Measurements and their errorsAQA A-Level Physics: Topic test

20 questions, 54 marks

AQA A-Level Physics

Measurements and their errors topic test

Total 54 marks

Name

Class

Date

1
A radio telescope receives a signal from a distant gas cloud at a frequency of 1.42 GHz. The detector records the signal in pulses, each lasting 35 μs.
(a)
What is the frequency of the signal in MHz?
[1 mark]
A1.42×10³
B1.42×10⁻³
C1.42×10⁶
D1.42×10⁹
(b)
What is the pulse duration of 35 μs in seconds?
[1 mark]
A3.5×10⁻² s
B3.5×10⁻⁵ s
C3.5×10⁻⁸ s
D3.5×10⁷ s
(c)
Calculate the energy of one photon of the signal in joules and in electronvolts. Use h = 6.63×10⁻³⁴ J s and e = 1.60×10⁻¹⁹ C.
[2 marks]
Total for question 1: 4 marks
2
A student measures the resistance of a wire. She records the potential difference across it with a digital voltmeter and the current through it with a digital ammeter, obtaining V = 4.60 ± 0.05 V and I = 0.250 ± 0.005 A.
(a)
What is the percentage uncertainty in the current?
[1 mark]
A0.50%
B0.020%
C2.0%
D20%
(b)
The percentage uncertainty in V is 1.09% and in I is 2.0%. What is the percentage uncertainty in the resistance R = V/I?
[1 mark]
A0.91%
B1.5%
C2.3%
D3.1%
(c)
Calculate the resistance of the wire and state it with its absolute uncertainty.
[2 marks]
Total for question 2: 4 marks
3
A student measures the resistance R of a uniform nichrome wire at several different lengths L and plots a graph of R against L. For a uniform wire R = ρL/A, where ρ is the resistivity and A is the cross-sectional area. The best-fit line has a gradient of 5.30 Ω m⁻¹, the steepest acceptable line has a gradient of 5.62 Ω m⁻¹ and the shallowest acceptable line has a gradient of 5.04 Ω m⁻¹. The diameter of the wire, measured with a micrometer, is 0.250 ± 0.005 mm.
(a)
Determine the percentage uncertainty in the gradient of the graph.
[3 marks]
(b)
Calculate the resistivity of the nichrome, with its absolute uncertainty. Use the percentage uncertainty from part (a).
[4 marks]
Total for question 3: 7 marks
4
A student wants to find the speed of a toy car running along a straight corridor. She marks out a distance of 8.00 m with a metre rule (uncertainty ±1 mm) and times the car by hand with a stopwatch that reads to 0.01 s. Five repeat times are 4.21 s, 4.58 s, 4.35 s, 4.62 s and 4.30 s. The mass of the car is 120 ± 1 g.
(a)
Evaluate the precision of the student's method and suggest how the investigation could be improved.
[6 marks]
(b)
Calculate the kinetic energy of the car when it travels at its mean speed, with its absolute uncertainty. Take the uncertainty in the time as half the range of the readings and ignore the uncertainty in the distance.
[6 marks]
Total for question 4: 12 marks
5
A small town has about 2×10⁴ residents who each use about 100 litres of water per day. Take 1 litre of water to have a mass of 1.0 kg, the density of water to be 1.0×10³ kg m⁻³ and g = 9.81 m s⁻².
(a)
Which is the best estimate, to the nearest order of magnitude, of the volume of water used by the town in one day?
[1 mark]
A10² m³
B10³ m³
C10⁶ m³
D10⁴ m³
(b)
The water is stored in a tank that is 10 m deep. Which is the best estimate of the pressure due to the water at the base of the tank?
[1 mark]
A10² Pa
B10³ Pa
C10⁴ Pa
D10⁵ Pa
(c)
Estimate the average power needed to pump the town's daily water supply through a height of 10 m in 24 hours, to the nearest order of magnitude.
[2 marks]
Total for question 5: 4 marks
6
A student investigates SI units in an experiment on waves on a stretched string. The tension in the string is a force, and the mass per unit length of the string is written as μ.
(a)
Which of the following gives the newton in SI base units?
[1 mark]
Akg m s⁻²
Bkg m² s⁻²
Ckg m s⁻¹
Dkg m⁻¹ s⁻²
(b)
The mass per unit length of the string is 2.5 g m⁻¹. What is this in kg m⁻¹?
[1 mark]
A2.5×10³
B2.5×10⁻⁶
C2.5×10⁻³
D2.5×10⁻²
(c)
The speed v of waves on the string is given by v = √(T/μ), where T is the tension. The tension is 40 N and μ = 2.5 g m⁻¹. Calculate v.
[2 marks]
Total for question 6: 4 marks
7
A student estimates the number of grains of sand on a beach. A typical grain is a sphere of diameter about 0.5 mm. The beach is about 200 m long and 30 m wide, and the sand is about 2 m deep. The grains fill about 60% of the volume of the sand, the rest being air.
(a)
Estimate the number of grains of sand on the beach, to the nearest order of magnitude.
[3 marks]
(b)
The density of the sand grains is 2.6×10³ kg m⁻³ and a lorry can carry 2.0×10⁴ kg of sand. Estimate the number of lorry loads needed to remove all the sand, to the nearest order of magnitude.
[4 marks]
Total for question 7: 7 marks
8
A student wants to find the thickness of a single sheet of printer paper. She measures a stack of 500 sheets with a rule that reads to the nearest millimetre and finds a height of 4.8 cm. She then measures a stack of 100 sheets and finds a height of 1.0 cm. She takes the uncertainty in each height to be ±1 mm.
(a)
Evaluate the two methods and decide which gives the more reliable thickness for one sheet. Suggest how the result could be made more accurate.
[6 marks]
(b)
A library holds about 2×10⁵ books, each with about 300 pages printed on both sides of 150 sheets. Use the student's result from the 500-sheet stack to estimate the total thickness of paper in the library's books, in metres and in kilometres, and compare it, to the nearest order of magnitude, with the height of the Burj Khalifa, which is 830 m.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).