Sparta
Sparta
Sparta
Data
Formulae
Gm
gravitational potential, φ =–
r
hydrostatic pressure, p = ρgh
Nm 2
pressure of an ideal gas, p = V
<c >
Q
electric potential, V =
4πε0r
capacitors in series, 1/C = 1/C1 + 1/C2 + . . .
capacitors in parallel, C = C1 + C2 + . . .
resistors in series, R = R1 + R2 + . . .
0.693
decay constant, λ =
t
length 1750 mm ± 3 mm
Fig. 1.1
(a) State the appropriate instruments used to make each of these measurements.
(i) length
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(ii) diameter
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(iii) resistance
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(b) (i) Show that the resistivity of the metal is calculated to be 4.86 × 10–7 Ω m.
[2]
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(b) A car is travelling along a road that has a uniform downhill gradient, as shown in
Fig. 2.1.
25 m s–1
7.5°
Fig. 2.1
The car has a total mass of 850 kg. The angle of the road to the horizontal is 7.5°.
Calculate the component of the weight of the car down the slope.
(c) The car in (b) is travelling at a constant speed of 25 m s–1. The driver then applies the
brakes to stop the car. The constant force resisting the motion of the car is 4600 N.
(i) Show that the deceleration of the car with the brakes applied is 4.1 m s–2.
[2]
(ii) Calculate the distance the car travels from when the brakes are applied until the
car comes to rest.
(iv) The quantities in (iii) part 1 and in (iii) part 2 are not equal. Explain why these two
quantities are not equal.
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[Total : 8]
6.0 Ω
Fig. 5.1
The variable resistor is connected in series with a 12 V power supply of negligible internal
resistance, an ammeter and a 6.0 Ω resistor. The resistance R of the variable resistor
can be varied between 0 and 12 Ω.
(i) The maximum possible current in the circuit is 2.0 A. Calculate the minimum
possible current.
(ii) On Fig. 5.2, sketch the variation with R of current I1 in the circuit.
2.0
I1 / A
1.0
0
0 4 8 12 R/Ω
[2]
Fig. 5.2
I2
A
6.0 Ω
Fig. 5.3
Calculate the maximum possible and minimum possible current I2 in the ammeter.
maximum I2 = ................................................... A
minimum I2 = ................................................... A
[2]
0
0
V
[2]
Fig. 5.4
[Total : 8]
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Describe
(i) the apparatus used to produce two sources of coherent waves that have circular
wavefronts,
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© UCLES 2011 9702/21/M/J/11 [Turn over
(c) A wave pattern produced in (b) is shown in Fig. 7.1. For
Examiner’s
Use
Fig. 7.1
On Fig. 7.1,
(i) draw two lines to show where maxima would be seen (label each of these lines
with the letter X), [1]
(ii) draw one line to show where minima would be seen (label this line with the letter N).
[1]
[Total : 7]
5 (a) Complete Fig. 1.1 to indicate whether each of the quantities is a vector or a scalar.
Fig. 1.1
[2]
(b) A ball is projected with a horizontal velocity of 1.1 m s–1 from point A at the edge of a table, as
shown in Fig. 1.2.
B
horizontal
ground
0.43 m
Fig. 1.2
The ball lands on horizontal ground at point B which is a distance of 0.43 m from the base of
the table. Air resistance is negligible.
(i) Calculate the time taken for the ball to fall from A to B.
(ii) Use your answer in (b)(i) to determine the height of the table.
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(b) A leisure-park ride consists of a carriage that moves along a railed track. Part of the track lies
in a vertical plane and follows an arc XY of a circle of radius 13 m, as shown in Fig. 2.1.
13 m
Y
13 m
carriage
mass 580 kg 22 m s–1 track
X
Fig. 2.1
The mass of the carriage is 580 kg. At point X, the carriage has velocity 22 m s–1 in a horizontal
direction. The velocity of the carriage then decreases to 12 m s–1 in a vertical direction at
point Y.
[2]
[1]
(iii) Use your answers in (b)(i) and (b)(ii) to calculate the average resistive force acting on
the carriage as it moves from X to Y.
(iv) Describe the change in the direction of the linear momentum of the carriage as it moves
from X to Y.
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[Total: 10]
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(b) Two batteries, each of electromotive force (e.m.f.) 6.0 V and negligible internal resistance, are
connected in series with three resistors, as shown in Fig. 5.1.
R
4.0 Ω X 6.0 V
6.0 V Y 1.5 Ω
Fig. 5.1
(i) The resistance R of the variable resistor is changed until the voltmeter in the circuit reads
zero.
Calculate
I = ....................................................... A [1]
2. the resistance R.
R = ...................................................... Ω [2]
State and explain the effect of the increase in R on the power transformed by each of the
batteries.
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[Total: 10]
(a) State the change, if any, to the number of neutrons in a nucleus of the sample that emits a
β– particle.
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(b) The number of β– particles passing a fixed point in the beam in a time of 2.0 minutes is
9.8 × 1010.
(c) Suggest why the β– particles are emitted with a range of kinetic energies.
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[Total: 5]