NJC 2022 H2 Physics Prelim P3 QP
NJC 2022 H2 Physics Prelim P3 QP
NJC 2022 H2 Physics Prelim P3 QP
Higher 2
CANDIDATE
NAME
SUBJECT REGISTRATION
CLASS NUMBER
PHYSICS 9749/03
Paper 3 Structured Questions
26 Aug 2022
2 hours
Candidate answers on the Question Paper.
The number of marks is given in brackets [ ] at the end of each question or part 7
/ 20
question.
8
/ 20
Total
(80)
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3
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Section A
1 If an object is projected vertically upwards from the surface of a planet at a fast enough speed, it can
escape the planet’s gravitational field. This means that the object can arrive at infinity where it has zero
kinetic energy. The speed that is just enough for this to happen is known as the escape speed.
energy
0 r
surface
of planet
Fig. 1.1
[3]
(b) (i) By equating the kinetic energy of the object at the planet’s surface to its total gain of
potential energy in going to infinity, show that the escape speed v is given by
2GM
v2 =
R
[1]
5
[2]
3
Ek = kT
2
(i) Using the equation in (b)(ii), estimate the temperature at the Earth’s surface such that
helium atoms of mass 6.6 × 10–27 kg could escape to infinity.
You may assume that helium gas behaves as an ideal gas and that the radius of Earth is
6.4 × 106 m.
(ii) The temperature estimated in (i) is measured in thermodynamic scale. Explain what is
absolute zero in the thermodynamic scale.
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[Total: 10]
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2 A container contains an ideal gas at a thermodynamic temperature T. The kinetic theory of gas assumes
that the molecules of the gas behave as hard, identical spheres that are in continuous random motion.
The theory shows that
• the pressure exerted on the wall of the container by the gas is due to the elastic collisions of the
molecules with the wall of the container
• the pressure is proportional to the mean-square speed of the molecules
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• the mean translational kinetic energy of a molecule is EK = kT where k is the Boltzmann
2
constant.
(a) Explain why the internal energy of the gas is equal to the total kinetic energy of the molecules of
the gas.
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(b) A container with 1.2 mol of an ideal gas. The gas has a mass of 0.0384 kg.
• the volume of the gas increases (the container does not have a fixed volume)
• the pressure of the gas remains constant
• the temperature of the gas changes from 280K to 460K
• the gas does 1.3 × 103 J of work.
(i) Explain, in terms of the force produced by the molecules of the gas, how the pressure
remains constant as the volume increases.
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(ii) Use the first law of thermodynamics to determine the specific heat capacity of the gas.
(c) The container in (b) is now replaced with one that has a fixed volume. Thermal energy is supplied
to the gas to increase its temperature from 280K to 460K.
Suggest, with a reason, how the specific heat capacity of the gas would now compare with the
value in (b)(ii).
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[Total: 12]
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3 Hydrogen gas at low pressure can be made to emit photons in a discharge tube using a high voltage
supply, as shown Fig. 3.1.
discharge tube
with low pressure
hydrogen gas
high +
voltage
source
–
diffraction
grating
Fig. 3.1
The photons are incident normally on a diffraction grating and projected on a screen.
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(b) Explain how the line spectrum of the hydrogen provides evidence for the existence of discrete
energy levels in atoms.
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(c) Some electron energy levels in atomic hydrogen are illustrated in Fig. 3.2.
–0.85 eV
C
–1.50 eV
A B energy
–3.41 eV
The electron transitions A and B cause light of visible wavelengths 654 nm and 488 nm to be
emitted.
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(d) The central maximum and the first order maxima of the two visible wavelengths from the hydrogen
gas in (c) on the screen is shown in Fig. 3.3.
screen
240 cm
240.0 cm
(i) Explain how the diffraction and the interference of light at the diffraction grating leads to the
first order maxima for λ1.
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x = ………………………………………………. cm [4]
[Total: 14]
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(b) Use the theory of the particulate nature of electromagnetic radiation to explain why there is a
threshold frequency for the photoelectric effect.
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(c) A circuit was used to investigate the photoelectric effect as shown in Fig. 4.1
Fig 4.1
13
I/A
− 2.4 0 V/V
Fig. 4.2
(i) Explain why there is a minimum stopping potential difference Vs to reduce the current to zero.
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(ii) Explain why the current does not continue to increase for positive values of V.
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(iii) The work function of anode A is 1.6 eV. Use Fig. 4.2 to calculate the frequency of the
electromagnetic radiation used.
(iv) The frequency of the electromagnetic radiation is kept constant as its intensity is doubled. On
Fig. 4.2 sketch a graph to show the variation with V of I for this increase in intensity. [2]
[Total: 10]
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5 A long straight wire carries a steady direct current. A circular loop of conducting wire is placed directly
below the straight wire such that the wire is in the plane of the loop.
The loop falls vertically due to gravity from the wire as shown in Fig. 5.1.
current
wire
circular loop of
conducting wire
direction of fall
Fig 5.1
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(b) The circular loop has a radius of 5.0 cm, The magnetic flux density within the loop decreases
from 120 mT to 30 mT in 0.040 s.
Show the magnitude of the average e.m.f. induced in the loop during this time is 18 mV.
[1]
[Total: 6 m]
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6 The variation with time t of the sinusoidal current I in a resistor 450 is shown in Fig. 6.1.
Fig. 6.1
Use data from Fig. 6.1 to determine, for the time t = 0 to t = 30 ms,
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[Total: 8]
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Section B
Progressive …………………………………………………………………………………………………………..
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Longitudinal …………………………………………………………………………………………………………..
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(b) Fig. 7.2 shows the variation of displacement y with time t of a sound wave incident on a person’s
ear drum.
Fig. 7.2
Assume that the eardrum vibrates with simple harmonic motion and with the same frequency and
amplitude as the incident sound wave.
(ii) Show maximum speed of the oscillating eardrum is 6.3 x 10-8 m s-1.
[1]
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(iii) Determine the mass of a human eardrum if the maximum kinetic energy of the oscillating
eardrum is 2.4 ×10-19 J.
(iv) On the axes of Fig. 7.3, sketch a clearly labelled graph to show the variation of the velocity of
the ear drum v with displacement y.
v / m s–1
0 y / nm
Fig. 7.3
[2]
(c) Hummingbirds can hover around flowers by beating their wings at a frequency between 20 and 80
times per second. It can be assumed that the air molecules around the birds vibrate at the same
frequency.
(i) Deduce why a person standing near a hovering hummingbird may hear a buzzing sound.
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(ii) A bird watcher is initially 2.0 m from a hummingbird. To pick up a louder buzz, the bird watcher
moves nearer to the bird by a distance x. Determine the value of x, in metres, for an increased
intensity of 60%.
x = ………………….…………………………….. m [3]
(iii) It is assumed that for a hummingbird which beats its wings at 75 times per second, the air
molecules around it can vibrate in simple harmonic motion at an amplitude of 5.0 x 10-9 m.
Calculate the distance covered by an air molecule over the duration in which the hummingbird
beats its wings for 1800 times.
(iv) Another bird watcher dislikes the buzzing sound and uses noise-cancelling technology to
generate certain frequencies to cancel out the buzzing sound. Explain how the generation of
such frequencies could cancel out the buzzing sound.
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[Total:20]
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8 (a) (i) Force-fields may be represented using lines that have direction. Conventionally, arrows on
the field lines define the direction of a force acting on a test object.
State the property of the object that experiences a force in this direction for
1. gravitational field,
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2. an electric field
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(ii) Suggest why, when defining electric field strength, the object must be stationary.
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(b) Two long wires X and Y carrying the same current 290 A but in opposite direction is placed parallel
to each other as shown in Fig. 8.1. Distance between each wire is 5.0 cm.
wire X
wire Y
Fig. 8.1
(i) Show that the magnitude of magnetic flux density at wire X is 1.2 × 10–3 T.
[1]
(ii) Calculate the force per unit length on wire X.
(c) An electron is halfway between the wires X and Y in (b), travelling at a speed of 2.9 × 107 m s–1
parallel to the wires as shown in Fig. 8.2.
wire X
wire Y
Fig. 8.2
(i) The magnetic flux density halfway between the wires is 4.64 mT. Show that the resultant
force acting on the electron is 2.2 × 10–14 N.
[2]
(ii) A student claims that this electron will perform a circular motion between the wires.
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wire X
wire Y
Fig. 8.3
[1]
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(d) Suppose that an electron travels in a region with a magnetic field and an electric field due to two
parallel metal plates as shown in Fig. 8.4.
wire X
wire Y
Fig. 8.4
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(e) Assume that the Earth is an isolated perfect sphere as shown in Fig. 8.5, draw its gravitational
field lines with solid line and equipotential surfaces with dashed line.
Fig. 8.5
[3]
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(f) The Earth E and the Moon M can be considered as isolated point masses at their centres. The
mass of the Earth is 5.98 × 1024 kg and the mass of the Moon is 7.35 × 1022 kg. The Earth and
Moon are separated by a distance of 3.84 × 105 km as shown in Fig. 8.6.
3.84 x 105 km
Point P is a point along the line joining the centres of E and M, where the resultant gravitational
field strength is zero. Point P is at a distance x from centre of the Earth.
[2]
(ii) The resultant force on a 2.5 × 104 kg spaceship is zero at point P. The force would increase
by approximately 0.50 N for every 10 km moved away from point P towards the Earth.
A student claims that the spaceship will perform simple harmonic motion about point P.
Deduce whether or not the student’s claim is correct. (No further calculations are required.)
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[Total: 20 m]
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