A LevelPhysicsAQAExam Questions1. Measurements & Their Errors1.2 Limitation of Physical Measurements

Limitation of Physical Measurements (AQA A Level Physics)

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1.2 Limitation of Physical Measurements

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1.2 Limitation of Physical Measurements

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11 mark

What is the reading shown on this milliammeter?

q1_limitation-of-physical-measurements_aqa-as-mcq

  • 2.35 mA

  • 2.7 mA

  • 3.4 mA

  • 3.7 mA

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21 mark

A micrometer is used to measure the diameters of two spheres.

diameter of first sphere = 15.01 ± 0.01 mm

diameter of second sphere = 17.38 ± 0.02 mm

The difference in the diameters is calculated.

What is the uncertainty in this difference?

  • ± 0.01 mm

  • ± 0.02 mm

  • ± 0.03 mm

  • ± 0.06 mm

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31 mark

A student carries out a series of determinations of the acceleration of free fall g. The table shows the results.

g / m s–2
4.91 4.89 4.88 4.90 4.93 4.92

What can be said about this experiment?

  • it is accurate and precise

  • it is accurate but not precise

  • it is not accurate and not precise

  • it is not accurate but is precise

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41 mark

The diagrams show digital voltmeter and analogue ammeter readings from a circuit in which electrical heating is occurring.

q4_limitation-of-physical-measurements_aqa-as-mcq

What is the electrical power of the heater?

  • 0.53 W

  • 0.58 W

  • 530 W

  • 580 W

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51 mark

A fixed quantity x subscript 0 is measured many times in an experiment that has experimental uncertainty. A graph is plotted to show the number n of times that a particular value x is obtained.

Which graph could be obtained if the measurement of x subscript 0 has a high precision and a low accuracy?

 q6_limitation-of-physical-measurements_aqa-as-mcq

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    61 mark

    Four people participate in a shooting competition. Each person gets four shots. The diagram shows the target boards of each participant after their turn.

    Which target has a low precision and a high accuracy?

    q7_limitation-of-physical-measurements_aqa-as-mcq

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      71 mark

      The diagram below shows the intensity peaks produced in four different diffraction experiments.

       Which of the following shows the intensity peaks with the highest resolution?

      q8_limitation-of-physical-measurements_aqa-as-mcq

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        81 mark

        An ammeter has a systematic error of –0.05 A. The ammeter is then connected to a circuit and shows a reading of 2.45 A.

        What should the real reading be?

        • 2.35 A

        • 2.40 A

        • 2.50 A

        • 2.55 A

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        91 mark

        The diagram shows the stem of a Celsius thermometer marked to show initial and final temperature values.

        q10_limitation-of-physical-measurements_aqa-as-mcq

        What is the temperature change expressed to an appropriate number of significant figures?

        • 14°C

        • 20.5°C

        • 21°C

        • 22.0°C

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        11 mark

        The measurement of a physical quantity may be subject to random errors and systematic errors.

        Which statement is correct?

        • random errors can be reduced by taking the average of several measurements

        • random errors are always caused by the person taking the measurement

        • a systematic error cannot be reduced by adjusting the apparatus

        • a systematic error results in a different reading each time the measurement is taken

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        21 mark

        In an experiment, a radio-controlled car takes 2.50 ± 0.05 s to travel 40.0 ± 0.1 m.

        What is the car’s average speed and the uncertainty in this value?

        • 16 ± 1 m s–1

        • 16.0 ± 0.2 m s–1

        • 16.0 ± 0.4 m s–1

        • 16.00 ± 0.36 m s–1

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        31 mark

        Four students each made a series of measurements of the acceleration of free fall g. The table shows the results obtained.

        Which set of results could be described as precise but not accurate?

        g / m s–2

        A

        9.81

        9.79

        9.84

        9.83

        B

        9.81

        10.12

        9.89

        9.94

        C

        9.45

        9.21

        8.99

        8.76

        D

        8.45

        8.46

        8.50

        8.41

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          41 mark

          The Young modulus of the material of a wire is to be found. The Young modulus E is given by the equation below.

          E = fraction numerator 4 F l over denominator pi d squared x end fraction

          The wire is extended by a known force and the following measurements are made.

          Which measurement has the largest effect on the uncertainty in the calculated value of the Young modulus?

           

          measurement

          symbol

          value

          A

          length of wire before force applied

          l

          2.043 ± 0.002 m

          B

          diameter of wire

          d

          0.54 ± 0.02 mm

          C

          force applied

          F

          19.62 ± 0.01 N

          D

          extension of wire with force applied

          x

          5.2 ± 0.2 mm

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            51 mark

            The strain energy W of a spring is determined from its spring constant k and extension x. The spring obeys Hooke’s law and the value of W is calculated using the equation shown.

            W space equals 1 half space k x squared

            The spring constant k is 100 ± 2 N m–1 and the extension x is 0.050 ± 0.002 m.

            What is the percentage uncertainty in the calculated value of W?

            • 6%

            • 10%

            • 16%

            • 32%

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            61 mark

            Four different students use a ruler to measure the length of a 15.0 cm pencil. Their measurements are recorded on four different charts.

            Which chart shows measurements that are precise but not accurate?

            q16_limitation-of-physical-measurements_aqa-as-mcq

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              71 mark

              Some students carry out an experiment to determine the resistivity of a metal wire.

              They determine the resistance from measurements of potential difference between the ends of the wire and the corresponding current.

              They measure the length of the wire with a ruler and the diameter of the wire using a micrometer. Each measurement is made with an uncertainty of 1 %.

              Which measurement gives the largest uncertainty in the calculated value of the resistivity?

              • current

              • diameter

              • length

              • potential difference

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              81 mark

              When comparing systematic and random errors, the following properties of errors were recorded:


              1

              The error is consistently too high or too low and by different amounts

              2

              The error is constantly too high or low and by the same amount each time

              3

              The error can be fully eliminated

              4

              The error cannot be fully eliminated

              5

              The error can be reduced by averaging repeated measurements

              6

              The error cannot be reduced by averaging repeated measurements

              Which properties apply to random errors?



              • 1, 3 and 6

              • 2, 4 and 6

              • 2, 3 and 6

              • 1, 4 and 5

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              91 mark

              A steel wire is stretched in an experiment to determine the Young modulus for steel.

              The uncertainties in the measurements are given below.

              measurement

              uncertainty

              load on wire

              ±2%

              length of wire

              ±0.2%

              diameter of wire

              ±1.5%

              extension

              ±1%

              What is the percentage uncertainty in the Young modulus?

              • 1.3%

              • 1.8%

              • 4.7%

              • 6.2%

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              101 mark

              A researcher plots a graph to investigate the variation of current and potential difference of a resistor, as shown in the diagram.

              q20_limitation-of-physical-measurements_aqa-as-mcq

              After realising they have read the manufacturers label of their electrical equipment incorrectly, they determine the size of the error bars shown should decrease.

              Which row correctly describes how this will affect the value of the maximum gradient Gmax, the minimum gradient Gmin, and the resistance of the resistor R?

               

              Gmax

              Gmin

              R

              A

              increase

              increase

              increase

              B

              decrease

              decrease

              decrease

              C

              increase

              decrease

              no change

              D

              decrease

              increase

              no change

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                11 mark

                In an experiment investigating the electrolysis of copper, a student sets out to find the electrochemical equivalent, Z.

                The electrochemical equivalent of a substance is the amount of substance deposited on a cathode per Coulomb of charge.

                This can be determined using the equation:

                 

                Z = fraction numerator m subscript 1 minus m subscript 2 over denominator I t end fraction

                Where:

                • Mass of cathode before passing current, m1 = (56.32 ± 0.01) × 10–3 kg
                • Mass of cathode after passing current, m2= (51.28 ± 0.01) × 10–3 kg
                • Current, I = (3.00 ± 0.05) A
                • Time, t = (4800 ± 1) s

                What is the largest possible value of Z from these readings?

                • 3.43 × 10–7 kg C–1

                • 3.50 × 10–7  kg C–1

                • 3.57 × 10–7 kg C–1

                • 3.65 × 10–7 kg C–1

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                21 mark

                A student uses a digital ammeter to measure a current. The reading of the ammeter is found to fluctuate between 1.98 A and 2.02 A.

                The manufacturer of the ammeter states that any reading has a systematic uncertainty of ±1%.

                Which value of current should be quoted by the student?

                • (1.98 ± 0.04) A

                • (2.00 ± 0.02) A

                • (2.02 ± 0.02) A

                • (2.00 ± 0.04) A

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                31 mark

                The uncertainty in the value of the momentum of a trolley passing between two points X and Y varies with the choice of measuring devices.

                Measurements for the same trolley made by different instruments were recorded as follows:

                1

                distance between X and Y using a metre rule with cm divisions = 0.55 m

                2

                distance between X and Y using a metre rule with mm divisions = 0.547 m

                3

                timings using a wristwatch measuring to the nearest 0.5s at X = 0.0s and at Y = 4.5 s

                4

                timings using light gates measuring to the nearest 0.1s at X = 0.0s and at Y = 4.3 s

                5

                mass of trolley using a balance measuring to the nearest g = 6.4 × 10–2 kg

                6

                mass of trolley using a balance measuring to the nearest 10g = 6 × 10–2 kg

                Which measurements, one for each quantity measured, leads to the least uncertainty in the value of the momentum of the trolley?

                • 1, 3 and 6

                • 1, 4 and 6

                • 2, 3 and 6

                • 2, 4 and 5

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                41 mark

                In an experiment to determine the acceleration of free fall g, a ball bearing is held by an electromagnet.

                When the current to the electromagnet is switched off, a clock starts, and the ball bearing falls. After falling a distance h, the ball bearing strikes a switch to stop the clock which measures the time t of the fall.

                Systematic errors may cause t and h to be measured incorrectly.

                Which of the following must cause g to appear greater than 9.81 m s–2?

                • h measured as being smaller than it actually is and t is measured correctly

                • h measured as being smaller than it actually is and t measured as being larger than it actually is

                • h measured as being larger than it actually is and t measured as being larger than it actually is

                • h is measured correctly and t measured as being smaller than it actually is

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                51 mark

                The diagram shows an experiment to measure the speed of a small ball falling at constant speed through a clear liquid in a glass tube.

                q25_limitation-of-physical-measurements_aqa-as-mcq

                There are two marks on the tube. The top mark is positioned at 115 ± 1 mm on the adjacent rule and the lower mark at 385 ± 1 mm. The ball passes the top mark at 1.50 ± 0.02 s and passes the lower mark at 3.50 ± 0.02 s.

                The constant speed of the ball is calculated to be 135 mm s–1

                Which expression calculates the fractional uncertainty in the value of this speed?

                • 2 over 270 space plus space fraction numerator 0.04 over denominator 2.00 end fraction

                • 1 over 270 space plus space fraction numerator 0.02 over denominator 2.00 end fraction

                • 1 over 115 space plus space fraction numerator 0.02 over denominator 1.50 end fraction

                • 1 over 385 space plus space fraction numerator 0.02 over denominator 3.50 end fraction

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                61 mark

                A student finds the density of a liquid by measuring its mass and volume. The following is a summary of his measurements.

                mass of empty beaker = (20 ± 1) g

                mass of beaker + liquid = (70 ± 1) g

                volume of liquid = (10.0 ± 0.5) cm3

                He correctly calculates the density of the liquid as 5.0 g cm–3.

                What is the uncertainty in this value?

                • 0.3 g cm–3

                • 0.5 g cm–3

                • 0.6 g cm–3

                • 2.6 g cm–3

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                71 mark

                Max Planck was one of the pioneers of quantum theory. He proposed a system in which the base units are based on the speed of light, c, the gravitational constant, G, and the reduced Planck constant, h , which is equal to Planck’s constant, h, divided by 2π:

                h equals fraction numerator h over denominator 2 pi end fraction

                In the Planck system, length is replaced by the Planck length, l subscript p, which is theorised to be the smallest distance there is. l subscript p is defined by

                l subscript p = square root of fraction numerator h G over denominator c cubed end fraction end root

                The percentage uncertainties in the accepted values of G and h are ±7 × 10–2 % and ±6 × 10–4 % respectively.

                What is the corresponding percentage uncertainty in the conversion factor between the Planck length and metres?

                • 0.02 %

                • 0.04 %

                • 0.08 %

                • 0.16 %

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                81 mark

                A mass is dropped from rest and falls through a distance of 2.0 m in a vacuum. An observer records the time taken for the mass to fall through this distance using a manually operated stopwatch and repeats the measurements a further two times.

                The average result of these measured times, displayed in the table below, was used to determine a value for the acceleration of free fall. This was calculated to be 9.8 m s–2.

                 

                first measurement

                second measurement

                third measurement

                average
                time/ s

                0.6

                0.73

                0.59

                0.64

                Which statement best describes the quality of the measurements taken for this experiment?

                • The measurements are precise and accurate with no evidence of random errors.

                • The measurements are not accurate and not always recorded to the degree of precision of the measuring device but the calculated experimental result is accurate.

                • The measurements are not always recorded to the degree of precision of the measuring device but are accurate. Systematic errors may be present.

                • The range of results shows that there were random errors made but the calculated value is correct so the experiment was successful.

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                91 mark

                A student collects values of the time period, T, of a pendulum at different lengths of string, L. They want to investigate the relationship:

                T = 2π square root of L over g end root

                They plot the values on a graph along with the error bars associated with each point, as shown in the diagram.

                q29_limitation-of-physical-measurements_aqa-as-mcq

                What is the percentage uncertainty in the experimental value of g?

                • 1.3 %

                • 2.6 %

                • 3.8 %

                • 4.6 %

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                101 mark

                Which of the following experimental techniques would not reduce the random error of the quantity being investigated?

                • Calibrating the Y-sensitivity of the oscilloscope before measuring a voltage

                • Timing a large number of oscillations to determine a time period

                • Plotting a graph of voltage and current readings for an ohmic device and using its gradient to determine resistance

                • Measuring several internodal distances on a standing wave to find the mean internodal distance

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