Download Answer ALL questions. Write your answers in the spaces provided in

ii
iii
1.
Answer ALL questions.
Write your answers in the spaces provided in this Question-Answer
steps of your calculations.
Assume:
speed of light in air = 3 x 108 m S-l
acceleration due to gravity = 10 m S-2
Book.
You should show all the main
A light spring is fixed vertically to a trolley and a light platform is attached to its upper end. A small block
of mass m is placed on this horizontal platform. When the system achieves static equilibrium, the spring is
compressed by 0.05 m as shown in Figure 1.1
0.05 m ~~ ~~~~- - - - - - - - - - - - - - - - - - - - - --
uncompressed position
of the spring
The block is released from the uncompressed position of the spring. The trolley is then given a push so that
it moves together with the block at a uniform velocity on a smooth horizontal surface. Neglect air resistance
and assume that there is no slipping between the block and the platform.
I
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(iii)
Suppose the mass of the block is halved and the force constant of the spring is doubled while
its natural length remains unchanged. If the block is again released from the same position
and the trolley is given the same uniform velocity as before, find the block's period of
oscillation and draw the corresponding
indicate the position of the block.
stroboscopic
photograph
in Figure 1.2.
Use X to
(5 marks)
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S
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.- - - ---
- - - ----
'0
- - - - - -----
- - - - ---
- - - - - - - - - - - - - - - - - ---
- - - - - - ---
- - - - - - - - --
- - - - - - ------
------
- --
- - - --
- - - - --
--
- - --
- - - --
- - - - - - - - - - - ----
- --
- - - - - - - - - - - - - - - --
--
- -----
- - - ---
The trolley is stopped suddenly when the block is just at its highest position. The block slips on
the platform and then moves off from it. Describe and explain the subsequent motion of the block
as seen by a stationary observer on the ground.
(3 marks)
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----------.- -
-.------------------------------------------..-.-----------------------------------
Q)
-B
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s::
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•...
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<r::
.. - -- ---
------ - - - - - -- - - - - --- - - - - ---- - -- - -- - - - -- - - -- - - - - - - --- - --------- - - - - - - --- --- ------ - - - - - - --. - - - -- -- - - -- - - - -- - - - - - - - - - - ------ - - - - - - - - - -- - -.- --. --
----------------------------------------------------------------------------------------------------------------------.----------------_._-------_._--_
.
.
2.
Longitudinal waves can be produced in a metallic slinky spring and the propagation
JkL
speed of the waves is
2
.
Iy given
.
by v
approxunate
=
-;;;
h
were
k = force constant of the slinky spring
L = length of the slinky spring
m = mass of the slinky spring
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8
A student conducts an experiment to verify this relationship. The spring is stretched to a length of2.2 mas
shown in Figure 2.2. A battery is connected across the spring and two search coils are placed at A and B
which are at a fixed distance 1.0 m apart. The search coils are connected to the respective Y-inputs of a dual
trace CRO.
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~11111111111111111111111111
Figure 2.2
A
search •
coil
1.0 m
B
•
D
A sharp push is made at the left end of the slinky spring so that a compression pulse travels along the spring.
When the compression pulse passes the search coil at A, the following trace is described on the screen of the
CRO.
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'"0
v
~
ti3
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(c)
The time interval for the pulse to travel from A to B can be found from the corresponding traces
registered by the search coils. The experiment is repeated with the slinky spring stretched to
different lengths and the corresponding time intervals found are tabulated below.
Complete the table by choosing a suitable physical quantity and plot a straight line graph to
verify the given relationship.
(4 marks)
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(l)
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Length of the slinky spring, L / m
2.2
1.8
2.0
1.6
1.4
(l)
•..o
..0
s::
Time interval for the pulse
travel from A to B, t / s
to
0.51
0.62
0.56
0.70
.; ;'
,
;
+
:
;
,
;
:
:
", i,,:
·-i··';·_·;'·+-
0.79
Calculate the slope of the graph obtained. Hence, estimate a value for the force constant k
when the mass of the spring is 0.25 kg.
(3 marks)
Another student wants to verify whether the propagation speed of the waves is inversely
proportional to the square root of the spring's mass. He suggests using slinky springs of .£3
different masses stretched to the same length to repeat the experiment. Explain whether he .5
can verify this relationship by plotting a suitable straight line graph.
(2 marks) ~
.~
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3.
A student employs the experimental set-up in Figure 3.1 to study a piece of glass of refractive index 1.5
coated with a thin film of refractive index 1.22.
Diagram NOT
drawn to scale
diffraction
grating
thin coating,
refractive index 1.22
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White light of continuous spectrum from 400 nm to 700 nm is shone normally onto the coated glass. The
light reflected by the coated glass is partly reflected by a 45° partially silvered mirror and incident
normally on a diffraction grating with 1000 lines per rom. The colour spectra produced are observed on
the screen.
E
Cl)
::
o
t::
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en
What is the highest order of complete colour spectrum produced?
calculations.
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.------
Explain briefly with the aid of
(3 marks)
--------- -.--------------------.-.-.------.--.----.-----------------------..----.--.-----------------------------------------.--------------------
.~
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(b)
In the fIrst-order spectrum produced by the diffraction grating, an intensity minimum is observed at
an angular position 33°.
(ii)
Which interface(s) of the coated glass will generate a TC phase change to the reflected
light? Explain why there is an intensity minimum in the spectrum. Hence, estimate the
minimum possible thickness of the coating on the glass.
(5 marks)
.§:
en
.S
..--.. -------------------------------------.-----------------------------------------------------------------------------------------------.---.------------------
~
S
(c)
The student suggests that the thickness of the coating could be determined more accurately when
the white light source is replaced by a monochromatic laser. Comment on the suggestion.(2 marks)
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4.
A certain d.c. motor designed to work from a 12 V supply of negligible internal resistance has an armature
resistance of 0.25 n. When running freely without any mechanical load, the motor draws a current of
2.0 A from the supply. The magnetic field provided by two curved pole pieces is always parallel to the
plane of the armature coil.
Figure 4.1 shows the side view of the armature coil. At the moment shown, the current is
into the paper through arm P while it is out of the paper through arm Q. Indicate the
directions of the magnetic forces acting on the arms P and Q. State the sense of rotation
of the coil.
(2 marks)
B'
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6
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Q)
~
Figure 4.1
Q)
.s
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Q)
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~
'"•...
~
'"
~
•...
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The motor is now connected to a mechanical load, and its running speed becomes 80% of the free
running speed when steady state is reached. Calculate
(i)
(ii)
(iii)
the
the
the
9.0
corresponding back e.m.f.,
current drawn from the supply,
torque on the armature coil if it is a rectangular
x 10-4 m2; and the magnetic field B is 0.1 T.
coil of 50 turns and area
<C
~v
.
.. __.__
_
_
_.
~
~v
~
E
_._._
(d)
_
__
_.. _
.__.. _._
__.. __
With the motor connected to the mechanical load, sketch the time variation of the current drawn
from the supply when the motor is switched on. Mark the known current values on the vertical
axis.
(2 marks)
current
Sources of materials used in this paper will be acknowledged in the Examination Report and Question Papers
published by the Hong Kong Examinations and Assessment Authority at a later stage.
Answers written in the margins will not be marked.
E
Answer ALL questions.
Write your answers in the spaces provided in this Question-Answer
steps of your calculations.
Assume:
speed of light in air = 3 x 108 m S-1
acceleration due to gravity = 10 m S-2
ii
iii
5.
Book.
You should show all the main
In Figure 5.1, a toy is placed on a smooth horizontal surface. It is equipped with a fan powered by a battery.
When the fan is switched on, the toy moves to the right and reaches a constant speed eventually.
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With the aid of a speed-time graph, explain the motion of the toy after the fan is switched on.
(4 marks)
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.•...
o
-.~
.
_.
_
_
s=
._---------------------------------_
..__
_.------._
_---_
.. __
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<I.l
-B
--
-
-------.-----.-------
-------.-
--------------------
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s=
Q)
._----------------------------_
.•••••••
_------.-------------------------------.--
.. _._----------_
..
'E;::
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Cf)
s=
-<r.:
.
•
•
-----------------------------------.
••
The toy of total mass m is now attached to a fixed point on the ceiling by a light inextensible string
of length L. It is set into a uniform horizontal circular motion as shown in Figure 5.2. The string
makes an angle to the vertical when the speed of the toy is v.
e
.
.
.........
........
.....
e
Write down TWO equations of motion of the toy. Hence, show that the angle satisfies the
equation 2 cos2e + cos
2 = 0 if m = 0.1 kg, L = 0.8 m and v = 2 m S-l and calculate the
values of and T.
(5 marks)
e
e-
•
•
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0
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a
e
0
.0
•....
0
s::
-.~
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.5
0/}
a
e
0
..s::
•....
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s::
0
.1E•....
~
•....
'"0
~
s::
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«
(iii)
If the output voltage of the battery inside the toy drops slightly, describe and explain its
subsequent motion in terms of v, and T.
(3 marks)
e
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6.
The set-up shown in Figure 6.1 is used to study photoelectric effect. Light of a certain frequency is
directed towards the photo-sensitive electrode B of a photocell.
The potential difference across the
electrodes A and B can be varied by adjusting the variable supply.
Given Planck constant h = 6.63 X 10-34 J s
Charge of electron e = 1.60 X 10-19 C
light
~
--1
I
electrometer
AI
photocell
~IB
I
I
variable
supply
(a)
When the voltage VB of the electrode B is zero, the electrometer still detects a current.
phenomenon and state the direction of the current in the photocell.
Explain this
(2 marks)
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-t=
--
.........................•............•••.••.
--- .........••.••....
-
----
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-.. - ................•....
-
-- .•..••••••••.................•.....
._--------------------------------------------.------------------------------------------------.---------------.--------------------------------------------------
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a
The work function of electrode B IS 2.3 eV. The graph in Figure 6.2 shows the variation of the
current f with the voltage VB when the variable supply is adjusted.
fila-loA
""
What is the maximum kinetic energy, in eV, of the photoelectrons produced?
the wavelength of the light waves used and name this kind oflight waves.
~~
~
8
-
.~
.
Hence, find
(4 marks)
- ~_ ..- _. - - -- - - ---- - - - -- - -- -- - - -- - - - - - - - -- - --- - -- - - - - - - - -- - - -- - -- --- - - - ----- - - - - - - - - --- - - - --- ----- - - -- -- - - - - - - - - - -- - - - --- - -- - - - --- - - ---- - - - --- - ---- ----- -- - --- - - -_----
--
_
_
.._-
_-_
__
---
-_._
_
_---
-
__ ..- ..-._._.
_
.------.-------------------------------------------------------.--------------------------------------------------------------------------------------------------
.5
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8
.5
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•....
~
_._._._. ._
_
_._
.._.__
In Figure 6.2, sketch the current-voltage
light intensity doubled.
_._ _
_
.._._
_
.
variation when the experiment is repeated with the
(2 marks)
Referring to the graphs in Figure 6.2, elaborate one observation of the photoelectric effect that
cannot be explained by the wave theory.
(2 marks)
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~~
~
8
Figure 7.1 shows an LRC circuit connected to an a.c. source of variable frequency and negligible
impedance. The r.m.s. voltage Vs of the source IS 10 V. The resistance of the resistor R is 40 nand L is a
pure inductor.
r.m.s. voltage across
the resistor VRI V
/
/
/
/
~
V
R
/
/11
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 28
frequency f/ kHz
With the switch S open and the variable capacitor C set at 1 JlF, the frequency f of the source is
varied and the corresponding variation of the r.m.s. voltage VR across the resistor is shown in the
above graph.
(i)
Determine the resonant frequency
fa and the maximum
value of the r.m.s. current.
(3 marks)
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aa
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a
.p
II)
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en
II)
.•••_••- _••_••••. - - -- - - - - - -. - ••- - _. - - - - - - _••_. _••••••••- _••--. - -- _. - - -- -- - - - - - - - - - - -- _. - -- ••••••- _. _•••••- _•••_•••.. - - - - - - - - -- _. - - -- ••••- -- -- -- - -- -- -- - -- - _•••••••
s::
<
(ii)
At resonance, the r.m.s. voltage VL across the inductor is 25 V, which is greater than the
r.m.s. voltage of the source. Explain why this is so and find the inductance L. (3 marks)
(b)
"0
With the switch S still open and the frequency of the source fixed at a certain value ii, the
capacitance of the capacitor C is varied so as to study the average power P dissipated in the circuit.
.............•••••..•••.•••.••.•••...
- ...••.•••••••... - .. -.- .••••.•....................
- ..•........................................
-
--.- .. -
.
II)
]
S
II)
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Calculate the maximum value of P and state the condition for attaining this value.
(3 marks)
os::
.~
tn
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.. _---- .. ------------------------------------------------------------------.--------------------------------------------------------------------------------------
~
S
.5
.-.------------.--._--_
... -------.------..-..... ------__.....
e
•••
.------------------.------------------------------.----
s::
.~
_. __ ._-_
.
~
rn
l-l
II)
.-----------------------------------.----.----------.--.--.-----------------------
•••-- ••••••••••••• ---------------
••••••••• ------------.-.--.---------.-
•••••••••
~
~
(c)
With the switch S closed and the capacitance fixed, sketch the variation of the Lm.S. voltage
across the resistor with the frequency of the source.
(2 marks)
r.m.s. voltage across
the resistor VR
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8.
Two chambers, X and Y, are separated by a freely movable insulated piston. Each chamber holds
0.15 mole of a monatomic ideal gas. Chamber X is insulated, and chamber Y is maintained at a constant
temperature of 20°C. Initially, the temperature in chamber X is 350°C, and the volume of each chamber is
2.0 x 10-3 m3 (see Figure 8.1). (Given: universal gas constant R = 8.31 J mor1K-1)
insulating
wall
I
/
/
"'-
I
Chamber X
2.0 x 10-3 m3 , 350°C
Chamber Y
2.0 X 10-3 m3 ,20°C
....•
....•
applied force F
heat
reservoir
20DC
Figure 8.1 Initial states of the chambers
The piston is initially kept at rest by an applied force F as shown. The magnitude of F decreases gradually so
that the piston moves to the right very slowly until reaching the final static equilibrium position. The
variation in pressure of the chambers during the process is shown in the graph below. The volume of
chamber X is taken as the horizontal axis.
Pressure II 05 Pa
(a)
Use the graph to find the magnitude of the applied force F required to hold the piston at rest initially.
Given that the cross-sectional
area of the piston is 4.0 x 10-3 m 2.
(2 marks)
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--.-------------------------------
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---------.-------------------
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(iii)
the work done on the gas in chamber Y, given that the gas in chamber X does a work of 58 J
against the applied force F,
(2 marks)
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------ ..--
---------- ..-
---------------------------------------.----
--.--.-----------------.-----
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._--------------------------------------------_
•••••••••
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-----------_
•• _----_
••••
-.---------------
--------
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s::
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.S .------------------------------------------- -------------
-------------------------------------------------.------------------------.-------
~
E
.5 -----.---------.--.----------------------------------- ----------------------------------------------------------------..-------.--
-----------------
s::
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. - ---
- - - -- --- - -_ .....--.- - - - - - - - - - --- ---- - -- - -- - - ---- - -- - -- - - - ---- - - -_ .... - - - --~~~.~---.--- - - ---- - - - -- -- - - -- --. -~- - ---.- - - - - -- - - - - - -- -- - - -- - ---- - - - - - - - - - - _. _ .. -_.
(iv)
the heat absorbed or liberated by the gas in chamber Y.
(2 marks)
Sources of materials used in this paper will be acknowledged in the Examination Report and Question Papers
published by the Hong Kong Examinations and Assessment Authority at a later stage.
u2
a=-=OJ
2
fLo
B=-
r
1
2w
r
fLoN1
B=-I
F= Gmtm2
r2
F
=
fLOII/2
force per unit length between long parallel
straight current-carrying conductors
2w
torque on a rectangular current-carrying
coil in a uniform magnetic field
U=_GMm
r
r 3 / T2
= constant
ratio of secondary voltage
voltage in a transformer
velocity of transverse wave motion in a
stretched string
velocity oflongitudinal
a solid
u=~
wave motion in
= -L
f.
to primary
dI
dt
E =~LI2
2
d=AD
a
XC=-
1
we
12
10 loglO(-)
II
1
1
1
U
v
f
E=
Q
41r&or2
pV=-Nmc
3
electric
charge
field strength
due to a point
E
= ~CV2
macroscopic
modulus
relationship
energy
F=- dU
dr
decay of charge with
capacitor discharges
= Qo(l-e-tIRC)
3RT =~kT
2N A
2
time
when
a
rise of charge with time when charging
a capacitor
1
P+_pu2
2
+pgh
!-'U=Q+W
= _13.6
E
eV
n2
n
2
1 =nAuQ
R= pi
A
F
C12.
= BQusinB
V=
BI
nQt
definition
of
Young
1
E =-Fx
2
electric field between parallel plates
(numerically)
C=Q=&oA
V
d
Q
=
E=:/~
41r& or
d
E
k
V=_Q-
E=V
"""2
1
-+-=-
In2
tI
k
"2
force on a moving charge in a magnetic
field
~mu2
force on a current-carrying
a magnetic field
E
conductor in
2
m
= mc2
= hv-if>
between force and potential