley). A linear graph should be obtained showing the stopping distance is directly
proportional to the kinetic energy.
Question : Write down the procedures of this experiment.
(2 marks)
1. Set up the tilting runway as shown. Arrange a light gate for measuring the speed of the trolley
2.
3.
4.
5.
near the lower end of the tilting runway.
Measure the time taken for the card to pass the light gate and hence calculate the speed of the
trolley.
Measure the stopping distance of the trolley, which is from the light gate up to the place where
it stops.
Repeat steps 1 to 3 for releasing the trolley at different heights.
Plot a graph of stopping distance against the square of the speed recorded (representing the
kinetic energy of the trolley). A linear graph should be obtained showing the stopping distance
is directly proportional to the kinetic energy.
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Exercise : E_2
An experiment measuring the moment of the inertia of a flywheel.
W
A
R
M
A mass M is attached to the end of string which has its other end threaded through a hole in the axle
A of the flywheel W, the string being wound around the axle. When the mass M dropped the string
is unwound and when M reaches the ground the string just slips off axle, allowing it to continue to
turn. Let no. of revs. of W until M hits ground be n and the further no. of revs. after this until W
comes to rest be n’ - and time t is taken by a stopwatch. The no. of revs. can be obtained by
observing a mark on rim of flywheel, R.
Question : Write down the procedures of this experiment.
(5 marks)
1. Set up the apparatus as shown.
2. Attach a mass M to the end of string which has its other end threaded through a hole in the axle
A of the flywheel W, the string being wound around the axle.
1A
3.
4.
5.
6.
Release the mass M and the string is unwound.
1A
When M reaches the ground the string just slips off axle, allowing it to continue to turn. 1A
Measure n, no. of revs. of W until M hits ground and n’, the further no. of revs. after this until
W comes to rest by observing a mark on rim of flywheel, R
1A
At the same time, measure time t by a stopwatch.
1A
Exercise : E_3
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X
loudspeakers
O
Y
Two identical loudspeakers connected to the same signal generator are placed inside a room as
shown. All the surfaces of the room are covered with sound-absorbing materials. Point O is
equidistant from the loudspeakers and line XOY is parallel to the line joining the loudspeakers. The
variation of sound intensity along XOY is shown below :
sound intensity
position
X
O
Y
Question : Write down the procedures of this experiment.
(3 marks)
1. Set up the apparatus as shown.
2. Connect the two identical loudspeakers to the same signal generator.
3. Cover all the surfaces of the room with sound-absorbing materials.
4. Measure the variation of sound intensity along XOY.
1A
1A
1A
Exercise : E_4
Finding the speed of sound in air by using Kundt’s tube together with a loudspeaker.
(or cork dust)
The loudspeaker produces progressive longitudinal waves travelling towards the end of the cylinder
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where they are reflected to interfere/superpose the incident waves. The frequency of the
sound/signal generator is varied until resonance occurs. The stationary wave formed is revealed by
the lycopodium powder which swirls away from the antinodes (where the air is vibrating strongly)
and heaps are formed at the nodes. By measuring the average separation between the heaps (or
nodes), d. The speed of sound in air equals f (2d) where f = frequency of the sound waves.
Question : Write down the procedures of this experiment.
(4 marks)
1. Set up the apparatus as shown.
2. Vary the frequency of the sound/signal generator until resonance occurs.
1A
3. Observe the stationary wave formed from the lycopodium powder which swirls away from the
antinodes (where the air is vibrating strongly) and heaps are formed at the nodes.
1A
4. Measure the average separation between the heaps (or nodes), d.
1A
5. Calculate the speed of sound in air which equals f(2d) where f = frequency of the sound waves.
1A
Exercise : E_5
An experiment demonstrating the wave nature of light and estimating the wavelength of the light.
The filament lamp acts as a single slit, and the diffracted light beams from the two narrow slits
overlap in the region beyond the slits (accept idea presented using diagram). Use a filter to obtain
monochromatic light so that alternate bright and dark, equally spaced interference fringes are
observed (at the cross-wires of the travelling eyepiece). This shows the wave nature of light. The
average fringe spacing y is found by measuring across as many fringes as possible with the
travelling eyepiece. A metre rule is used to measure the separation d between the double slit and the
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travelling eyepiece. The slit separation a is measured directly with a travelling microscope. The
wavelength λ of the monochromatic light is approximated by λ =
ay
.
d
Question : Write down the procedures of this experiment.
(4 marks)
1. Set up the apparatus as shown.
2. Use a filter to obtain monochromatic light and observe alternate bright and dark, equally
spaced interference fringes at the cross-wires of the travelling eyepiece. This shows the wave
nature of light.
1A
3. Measure across as many fringes as possible with the travelling eyepiece, find the average
fringe spacing y.
1A
4. Use a metre rule to measure the separation d between the double slit and the travelling
eyepiece. Measure the slit separation a directly with a travelling microscope.
1A
5.
Calculate the wavelength λ of the monochromatic light approximatly by λ =
ay
.
d
1A
Exercise : E_6
An experiment measuring the wavelength of monochromatic light using a spectrometer and a
diffraction grating
collimator
telescope
*
light
source
crosswire
platform
Usual adjustments are first made on (i) cross-wires, (ii) telescope and (iii) collimator of the
spectrometer so that the collimator produces parallel light and the telescope focuses it at the
cross-wires. The table with the grating are turned so that the incident light falls on the grating
normally. The telescope is rotated, say to T1, and the reading corresponding to the first-order image
is taken. The first-order reading on the other side of the normal, say at T2, is also taken.
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incident
light
T1
grating


T2
Halve the angle between these two readings gives θ, from which λ can be calculated using nλ
= d sinθ where d is the grating spacing and n = 1.
Question : Write down the procedures of this experiment.
(5 marks)
1. Set up the apparatus as shown.
2. Make usual adjustments on (i) cross-wires, (ii) telescope and (iii) collimator of the
spectrometer so that the collimator produces parallel light and the telescope focuses it at the
cross-wires.
1A
3.
4.
5.
6.
Turn the table with the grating so that the incident light falls on the grating normally.
1A
Rotate the telescope, say to T1, and take the reading corresponding to the first-order image. 1A
Also take the first-order reading on the other side of the normal, say at T2,
1A
Halve the angle between these two readings gives θ, hence calculate λ by nλ = d sinθ
where d is the grating spacing and n = 1.
1A
Exercise : E_7
An experiment investigating the variation of magnetic flux density along the axis of a solenoid by
using a Hall probe.
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Ammeter
D.C.
Supply
metre rule
solenoid
Hall
Probe
Control
Box
CRO
(or millivoltmeter)
Place the solenoid along east-west direction so that it is perpendicular to the earth’s magnetic field.
(or, before making any measurement, adjust the potentiometer in the control box to set the
millivoltmeter to zero.) The current should be kept constant. Slightly move the semiconductor slice
inside the solenoid and record the maximum Hall voltage to ensure that the slice is perpendicular to
the magnetic field in the solenoid. Repeat the procedure at different positions along the solenoid, so
as to obtain the variation of magnetic flux density along the axis of the solenoid.
Question : Write down the procedures of this experiment.
(4 marks)
1. Set up the apparatus as shown.
2. Place the solenoid along east-west direction so that it is perpendicular to the earth’s magnetic
field. (or, before making any measurement, adjust the potentiometer in the control box to set
the millivoltmeter to zero.)
1A
3.
4.
5.
Keep the current constant.
1A
Slightly move the semiconductor slice inside the solenoid and record the maximum Hall
voltage to ensure that the slice is perpendicular to the magnetic field in the solenoid.
1A
Repeat step 4 at different positions along the solenoid, so as to obtain the variation of magnetic
flux density along the axis of the solenoid.
1A
Exercise : E_8
Using a simple current balance, an experiment investigates how the magnetic force depends on the
length of the current-carrying conductor in the magnetic field.
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Stop
R
Pin
Insulator
S
P
Razor
N
Rider S
Q
magnets
Copper
on yoke
wire frame
To rheostat and
5 A smooth d.c.
supply
Set up the current balance and place one pair of magnadur magnets around the current-carrying arm.
With one rider placed on the arm, adjust the current by shifting the rheostat to restore the balance.
With the current remains unchanged, place another pair of magnadur magnets next to the first one.
Equilibrium can be restored by placing another rider on the arm.
This shows that the magnetic force (i.e. no. of riders) is directly proportional to the length of
current-carrying conductor in the magnetic field.
Question : Write down the procedures of this experiment.
(4 marks)
1. Set up the apparatus as shown.
2.
3.
4.
5.
With one rider placed on the arm, adjust the current by shifting the rheostat to restore the
balance.
1A
With the current remains unchanged, place another pair of magnadur magnets next to the first
one.
1A
Place another rider on the arm to restore equilibrium.
1A
This shows that the magnetic force (i.e. no. of riders) is directly proportional to the length of
current-carrying conductor in the magnetic field.
1A
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Assessing area
F. Precautions : The precautions with relevant explanations.
Exercise : F_1
The viscosity of a liquid can be measured by using Stokes’ law. Ball-bearings are dropped into a
long vertical glass tube containing the liquid and their respective terminal velocities are measured
for calculating the coefficient of viscosity of the liquid.
Marker A
long glass
tube
containing
liquid
falling ballbearing
Marker B
Question : What are the precautions of this experiment ?
(3 marks)
Any THREE of the bellows @ 1A.
1. The diameter of the tube is large compared with the diameters of ball-bearings so that
streamline conditions are satisfied.
2. Marker A is far enough below the liquid surface for the ball-bearing to have its terminal
velocity at A.
3. Dip the ball-bearing in the liquid and thereby coated, before dropping so as to reduce the
chance of air bubbles adhering to the falling ball-bearing.
4. Avoid using ball-bearings of large radii as their terminal velocities are high and vortices may
5.
6.
form .
Release the ball-bearing at the centre of the tube to reduce the effect of the wall of the tube on
the streamlines.
Marker B is at a considerable distance from the bottom of the tube so as to reduce the effect of
the bottom of the tube on the streamlines.
Exercise : F_2
Young’s double slit experiment shows that light propagates as a wave motion.
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Screen
Filament
lamp
S1
S2
Question : What are the precautions of this experiment ?
(3 marks)
Any THREE of the bellows @ 1A.
1. Light source should be strong (or black out the laboratory as much as possible) and properly
shielded so that no stray light falls on the screen.
2. A monochromatic light source can be used in order to obtain sharper fringes.
3. Both slits S1 and S2 should be as narrow as possible so that the light emerging from the slits
undergoes significant diffraction.
4.
5.
6.
The slits should be separated by a very small distance (~ 0.5 mm) so that the light from the two
slits overlap somewhere in front of the screen.
The screen should be placed at an appreciable distance (1 ~ 2 m) from the slits so that the
separation of fringes is observable while the intensity is not too low.
Make sure that the filament is parallel to the slits S1 and S2. (or if a source slit is used it should
be parallel to the two slits S1 and S2.)
Exercise : F_3
Using a simple current balance, an experiment investigates how the magnetic force depends on the
length of the current-carrying conductor in the magnetic field.
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R
Stop
Pin
Insulator
S
P
N
Rider S
Q
magnets
Copper
on yoke
wire frame
Razor
To rheostat and
5 A smooth d.c.
supply
Procedures
Set up the current balance and place one pair of magnadur magnets around the current-carrying arm.
With one rider placed on the arm, adjust the current by shifting the rheostat to restore the balance.
With the current remains unchanged, place another pair of magnadur magnets next to the first one.
Equilibrium can be restored by placing another rider on the arm.
This shows that the magnetic force (i.e. no. of riders) is directly proportional to the length of
current-carrying conductor in the magnetic field.
Question : What are the precautions of this experiment ?
(3 marks)
Any THREE of the bellows @ 1A.
1. To avoid overheating, the current should be switched off as soon as observations have been
2. Make sure the direction of the magnetic field is perpendicular to the current-carrying arm.
3.
4.
5
Shield the set-up from the disturbance of wind.
Minimize the effect of the earth’s magnetic field by aligning the current-carrying arm along the
N-S direction.
The set-up should be far from any current-carrying conductors so as to avoid the effect of stray
magnetic fields.
Exercise : F_4
Experiment comparing viscosities of two liquids.
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6av0
A
W-U
B
Ball bearings of radius a dropped in liquids and passage timed between marks A and B, where they
should have reached a constant terminal velocity v0, using a stop-watch.
Question : What are the precautions of this experiment ?
(3 marks)
Any THREE of the bellows @ 1A.
1. Ensure terminal velocity reached (vary position of A).
2. Drop ball bearings vertically and along axis of cylindrical container.
3. Use wide container or make correction for walls (could be estimated using different sizes).
4.
Timing accuracy could be increased by using laser beams/photo-diode ‘gates’ in positions A
and B and counting cycles of an a.c. oscillator ( f ~ 1 kHz).
5.
Rub ball bearings in liquid before dropping in to prevent air bubbles from adhering onto the
ball bearings.
Exercise : F_5
L
The above figure shows a simple pendulum experiment which consists of a bob suspended by a
light, inextensible string of length L from a fixed point. If the bob is slightly displaced to one side
and then released, it will perform s.h.m. The set-up can be used to measure the acceleration due to
gravity g.
Measure the period T of the simple pendulum using a stop watch for different values of L. A graph
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of T2 against L is plotted which is a straight line passing through the origin.
Question : What are the precautions of this experiment ?
(2 marks)
Any TWO of the bellows @ 1A.
1. Ensure the pendulum oscillates with small amplitude (less than 10∘).
2.
3.
Make sure the pendulum oscillates on the same vertical plane.
In measuring period T, at least 20 oscillations should be counted.
Exercise : F_6
A student tries to measure the density of steel. He puts 20 identical steel ball bearings into a
measuring cylinder half filled with water. Figure below shows the readings of the water level before
and after placing the bearings into the cylinder. The ruler used is graduated in mm.
5 cm
4
5 cm
4
3
2
1
0
3
2
1
0
Without
ball bearings
With
ball bearings
Question : What are the precautions of this experiment ?
(2 marks)
Any TWO of the bellows @ 1A.
1. Avoid the formation of bubbles adhering the ball bearings, which will affect the volume
2.
3.
measured.
Tilting the measuring cylinder and let the bearings run along the wall of the cylinder.
Avoid the splashing of water when putting the bearings into the cylinder.
Exercise : F_7
Your group decides to investigate the magnetic field pattern around two parallel current-carrying
wires by using the following experiment. The set-up is shown below. With the time base of the CRO
switched off, a vertical trace is observed on the screen of the CRO. The measured result is very
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weak.
signal generator
long parallel wires
A
a.c. ammeter
search
coil
CRO
Question : What are the precautions of this experiment ?
(3 marks)
Any THREE of the bellows @ 1A.
1. The length of the wire should be as long as possible ~ 2 m.
2. The two wires should be well away from any magnetic materials.
3. Set-up should be well away from any stray fields, such as those from mains socket.
4. Twist the two connecting wires.
5.
6.
Adjust the orientation of the coil so that the peak-to-peak value of the trace on the CRO is
maximum
Avoid placing the coil near the ends of the wires
Exercise : F_8
In this experiment, we study the equipotential lines and electric field lines by plotting equipotential
lines on a high-resistance conducting surface.
movable
probe
Light beam
galvanometer
electrode
battery
box
electrode
fixed
probe
high resistance
conducting plate
Fix one fixed probe and one movable probe to the center-zero galvanometer. Hold the movable
firmly with your hand. Mark the position of the fixed probe on Move the movable probe on the
conducting plate. The two probes are at the same potential when the galvanometer shows zero
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reading. Repeat it to obtain at least 7 points of the same potential. Draw a smooth line across these
points. This line is an equipotential line.
Question : What are the precautions of this experiment ?
(2 marks)
Any TWO of the bellows @ 1A.
1. The probe and the electrode never be too close together.
2. The movable probe is hold firmly.
3. Make sure the electrodes, probes and the plate are in conduction.
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Assessing area
G. Results : All the original data and observation presented in appropriate forms such as tables.
Beware of the different units used for different apparatus, don’t mix them up. Keep the
accuracy of the measured value consistent with the apparatus, i.e. you cannot use a metre rule
to get a data 1.00047 m!
Exercise : G_1
A student do an experiment. The followings are the raw data.
L = 0.6 m, 50 T = 41, 43, 46 s. L = 0.8 m, 50 T = 51, 47, 48 s. L = 1.0 m, 50 T = 55, 53, 58 s.
m =0.20 kg.
Question : Fill in the table below with the raw data and make the necessary calculation. (2 marks)
Length of string L / m
First trial
Time for 50 revolutions 50 T / s
Second trial
Third trial
Average time for 50 revolutions 50 T / s

2
T
mω2L / N
Correctly fill in the measured data 1A, correctly calculate the results 1A.
Length of string L / m
Time for 50 revolutions 50 T / s
0.60
0.80
1.00
First trial
41
51
55
Second trial
43
47
53
Third trial
46
48
58
43
49
55
7.3
6.4
5.7
6.4
6.6
6.5
Average time for 50 revolutions 50 T / s

2
T
mω2L / N
Exercise : G_2
A student do an experiment. The followings are the raw data.
m = 0.2 kg, T1 = 30 s, T2 = 31 s. m = 0.3 kg, T1 = 37 s, T2 = 35 s. m = 0.4 kg, T1 = 39 s, T2 = 44 s.
Question : Fill in the table below with the raw data and make the necessary calculation. (2 marks)
)
T1 (
)
T2 (
)
mean T
T2
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Correctly fill in the measured data 1A, correctly calculate the results 1A.
0.2
0.3
0.4
T1 (s)
30
37
39
T2 (s)
31
35
44
mean T
30.5
36
41.5
T
2
930
1296 1722
Exercise : G_3
A student do an experiment. The followings are the raw data.
For wire A : Maximum load = 30 kg, Breaking stress = 2 000 N/m2, Young modulus = 206 N/m2.
For the longer wire B : Maximum load = 40 kg, Breaking stress = 1 900 N/m2, Young modulus =
124 N/m2.
Question : Fill in the table below with the raw data and make the necessary calculation.
First wire
(2 marks)
Shorter wire
Breaking stress (
)
Young modulus(
)
Correctly fill in the measured data 1A, correctly calculate the results 1A.
First wire
Shorter wire
30
40
Breaking stress (N/m )
2 000
1 900
Young modulus (N/m2)
206
124
2
Exercise : G_4
A student do an experiment. The followings are the raw data.
1 : 3.0 V, 200 Hz, 20.5 mA. 2 : 3.0 V, 300 Hz, 31.2 mA. 3 : 3.0 V, 400 Hz, 39.5 mA.
4 : 4.5 V, 200 Hz, 29.8 mA. 5 : 4.5 V, 300 Hz, 47.2 mA. 6 : 4.5 V, 400 Hz, 60.2 mA.
C (mF) = I / ( V f )
Question : Fill in the table below with the raw data and make the necessary calculation.
Trial
1
Battery e.m.f. V0 (
)
Frequency f (
)
Average current I (
)
Capacitance C (
)
2
3
4
(2 marks)
5
Mean capacitance C (
6
)
Correctly fill in the measured data 1A, correctly calculate the results 1A.
Trial
Battery e.m.f. V0 (V)
1
2
3
4
5
6
3.0
3.0
3.0
4.5
4.5
4.5
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Frequency f (Hz)
200
300
400
200
300
400
Average current I (mA)
20.5
31.2
39.5
29.8
47.2
60.2
Capacitance C (mF)
0.034
0.035
0.033
0.033
0.035
0.033
Mean capacitance C (mF)
0.034
Exercise : G_5
An experiment is done. The followings are the raw data.
(t, VC) = (0 s, 0 V), (10 s, 2.0 V), (20 s, 3.8 V), (30 s, 5.4 V), (40 s, 7.0 V), (50 s, 7.8 V),
(60 s, 8.4 V).
Question : Fill in the table below with the raw data and make the necessary calculation. (2 marks)
t( )
VC ( )
ln (VC)
Correctly fill in the measured data 1A, correctly calculate the results 1A.
t (s)
0
10
20
30
40
50
60
VC (V)
0
2
3.8
5.4
7.0
7.8
8.4
ln (VC)
-
0.69
1.34
1.69
1.95
2.05
2.13
Exercise : G_6
An experiment is done. The followings are the raw data.
Start measure VC at t = 0 s and take it in a 10 s interval.
VC = 0 V, 0.40 V, 0.79 V, 1.21 V, 1.55 V.
Initial charging current, I0 = 0.025 A and Q (C) = I0  t.
Question : Fill in the table below with the raw data and make the necessary calculation.
(2 marks)
t( )
VC ( )
Q( )
Correctly fill in the measured data 1A, correctly calculate the results 1A.
t (s)
0
10
20
30
40
VC (V)
0
0.40
0.79
1.21
1.55
Q (C)
0
0.25
0.50
0.75
1.00
Exercise : G_7
An experiment is done. The followings are the raw data.
For the first two trials, t = 30 s, 31 s, n1 = 20, 19, n2 = 31, 30.
The mean t = 30 s, n1 = 19, n2 = 31.
Question : Fill in the table below with the raw data and make the necessary calculation.
First trial
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Second trial
Third trial
(2 marks)
Mean
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Time t / s
No. of revolutions n1
No. of revolutions n2
Correctly fill in the measured data 1A, correctly calculate the results 1A.
First trial
Second trial
Third trial
Mean
Time t / s
30
31
29
30
No. of revolutions n1
20
19
18
19
No. of revolutions n2
31
30
29
31
Exercise : G_8
An experiment is done. The followings are the raw data.
For l = 30 cm, T1 = 40 s and T2 = 42 s. For l = 40 cm, T1 = 33 s, T2 = 34 s.
For l = 50 cm, T1 = 32 s and T2 = 31 s. For l = 60 cm, T1 = 27 s, T2 = 28 s.
Question : Fill in the table below with the raw data and make the necessary calculation.
Length, l (
(2 marks)
)
T1 (
)
T2 (
)
mean T
T2
Correctly fill in the measured data 1A, correctly calculate the results 1A.
Length, l (cm)
30
40
50
60
T1 (s)
40
33
32
27
T2 (s)
42
34
31
28
mean T
41
33.5
31.5
27.5
1700 1100
990
760
T2
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Assessing area
H. Measured data : Getting the correct result by calculation and interpret it.
Exercise : H_1
For an experiment measuring the moment of inertia of the flywheel, we have the following results:
First trial
Second trial
Third trial
Time t / s
8.5
7.9
8.3
No. of revolutions n1
11
12
10
No. of revolutions n2
22
21
23
Mean
Complete the table above and find the moment of inertia of the flywheel (unit = kg m 2) by the
 n  gt 2

equation : I  mr 2  2 
 1 , where m = 1.2 kg, r = 0.4 m, h = 0.8 m and g = 9.8 N/kg.

 n1 n2  2h
(3 marks)
First trial
Second trial
Third trial
Mean
Time t / s
8.5
7.9
8.3
8.2
No. of revolutions n1
11
12
10
11
No. of revolutions n2
22
21
23
22
Table 1A

22  9.8  8.2 2
2
I  1.20.4 
 1 = 53 kg m2.

 11  22  2  0.8

1A+1A
Exercise : H_2
For an experiment measuring dynamic coefficient of frictionμ, we have the following results:
Initial speed u / m s-1
First trial
Second trial
Third trial
0.51
0.49
0.50
Mean
Stopping distance s / m
0.317
0.320
0.319
Complete the table above and find the dynamic coefficient of friction μ by the equation :
s=
u2
, where g = 9.8 N/kg.
2 g
(3 marks)
First trial
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Second trial
Third trial
Mean
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Initial speed u / m s-1
0.51
0.49
0.50
0.50
Stopping distance s / m
0.317
0.320
0.319
0.319
Table 1A
2
s=
u
, 0.319 = 0.0128 /μ,μ = 0.040.
2 g
1A+1A
Exercise : H_3
For an experiment measuring maximum coefficient of frictionμ, we have the following results:
-1
First trial
Second trial
Third trial
4.45
4.43
4.44
Mean
Diameter d / m
1.99
1.98
2.02
Complete the table above and find the dynamic coefficient of friction μ by the equation :
2g
, where g = 9.8 N/kg.
d
ω =
(3 marks)
-1
Diameter d / m
First trial
Second trial
Third trial
Mean
4.45
4.43
4.44
4.44
1.99
1.98
2.02
2.00
Table 1A
ω =
2g
, 4.44 =
d
2  9 .8
,μ = 0.50.
  2.00
1A+1A
Exercise : H_4
For an experiment measuring the gravitational acceleration g, we have the following results:
First trial
Second trial
Third trial
Mass m / kg
0.205
0.210
0.200
Mass m1 / kg
0.105
0.100
0.105
Mass m2 / kg
0.110
0.105
0.110
Acceleration a / m s-2
0.079
0.077
0.078
Complete the table above and find the gravitational acceleration g by the equation :
m2  m1
a=
g.
2m  m1  m2
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Mean
(3 marks)
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First trial
Second trial
Third trial
Mean
Mass m / kg
0.205
0.210
0.200
0.205
Mass m1 / kg
0.105
0.100
0.105
0.103
0.110
0.105
0.110
0.108
0.079
0.077
0.078
0.078
Mass m2 / kg
Acceleration a / m s
-2
Table 1A
a=
m2  m1
g , 0.078 = 0.00805 g, g = 9.69 m s-2.
2m  m1  m2
1A+1A
Exercise : H_5
For an experiment measuring the gravitational acceleration g, we have the following results:
First trial
Second trial
Third trial
Length l / m
0.40
0.39
0.39
5.5
5.3
5.6
Angleθ/ ∘
34
37
35
Mean
Complete the table above and find the gravitational acceleration g by the equation : cos =
g
l 2
.
(3 marks)
First trial
Second trial
Third trial
Mean
Length l / m
0.40
0.39
0.39
0.39
5.5
5.3
5.6
5.5
Angleθ/ ∘
34
37
35
35
Table 1A
cos =
g
l
2
, g = lω2 cos = 0.39 ×5.52 ×cos35∘= 9.7 m s-2.
1A+1A
Exercise : H_6
For an experiment measuring the angular velocityω, we have the following results:
First trial
Second trial
Third trial
Mass m / kg
0.10
0.09
0.08
Weight W / N
2.2
2.3
2.1
Mean
Length L / kg
0.61
0.59
0.60
Complete the table above and find the angular velocityω by the equation : W = mω2 L. (3 marks)
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First trial
Second trial
Third trial
Mean
Mass m / kg
0.10
0.09
0.08
0.09
Weight W / N
2.2
2.3
2.1
2.2
Length L / kg
0.61
0.59
0.60
0.60
2
2
Table 1A
1A+1A
-1
W = mω L, 2.2 = 0.09 ×ω ×0.60, ω = 6.4 rad s .
Exercise : H_7
For an experiment measuring the speed v of a bullet, we have the following results:
First trial
Second trial
Third trial
Mass of the bullet m / kg
0.020
0.019
0.018
Mass of the block M / kg
1.00
1.01
1.02
Length L / m
Angleθ/ ∘
0.50
0.49
0.50
25
26
24
Complete
the
table
above
and
find
speed
v
of
the
bullet
by
mM 
v
 2 gL1  cos   , where g = 9.8 N/kg.
 m 
Mean
the
equation
:
(3 marks)
First trial
Second trial
Third trial
Mean
Mass of the bullet m / kg
0.020
0.019
0.018
0.019
Mass of the block M / kg
1.00
1.01
1.02
1.01
Length L / m
Angleθ/ ∘
0.50
0.49
0.50
0.50
25
26
24
25
Table 1A
mM 
 0.019  1.01 
v
 2 gL1  cos    
 2  9.8  0.501  cos 24 = 50 m s-1. 1A+1A
m
0
.
019




Exercise : H_8
An experiment demonstrating the interference of a 3 cm microwave using one microwave
transmitter.
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6 cm
Transmitter
3 cm
3 cm
Probe
Metal
plates
Interference occurs between the two wave-trains diffracted from the two slots that act as two
coherent sources. The receiver detects the maxima and minima of the interference pattern as it is
moved around. Constructive and destructive interference occur whenever the path difference of the
1
microwaves from the slots is nλ and ( n  ) respectively.
2
Question : How do you interpret the measured result?
(2 marks)
1. Interference do occurs in microwaves.
1A
2. Wavelength of the microwaves can be found from the positions of constructive and destructive
interference.
1A
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Assessing area
I1. Discussion : Interpretation of the graphical result.
Exercise : I1_1
L
The above figure shows a simple pendulum experiment which consists of a bob suspended by a
light, inextensible string of length L from a fixed point. If the bob is slightly displaced to one side
and then released, it will perform s.h.m. The set-up can be used to measure the acceleration due to
gravity g.
Measure the period T of the simple pendulum using a stop watch for different values of L. A graph
of T2 against L is plotted which is a straight line passing through the origin.
Question : How do you interpret the graphical result?
(1 mark)
T2 is proportional to L which is consistent with the theoretical formula T2 =
4 2 L
.
g
1A
Exercise : I1_2
An experiment illustrating the particle nature of light.
To vacuum
pump
Vs/V
Vacuum chamber
C
Y
Monochromatic
Light from
spectrometer
K
R
Z
X
Window
E
3
2
f0
1
Vs
[N.B. could be greatly simplified]
0
4
8
f/1014 Hz
12
Monochromatic light (f varied using spectrometer) incident on metal X. Emitted photo-electrons
collected by C and current measured by electrometer E. Vs is the stopping potential just stopping
the collection of emitted photo-electrons.
Question : How do you interpret the graphical result?
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1. Vs is zero until a threshold of frequency f0 is attained by the frequency of the monochromatic
light.
1A
2. After that, Vs increases linearly with frequency f.
1A
Exercise : I1_3
Franck-Hertz experiment
4.9 V
current
D
C
B
0
5
10
15
V in volts
The voltage +V is varied between the cathode and anode of a vacuum tube containing Hg vapor.
A small retarding potential exists between an intermediate grid to prevent electrons reaching anode.
Question : How do you interpret the graphical result?
1. As V increases, the current show periodic peaks and troughs.
2. The separation of adjacent peaks is 4.9 V.
3. Besides, the peaks and troughs increase as V increases.
(3 marks)
1A
1A
1A
Exercise : I1_4
From an experiment, a typical X-ray spectrum is obtained.
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Intensity
K Series
L Series
Wavelength
0
 min
Question : How do you interpret the graphical result?
(3 marks)
1. Intensity is zero until a threshold of wavelength λmin is attained.
1A
2.
3.
1A
1A
After that, intensity increases, follows by a gently decreases.
Besides, groups of sharp peaks are also observed.
Exercise : I1_5
An experiment measuring a radioactive half-life. Diagrams below show the set-up and the result.
corrected
counts in ( N t )
each 10 s
interval
N0
N 0 /2
N 0 /4
t 1/2
t 1/2
t time/s
The half-life t½ is the time for the number of disintegrating nuclei to fall to half its
initial value.
Question : How do you interpret the graphical result?
(2 marks)
1. The radioactivity curve shows the typical decay characteristic.
2. The half-life can be found graphically by finding the length of t½.
1A
1A
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Exercise : I1_6
Franck-Hertz experiment investigating the effect of varying the electron energy.
C
Gas
G
A
I
Electrons
xenon-filled
thyratron
V1
0 - 25 V
S
Galvo
I
G
Q
V2
V2 ~ 1.5 V
P
R
VC
Question : How do you interpret the graphical result?
V1
(2 marks)
1. As V increases, the current show periodic peaks and troughs.
2. Besides, the peaks and troughs increase as V increases.
1A
1A
Exercise : I1_7
An experiment showing the energy spectrum of the β-particles emitted naturally by some nuclei.
No of beta
particles per
unit energy
range
Energy
E max
Question : How do you interpret the graphical result?
(2 marks)
1. As energy increases, the number of β-particles emitted increases and falls after attaining a
2.
peak value.
The number of β-particles emitted drops to zero when energy increases to Emax.
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1A
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Exercise : I1_8
For an experiment, a V/I against 1/I graph is plotted as below.
V / I ()
20
18
16
14
12
10
8
6
4
2
0
1
2
3
4
1 / I (A-1)
-2
If V = ε – Ir, find the values of ε and r from the graph.
(3 marks)
From V = ε – Ir,
V
1
 r.
I
I
So ε = slope of the graph =
16.0  4.0
= 6.0 V,
3.2  1.2
1A
1A
r = the magnitude of the y-intercept = 3.0 Ω.
1A
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Assessing area
I2. Discussion : Error estimation of the measured result.
Exercise : I2_1
A micrometer screw gauge is used to measure the diameter of a piece of wire. The following
-0.05  0.02 mm, and
mean apparent diameter +1.05  0.02 mm.
Write down the diameter of the wire together with its error.
(2 marks)
1.10  0.04 mm.
1A+1A
Exercise : I2_2
A vernier caliper is used to measure the diameter of a piece of wire. The following readings were
obtained :
-0.3  0.2 mm, and
mean apparent diameter +11.3  0.2 mm.
Write down the diameter of the wire together with its error.
(2 marks)
11.6  0.4 mm.
1A+1A
Exercise : I2_3
To determine the area of cross-section of a metal wire, a student measures its diameter and obtains a
value of 0.10 mm, subject to an error of  0.02 mm. Write down an expression of the result.
(3 marks)
0.0079  0.0031 mm2
1M+1A+1A
Exercise : I2_4
The period of oscillation, T, of a simple pendulum is related to its length, l, by the formula
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T  2
l
. To find experimentally the acceleration of free fall by using a simple pendulum, a
g
student takes the following measurements :
time for 10 oscillations : 10.1  0.2 s,
length of the pendulum : 0.234  0.001 m.
Write down an expression of the result.
(3 marks)
9.1  0.4 m s-2
1M+1A+1A
Exercise : I2_5
In an experiment to determine the period of oscillation, T, of a simple pendulum, the time, t, for a
number of complete oscillations is taken. It is found that the time for 20 complete oscillations is
19.7  0.2 s. Find an expression of the measured period T.
(2 marks)
0.99  0.01 s.
1A+1A
Exercise : I2_6
The formula T2 = 4π2l/g is used to calculate the acceleration due to gravity g. If the maximum
percentage error of l = 3 %, the maximum percentage error of T = 4 %. Find the maximum
percentage error for g.
(2 marks)
11 %
1M+1A
Exercise : I2_7
The diameter of the bore of a capillary tube can be determined by introducing a small quantity of
mercury into the capillary. It is possible to measure the length of the mercury thread to within 3 %
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and the mass of the mercury used to within 7 %. Assuming negligible error in the density of
mercury, find the maximum percentage error in the calculated diameter of the capillary bore.
(2 marks)
5%
1M+1A
Exercise : I2_8
In an experiment to measure the density of steel, a steel sphere was used. The following
measurements were obtained :
Mass of the sphere = 540 mg  1 mg
Diameter of the sphere = 0.51 cm  0.01 cm
Estimate the percentage error in the calculated value of the density of steel.
(2 marks)
6%
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Assessing area
I3. Discussion : Error estimation of the graphical result.
Exercise : I3_1
For an experiment of a vertical mass-spring oscillating system, we know that T
2
= 4 2
m
. The
k
measured results are :
2
2
T (s )
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.24
0.55
0.81
1.02
1.35
1.59
1.82
2.07
2.53
2.69
By plotting T 2 against m, find the measured value of k. Also by measuring the maximum and
minimum slope of the graph, find the maximum percentage error of k.
(4 marks)
Measured value of k = 15 N/m.
1A+1A
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_2
For an experiment of a simple pendulum, we know that T 2 = 4 2
l
. The measured results are :
g
Length, l (m)
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
T 2 (s2)
0.85
1.56
2.28
3.35
4.01
4.88
5.57
6.25
7.34
8.12
2
By plotting T against l, find the measured value of g. Also by measuring the maximum and
minimum slope of the graph, find the maximum percentage error of g.
(4 marks)
Measured value of g = 9.8 N/kg.
1A+1A
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_3
For an experiment finding the stress-strain graph of copper wire. The cross-sectional area and the
natural length of the copper wire are 0.126 mm2 and 2 m respectively. The results are shown below :
Extension(mm)
5
10
15
20
25
30
35
40
45
50
0.61
1.27
1.94
2.58
3.17
3.87
4.44
5.12
5.77
6.39
Stress (107 N/m2)
Strain (10-3)
Complete this table. As Young modulus = stress / strain. By plotting stress against strain, find the
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measured value of the Young modulus. Also by measuring the maximum and minimum slope of the
graph, find the maximum percentage error of the Young modulus.
(5 marks)
Stress (107 N/m2)
3.99
7.94
11.90 15.87 19.84 23.81 27.78 31.75 35.71 39.68
Strain (10-3)
0.31
0.64
0.97
11
1.29
1.59
1.94
2.22
2.56
2.89
3.20
Table 1A
1A+1A
2
The measured Young modulus is 1.24 ×10 N/m .
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_4
For an experiment charging a capacitor at a constant rate. The results are shown below:
VC (V)
0
0.40
0.79
1.21
1.55
Q (C)
0
0.25
0.50
0.75
1.00
Plot a Q against VC curve. Find the slope of the graph and the maximum error of it.
(3 marks)
Slope = 0.65 C/V.
1A
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_5
For an experiment discharging a capacitor by a resistor. The followings are the results:
t (s)
0
10
20
30
40
50
60
70
Q (C)
5.05
3.45
2.55
1.85
1.35
0.92
0.69
0.47
ln Q
Complete the table above and plot a ln Q against t curve. Find the slope of the graph and the
maximum error of it.
(4 marks)
t (s)
0
10
20
30
40
50
60
70
Q (C)
5.05
3.45
2.55
1.85
1.35
0.92
0.69
0.47
ln Q
1.62
1.24
0.94
0.62
0.30
-0.08
-0.37
0.76
Slope = -0.033
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Table 1A
1A
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Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_6
For an experiment discharging a capacitor via a resistor. The followings are the results:
t (s)
0
5
10
15
20
25
30
35
Q (C)
5.05
3.45
2.55
1.85
1.35
0.92
0.69
0.47
Plot a Q against t graph and find the half-life of the graph.
(2 marks)
The half-life of the graph is about 10.4 s.
1A+1A
Exercise : I3_7
In an experiment with an illuminated photocell using caesium as the cathode, a small current is
detected by the microammeter even when the anode is made slightly negative with respect to the
cathode, using the circuit as shown below.
V
The current falls to zero only when the reverse p.d. across the tube reaches a value Vs, which varies
with the frequency f of the radiation used to illuminate the cathode. The following table shows the
variation of Vs with f.
Vs (V)
0
0.25
0.50
0.75
1.00
1.25
1.50
14
4.6
5.2
6.0
6.3
7.5
7.8
8.4
f (10 Hz)
Plot a Vs against f curve. Find the slope of the graph and the maximum error of it.
(3 marks)
Slope = 3.9 ×10-15 V s.
1A
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_8
In an experiment to investigate the absorption of β and γ rays by materials, a source emitting
β and γ rays is placed at a distance of about 5 cm from a G-M tube as shown in Figure below.
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source
ratemeter
G-M tube
absorber
The count rates, N’, corrected for background, corresponding to different thicknesses, d, of lead
absorber plates are tabulated as follows :
d / mm
N’ / s
-1
1
2
3
4
5
6
7
29.0 24.8 22.0 20.0 18.2 16.8 16.0
ln N’
Complete the table on the previous page and plot a graph of ln N’ against d. Also find the slope of
the graph and the maximum error of it.
(4 marks)
d / mm
N’ / s
-1
ln N’
1
2
3
4
5
6
7
29.0 24.8 22.0 20.0 18.2 16.8 16.0
3.37 3.21 3.09 3.00 2.90 2.82 2.77
Table 1A
Slope =
2.86  3.14
= - 0.1 mm-1.
5 .6  2 . 8
1A
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_9
In an experiment, a student wants to determine the gravitational acceleration g at the earth’s surface.
He releases a block from rest and uses a stroboscope to take a photograph of the block’s downward
motion. The result is as shown. The time interval between successive exposure is 0.1 s and the first
exposure is at t = 0s when the disc is released.
time t / s
0
0.1
0.2
0.3
0.4
0.5
0.6
position s / m
0
0.03
0.22
0.45
0.79
1.29
1.79
time t2 / s2
Complete the above table and plot a graph of s against t2. By the equation s 
1 2
gt , find measured
2
value of g and the maximum error of it from the graph.
(5 marks)
time t / s
0
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0.1
0.2
0.3
0.4
0.5
0.6
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position s / m
0
0.03
0.22
0.45
0.79
1.29
1.79
time t2 / s2
0
0.01
0.04
0.09
0.16
0.25
0.36
Table 1A
Slope of the graph = 1.80 / 0.36 = 5 m s-2 =
1
g , hence the measured value of g = 10 m s-2. 1A+1A
2
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
Exercise : I3_10
In order to detect the acceleration of a car, a driver starts the car from rest with constant acceleration.
Another man on the ground use a laser detector to detect the speed of the car. The result is as shown.
The first detection is at t = 0 s when the car starts its motion.
position s / m
0
0.14
0.62
1.35
2.36
3.79
speed v / m s-1
0
1.5
3.0
4.5
6.0
7.5
2
speed v
Complete the above table and plot a graph of s against v2. By the equation v2 = 2 a s, find measured
value of a and the maximum error of it from the graph.
(5 marks)
position s / m
0
0.14
0.62
1.35
2.36
3.79
speed v / m s-1
0
1.5
3.0
4.5
6.0
7.5
0
2.25
9.00
2
speed v
20.25 36.00 56.25
Table 1A
As v2 = 2 a s, s =
1 2
1
v , so slope =
.
2a
2a
Slope of the graph = 3.76 / 56.3 = 0.0668 =
1A
1
, hence the measured value of a = 7.49 m s-2.
2a
1A
Plot the maximum and minimum slope graphs 1A, calculate the maximum percentage error 1A.
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Assessing area
I4. Source of errors : State the source of errors and limitations of the method used, suggestions for
improvement and further investigation. As you should try your best to eliminate the personnel
error as stated in the precaution, personnel error, i.e. taking the data erratically, is not
acceptable as a source of error.
Exercise : I4_1
An experiment demonstrating the relation between the angular velocity of the bodyand the radius of
the path.
l
glass
tube
paper marker
rubber
bung
screw nuts
The glass tube is held vertically, the bung is whirled around above his head by one student and the
speed of bung is increased until the marker is just below tube. Another student times, say, 50
revolutions of the bung. By moving marker the length l of the string can be varied and the relation
between l and the angular velocity () obtained.
Question : What are the sources of errors of this experiment?
(3 marks)
Any THREE of the bellows @ 1A.
1. Friction exists at the opening of the glass tube.
2.
3.
4.
The rubber bung is not swirled with constant speed.
The string is not inextensible.
The rubber bung is not swirled in a horizontal circle.
Exercise : I4_2
An experiment verifying a pendulum undergoes s.h.m.
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(1)
ticker tape
(2)
ticker timer
Ticker tape is attached to weight. Weight released from position (1) and swings to position (2),
ticker timer having been switched on. The dots on tape indicate displacements for equal time
intervals of 0.02s/0.01s. Using tape a displacement/time graph is plotted. Velocity at different times
is obtained by drawing a tangent at particular point on plot and determining slope.
Question : What are the sources of errors of this experiment?
(3 marks)
Any THREE of the bellows @ 1A.
1.
2.
3.
4.
Not S.H.M. : Due to finite amplitude the approximation sin  =  does not hold.
Damping of motion by ticker tape may seriously affect the period.
Not a point mass and so there is difficulty in measuring l.
Buoyancy of the air will reduce downward force on mass - affecting Period.
Exercise : I4_3
Objective : Investigating the geometric factors affecting the capacitance of a parallel plate capacitor.
Reed switch
(2)
(1)
25 cm
coil
f ~ 400 Hz from low
impedance output
of signal generator
12 V
R=
100 k 
25 cm
A
Metal
plates
V
Diode (to rectify a.c.)
A
Capacitor
C
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Sockets for
4-mm plugs
Polythene
spacer d
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Reed switch, switches alternately between contacts (1) and (2), charging C and then discharging C
with a frequency f. The generated current pulses are so rapid that the micro-ammeter deflection
remains steady, indicating an average current I, where I = Qf. Q being charge stored in C. Hence
capacitance of capacitor C = Q/V, V being measured by a voltmeter. Clearly the area of overlap of
plates A and the separation d (using various spacer thicknesses) can be varied and effects on C
determined.
Question : What are the sources of errors of this experiment?
(3 marks)
Any THREE of the bellows @ 1A.
1. R should prevent excessive current pulses but not be too large otherwise C does not completely
discharge
2. Finding effect of electric field at edges of plates affects dependence of C on areas A.
3. Stray capacitances to earth could affect the effective capacitance of C.
4. Leakage of charge from capacitor
5. Rebound of contact in reed switch.
Exercise : I4_4
To study a circular motion, a small rubber bung of mass m is attached to one end of a piece of string
passing through a thin glass tube, which has a weight W hanging at its other end. The rubber bung is
set into a horizontal circular motion by a student holding the glass tube.
L
A
glass
tube
paper
marker
rubber
bung
W
Question : What are the sources of errors of this experiment?

T=W

mg
(3 marks)
Any THREE of the bellows @ 1A.
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1.
2.
The string is extensible.
The rubber bung is not swirled in a horizontal circle.
3.
4.
Friction exists at the opening of the glass tube.
The rubber bung is not swirled with constant speed.
Exercise : I4_5
Experiment investigating the dependence of the stopping distance of a vehicle on its initial kinetic
energy under the action of a constant resistive force.
light
gate
h
Set up the tilting runway as shown. Arrange a light gate for measuring the speed of the trolley near
the lower end of the tilting runway. The speed of the trolley is calculated from the time taken for the
card to pass the light gate. Measure the stopping distance of the trolley, which is from the light gate
up to the place where it stops. Repeat the experiment by releasing the trolley at different heights.
Plot a graph of stopping distance against the square of the speed recorded (representing the kinetic
energy of the trolley). A linear graph should be obtained showing the stopping distance is directly
proportional to the kinetic energy.
Question : What are the sources of errors of this experiment?
1. The friction at the wheels of the trolley is not constant.
(1 mark)
1A
Exercise : I4_6
A long spiral spring of force constant k hangs vertically from a fixed support with a weight of mass
m attached to its bottom end. If the weight is pulled downwards and then released show that the
subsequent motion is s.h.m., with the displacement from the equilibrium position at any time t given
by x = a cosω0t, where a is a constant and ω0 the natural angular frequency of oscillation.
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Unstretched
position
Equilibrium
position
l
P
x
F = k ( l + x)
mg
Question : What are the sources of errors of this experiment?
(2 marks)
Any TWO of the bellows @ 1A.
1. The mass oscillates with large amplitude such that the spring doesn’t obey Hooke’s law.
2. The mass doesn’t oscillate vertically.
3. In measuring period, only a few oscillations is counted.
Exercise : I4_7
A student wants to use an ‘inertia table’ to determine the moment of inertia of a cylinder about its
central axis. The inertia table consists of a circular platform suspended by a wire, and can be set into
torsional oscillations. The cylinder is placed on the platform with its axis lying along the line AO.
A
O
Question : What are the sources of errors of this experiment?
(3 marks)
Any THREE of the bellows @ 1A.
1. Difficulty in locating axis of cylinder along OA.
2. Cylinder may slip on the table during oscillation.
3. Oscillation has too large amplitude.
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4.
The motion is not purely torsional oscillation.
Exercise : I4_8
A student use the apparatus shown below to determine the speed of sound in air. The distances
between the loudspeaker L and the reflecting plate R are measured by a metre rule with different
frequencies recorded from the screen of the signal generator.
signal
generator
CRO
X E Y
L
M
R
Question : What are the sources of systematic errors of this experiment?
(2 marks)
There exists systematic error in the measurement of the positions of M by the metre rule and in the
readings of the frequencies of the signal generator.
1A+1A
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Assessing area
J. Conclusion : State the conclusion supported by reasoned arguments. The final result together
with its error MUST be stated in the conclusion. Don’t just write one sentence for the
conclusion, you should write a few sentences to explain the reasons supporting the conclusion.
Exercise : J_1
A long solenoid carrying constant current will give a uniform magnetic field inside the solenoid. Set
up the apparatus as shown.
smoothed low voltage
power supply
To light-beam galvanometer
d.c. ammeter A
circuit box
solenoid
Hall probe
Adjust the rheostat so that there is a current of about 1 A through the solenoid. Insert the Hall probe
well inside the solenoid and adjust for zero deflection of the galvanometer before switching on the
current. Switch on the current and set the galvanometer to give a (large) deflection. Move the probe
about inside the solenoid over a cross-section and along the length of the solenoid.
The deflection of the galvanometer remains unchanged, which indicates the magnetic field due to
the solenoid is uniform.
Question : What is the conclusion of this experiment?
(1 mark)
Conclusion : The magnetic field inside a solenoid is uniform.
1A
Exercise : J_2
proton

B
C
X
A
beryllium
paraffinwax
D
E
amplifier
ionisation
chamber
A very penetrating radiation X (unaffected by magnetic fields and so not charged particles) was
observed when beryllium was bombarded by -particles. This radiation was found to be capable of
producing protons from paraffin-wax – a measure of their energy/velocity was obtained by inserting
thin sheets of mica until no current registered by the ionisation chamber. Experiment was repeated
with nitrogen in place of the paraffin-wax (hydrogen nuclei). Chadwick from a consideration of the
conservations of linear momentum/ energy to the proton collisions (assumed elastic) calculated the
HKAL Laboratory report writing exercise
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rest mass of a neutron ~ that of a proton.
Question : What is the conclusion of this experiment?
(1 mark)
Conclusion : The rest mass of a neutron is approximately the same as that of a proton.
1A
Exercise : J_3
A
12 V
low voltage
supply
24 W
12 V
V
Connect a high resistance voltmeter (0 – 15 V) across the terminals of a low voltage power supply
and adjust the output to 12 V, which is the e.m.f. E of the supply. The voltmeter reading drops
slightly after connecting the ray-box lamp and the ammeter.
Record the voltmeter reading V and the ammeter reading I. (I can also be estimated from the ratings
of the lamp 12 V 24 W without using the ammeter) The internal resistance r of the supply is given
by r =
E V
where I is the current delivered.
I
Question : What is the conclusion of this experiment?
(1 mark)
Conclusion : The internal resistance of the supply is r.
1A
Exercise : J_4
(1)
(1)
(2)
(2)
(3)

A
B 
d
crystal
d
A
 
B
P
Q
R

C
N
L
M
D
(3)
crystal
atomic
planes
Interference takes place between mono-chromatic X-rays reflected from atoms spaced throughout
crystal and in some directions of reflection maxima are detected – enables the separation of atomic
planes in a crystal to be determined, since 2d sin  = n.
Question : What is the conclusion of this experiment?
Conclusion : The separation of atomic planes in a crystal is d.
(1 mark)
1A
Exercise : J_5
HKAL Laboratory report writing exercise
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Set up a friction-compensated runway. To investigate the relation between force and acceleration, a
trolley is pulled by one, two and three identical elastic strings which are stretched by the same
amount. The corresponding accelerations are recorded and a graph of the force (number of elastic
strings) is plotted against the acceleration, which shows a straight line
passing through the
origin (linear relationship). To investigate the relation between mass and acceleration, use one
elastic string to pull one, two and three trolleys. The corresponding accelerations are recorded and a
graph of
1
is plotted against the acceleration, which shows a straight line passing through the
mass
origin (linear relationship). Thus, acceleration 
force
. For a body of mass 1 kg and moves with
mass
acceleration 1 m s-2, the force acting on it is 1 N.
Question : What is the conclusion of this experiment?
Conclusion : Force  mass × acceleration.
(1 mark)
1A
Exercise : J_6
Experiment investigating the dependence of the stopping distance of a vehicle on its initial kinetic
energy under the action of a constant resistive force.
light
gate
h
Set up the tilting runway as shown. Arrange a light gate for measuring the speed of the trolley near
the lower end of the tilting runway. The speed of the trolley is calculated from the time taken for the
card to pass the light gate. Measure the stopping distance of the trolley, which is from the light gate
up to the place where it stops. Repeat the experiment by releasing the trolley at different heights.
Plot a graph of stopping distance against the square of the speed recorded (representing the kinetic
energy of the trolley). A linear graph is obtained
Question : What is the conclusion of this experiment?
Conclusion : The stopping distance is directly proportional to the kinetic energy.
(1 mark)
1A
Exercise : J_7
HKAL Laboratory report writing exercise
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Glass tube is lowered slowly into the beaker of water until the air inside the tube is heard to vibrate
loudly (with the frequency of the tuning fork). Then a stationary wave motion of the air in the tube
is produced form the superposition of the incident and reflected waves from the air/ water surface.
Resonant frequency, f0 = v/4l, where l is the air column length and v velocity of sound. By
measuring f0 and l, the velocity of sound in air is found.
Question : What is the conclusion of this experiment?
(1 mark)
Conclusion : The velocity of sound in air is v.
1A
Exercise : J_8
Experiment for observing the absorption spectrum of iodine using a diffraction grating.
straight
filament lamp
iodine
vapour
grating
A continuous spectrum consisting of some dark lines is observed. The light from the lamp is a
continuous spectrum consisting of photons of a range of energies. When the light is incident on an
iodine molecule, it can only absorb energy from a photon whose energy is just enough for exciting
it to a higher energy state. When the excited molecule returns to ground state, it re-emits light of the
same wavelength of the photon but equally in all directions. So the intensity of the radiation in the
direction of the incident photon is reduced. However, photons of other wavelengths will pass
straight through. Thus a dark line, whose wavelength is that of the absorbed photon, is seen on the
background of a continuous spectrum.
Question : What is the conclusion of this experiment?
(1 mark)
Conclusion : The absorption spectrum of iodine is a continuous spectrum consisting of some dark
lines is observed.
1A
HKAL Laboratory report writing exercise
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