AL Physics 1999 Paper 1
SECTION A
i Answer ALL questions in this section.
ii Write your answers in the spaces provided in this question-answer book. In
calculations you should show all the main steps in your working.
iii Assume: velocity of light in air=3×108ms-1
Acceleration due to gravity=10ms-2
Question No
Marks
1
2
13
13
3
4
12
13
5
9
1.
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 1.1 shows the
readings of the water level before and after placing the bearings into the cylinder. The
ruler used is graduated in mm.
(a)
The rise in water level should be recorded as ______±_______(unit______)
(b)
State and explain one precaution when placing the bearings into the cylinder.
(1 marks)
(2
marks)
(c) The internal diameter of the measuring cylinder is found to be 9.40±0.05mm and
the total mass of the ball bearings is 25.00±0.01g.
(i)Name the instrument used for measuring the internal diameter of the cylinder
(1
marks)
(ii)Find the density of the steel ball bearings
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(iii)Give the percentage uncertainty in your calculated value in (ii) .Show your
working.
( 3 marks)
(d)State another method of measuring the density of the ball bearings with a smaller
percentage uncertainty. Explain briefly.
(3 marks)
2.(a)
Diagram O represents the equilibrium positions of a line of equally spaced selected
atoms in a metal. When an ultrasonic wave of a certain frequency travels from left to
right in the metal ,the positions of the atoms at different times within a period are
shown in diagrams P,Q and R.
(i)Which particles in diagram R correspond to rarefactions ?
(1 marks)
(ii)Find the wavelength, frequency and speed of the ultrasonic wave in the metal.
(4 marks)
(b)A student uses the set-up in Figure 2.1 to find the speed of sound in air. The
frequency of the signal generator is set at 2 kHz. When the microphone is moved
vertically along PQ perpendicular to the bench, a series of alternating maximum and
minimum signals are detected. The first maximum signal is found at P while Q
corresponds to the fifth maximum. The separation between P and Q is found to be 1.1
m.(Note: The microphone detects the change in pressure caused by the sound waves)
(i)When the microphone is moved on the bench between point P and the loudspeaker,
maximum signals are detected. What can you say about the effect of reflection on a
compression of the sound waves incident on the bench?
(1 marks)
(ii)Draw on Figure 2.1 the two paths along which sound waves propagate to Q from
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the loudspeaker. Explain why a series of maximum and minimum signals are detected
along PQ
(3 marks)
(iii)Calculate the speed of sound in air.(Hint :Some of the sound waves can be
treated as coming from the mirror image of the loudspeaker below the bench)
(4
marks)
3.A proton of mass m and charge q is accelerated from rest through a potential
difference V0 and enters perpendicularly through a small hole H on a screen S into a
region with a uniform magnetic field B pointing into the paper as shown in Fig.3.1
(a) Sketch the path of the proton in Fig.3.1 Indicate the magnetic force acting on the
proton at an arbitrary point on the path.
(b) (I)Derive an expression for the distance d from the hole H to the point where the
proton hits the screen. Find this distance for the proton if m=1.67×10-27kg,q=1.6×
10-19C,V0 =1000Vand B =0.05T.
(iii)Calculate the time the proton spends in the magnetic field (i.e. the time between
leaving H and hitting the screen)
(c) The proton is now replaced by an unknown nucleus X whose charge is double
that of a proton Nucleus X hits the screen at a distance of 0.26m from H .Compare
this with your result in (b)(I),and determine what X is. ( 3 marks )
4.(a)Figure 4.1 shows an operational amplifier circuit.
A graph of output voltage Vout plotted against input voltage Vin is shown below.
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(i) What is the resistance of the resistor Rf?
(2 marks)
(ii)With reference to the graph, explain the function of the above circuit
(3 marks)
(b)
Figure 4.2 shows the circuit of a comparator. The LED lights up when the input
voltage Vin is less than 4.5V,Find the resistance of R
(2
marks)
(c)A stable power supply is essential for the operation of computer parts, which
usually work at 5 Vd.c. A fluctuation in the supply voltage Vin of more than 10%is
certainly not tolerable, so it is therefore important to keep a regular check on it .Figure
4.3 shows a warning device designed for such a purpose.
(i)
Sate the potentials at P and at Q. Briefly explain the operation of the (3 marks)
circuit.
(ii) (ii)Calculate the resistance of the resistors R1and R2
(3 marks)
5.People are often killed in a fire as a result of suffocation. To minimize the loss of
lives, smoke detectors can be installed in buildings and a loud sound and a flashing
light are triggered when smoke is detected. Figure 5.1 shows a common ionization
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smoke detector which has a small radioactive source inside. During normal operation,
the radioactive source keeps emitting ionizing particles and a certain ionization
current is maintained inside the chamber of the detector.
(a)The manufacturer claims that the radioactive source in the smoke detector presents
no hazard to health in normal use. Comment on this claim and briefly explain which
type of radioactive source should be used in the smoke detector.
(3 marks)
(b)When the radioactive source in the detector is placed close to a GM-tube, the count
rate measured is 2000s-1.The average number of ion-pairs produced by each radiation
particle is 5×104and each ion carries a charge of 1.6×10-19C
(i) Estimate the maximum ionization current in the smoke detector. Why is the
ionization current in the smoke detector significantly less than this maximum value?
(3 marks)
(ii) The smoke detector should be disposed of when is maximum ionization current
drops below 5×10-12A.The manufacturer claims that the life of the detector is 10
years. Estimate the half-life of the radioactive source used in the detector. (3 marks)
SECTION B
i Answer ALL questions in this section.
Ii Write your answers in the spaces provided in this question-answer book. In
calculations you should show all the main steps in your working.
Iii Assume :velocity of light in air=3×108ms
Acceleration due to gravity=10ms-2
Question No
6
7
8
9
Marks
12
11
18
19
6.(a)Fox a source emitting electromagnetic waves of frequency f and moving towards
an observer with a velocity v, the frequency of the electromagnetic waves received by
the observer is given by
If v<<c, show that equation(*)can be approximated to f`=f(1+ v/c)
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(b)An earth satellite in an orbit near the earth’s surface emits a radio signal of
frequency 100 MHz. When the satellite passes over a tracking station on the earth’s
surface, the station detects beats between the received signal and the station’s own
signal of frequency f0.The beat frequency keeps on decreasing from an initial value of
7000Hz to 2000Hz within minutes.(The satellite can be considered as moving
horizontally with constant velocity during the period of observation)
(i)Explain why the beat frequency changes gradually and not abruptly
(ii)Find the speed of the satellite observed from the tracking station.
(2 marks)
(3 marks)
(iii)Calculate the frequency f0 of the station’s own signal.(Give your answer up to 6
sig. fig)
(2 marks)
(iv)A student thinks that the calculated value in (ii) is the orbital speed of the satellite.
Do you agree with him? Explain briefly.
(2 marks)
7.(a)A ball bearing of radius a is released from rest a at the edge of the concave side
of a cylindrical lens of radius R. The ball bearing rolls without slipping along the
curved surface and shows the subsequent oscillatory motion. Neglect the effects of air
resistance
(i)What forces do A,B and C represent? Which force(s)give(s)a torque on the bearing
about the contact point P with the lens?
(2 marks)
(ii)Explain why the motion of the ball bearing is confined to a vertical plane (2
marks)
(iii)For small oscillations, the displacement x of the ball bearing satisfies the
equation d2x/dt2+5g/(7R)=0 It is known that R =15cm.Calculate period of oscillation
of the ball bearing. (2 marks)
(iv)The ball bearing is replaced by a hollow sphere having the same mass and same
size, and is release from rest at the edge of the concave side of the lens .What is the
difference in their speeds when passing the center of the lens? Briefly explain your
answer.
(3 marks)
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(b)Figure 7.2shows a slotted weight placed on a horizontal platform. A student
attaches the platform to a simple harmonic oscillator which makes it oscillate
vertically with amplitude A and variable frequency f. The s.h.m. can be represented by
y=A sin(2 ft)
(i) Sketch graph to show the time variation of the force action on platform by the
slotted weight.(The slotted weight remains in contact with the platform)(2 marks)
(ii)The frequency of oscillation is gradually increased until it reaches a certain
frequency f0 such that the slotted weight starts to lose contact with the platform. Briefly
explain the observation and calculate the value of f0 if A=1.5cm
(4 marks)
(iii) If the slotted weight is replaced by another one of greater mass, state the change,
if any ,in the frequency f0 obtained. Explain briefly.
(2 marks)
8.(a)Figure8.1 shows an Rc circuit constructed from a capacitor C and a resistor R or
resistance 5.5Ω
(i)The frequency of the signal generator is slowly increased from zero. Assume that
the r.m.s. output voltage of the signal generator remains constant. Describe the change
n the reading of the a.c. ammeter A. Briefly explain your answer.
(3 marks)
(ii)The frequency of the signal generator is set at 2 kHz. Figure 8.2 shows the traces
of VR and Vo displayed on a CRO
(i)State the time base used. Use Figure 8.2 to determine the phase relationship
between VR and Vo
(4 marks)
(ii)Find the r.m.s. values of VR and Vo if the voltage gain used is 5 Vcm-1
(3
marks)
(iii)Calculate the capacitance of C
(3 marks)
(b)Figure 8.3 shows a circuit modified from that in Figure 8.1 .The inductor L has
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negligible resistance. Light bulbs X,Y and Z are identical .The frequency of the signal
generator is slowly increased from zero. When the frequency reaches 1 kHz ,bulbs X
and Y glow with equal brightness while bulb Z is dim.
(i)Describe the change in the brightness of the bulbs X and Y before the frequency of
the signal generator reaches 1kHz.Explain briefly.
(3 marks)
(ii)To investigate the voltages across the light bulbs X and Y –inputs Y1and Y2of a
dual trace CRO are connected to P and Q respectively .Sketch the traces displayed on
the CRO when the frequency of the signal generator is 1kHz and explain why the bulb
z is dim(Hint: The sum of currents X and Y is equal to the current through Z)
(3 marks)
9.In 1989,the spacecraft ’Voyager 2’ was sent from earth to the Neptunian system.
Before this expeition, two satellites of Neptune had discovered, namely Triton and
Nereid. Six more satellites were discovered after this expedition. Their diameters d,
pefiods T and orbital radii about Neptune r are as follows:
S atellite
D/km
T/hr
R/103km
New:
1989N1
1989N2
1989N3
1989N4
1989N5
1989N6
420
200
140
160
90
50
Previously known
Triton
2720
Nereid
340
26.9
13.3
8.0
9.5
7.5
7.1
117.6
73.6
52.5
60.0
50.0
48.2
140.9
8640
354.3
5500
Given: radius of the earth=6 400km
(a)(i)Calculate the gravitational potential at the earth’s surface
(2 marks)
(ii)Find the minimum energy supplied to each kilogram of the mass of the spacecraft
so at to enable it to escape from the earth’s gravitational pull. Show your working.
(2 marks)
(b)Suggest a reason why 1989 N1 was not discovered from earth even though it is
bigger than Nereid.
(1 marks)
(c )It can be shown that the orbital radius r and period T satisfy the relation
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r3/T2=GM/(4π2) where M is the mass of Neptune.
(i)What is the major assumption for the validity of the above relation?
(1 marks)
(ii)Using the information from the newly discovered satellites 1989 N2 to 1989 N6
of Neptune ,plot a suitable graph to find the mass of Neptune. Show your working(6
marks)(Given: Gravitational constant G=6.7×10-11Nm2kg-2)
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