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A-Level CAIE Physics 1 3 Errors And Uncertainties Question Bank

Practice A-Level CAIE Physics 1 3 Errors And Uncertainties questions by syllabus topic with past-paper context, marks, difficulty and question previews on Eduninja.

10 matching questions · Open interactive library

Question 1

1

2 marks

Question 1(c)

1(c)

The maximum useful output power P of a car travelling on a horizontal road is given by where v is the maximum speed of the car and b is a constant. For the car, and \(b=0.56 \pm 7 \%\) in SI units.

structured2 marks

Question 1(c)(ii)

1(c)(ii)

Determine the absolute uncertainty in the value of v. absolute uncertainty = \(\mathrm{ms}^{-1}\)

Mediumstructured2 marks

Answer

\[ \text { percentage uncertainty }=(5 \%+7 \%) / 3(=4 \%) \] or fractional uncertainty =(0.05+0.07) / 3(=0.04) C1 absolute uncertainty \(=0.04 \times 53\) \[ =( \pm) 2 \mathrm{~m} \mathrm{~s}^{-1} \] A1

Question 1

1

2 marks

Question 1(b)

1(b)

A square solar panel with sides of length 1300 mm is shown in Fig. 1.1. Light is incident normally on the solar panel.

structured2 marks

Question 1(b)(ii)

1(b)(ii)

The percentage uncertainty in the incident power is \(\pm 3 \%\). The uncertainty in the length of each side is \(\pm 5 \mathrm{~mm}\). Calculate the percentage uncertainty in the intensity of the light.

Mediumstructured2 marks

Answer

percentage uncertainty \(=3+2 \times(5 / 1300) \times 100\) C1 \[ \begin{aligned} =3+2 \times 0.38 =( \pm) 4 \% \end{aligned} \] A1

Question 1

1

A metal wire has a cross-section of diameter approximately 0.8 mm .

structured4 marks

Question 1(a)

1(a)

State what instrument should be used to measure the diameter of the wire.

Easystructured1 marks

Answer

micrometer/screw gauge/digital callipers B1 [1]

Question 1(b)

1(b)

State how the instrument in (a) is

structured3 marks

Question 1(b)(i)

1(b)(i)

checked so as to avoid a systematic error in the measurements,

Easystructured1 marks

Answer

look/check for zero error \(\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \quad\) B1

Question 1(b)(ii)

1(b)(ii)

used so as to reduce random errors.

Easystructured2 marks

Answer

take several readings M1 around the circumference/along the wire A1

Question 1

1

A digital voltmeter with a three-digit display is used to measure the potential difference across a resistor. The manufacturers of the meter state that its accuracy is \(\pm 1 \%\) and \(\pm 1\) digit. The reading on the voltmeter is 2.05 V .

structured4 marks

Question 1(a)

1(a)

For this reading, calculate, to the nearest digit,

structured2 marks

Question 1(a)(i)

1(a)(i)

a change of 1 % in the voltmeter reading, change = V

Easystructured1 marks

Answer

1 % of \(\pm 2.05\) is \(\pm 0.02\)

Question 1(a)(ii)

1(a)(ii)

the maximum possible value of the potential difference across the resistor. maximum value = V

Easystructured1 marks

Answer

max. value is 2.08 V

Question 1(b)

1(b)

The reading on the voltmeter has high precision. State and explain why the reading may not be accurate.

Easystructured2 marks

Answer

there may be a zero error/calibration error/systematic error which makes all readings either higher or lower than true value

Question 1

1

3 marks

Question 1(b)

1(b)

A uniform cylinder has diameter D, length L and mass M. The density \(\rho\) of the cylinder is given by Table 1.2 shows the data obtained from an experiment to determine the density of the cylinder.

structured3 marks

Question 1(b)(i)

1(b)(i)

Calculate the percentage uncertainties in D and L. Write your answers in Table 1.2.

Mediumstructured1 marks

Answer

% D=0.4 % and % L=0.6 % A1

Question 1(b)(iii)

1(b)(iii)

Calculate the percentage uncertainty in the density. percentage uncertainty = \%

Mediumstructured2 marks

Answer

percentage uncertainty \(=0.4+(2 \times 0.4)+0.6\) C1 = 1.8\% A1

Question 1

1

2 marks

Question 1(b)

1(b)

The radius of a small sphere is determined from a measurement of the volume of the sphere. The sphere is submerged in water, displacing some of the water into a measuring cylinder as shown in Fig. 1.1. The measured volume of displaced water is \((28.0 \pm 0.5) \mathrm{cm}^{3}\). Calculate:

structured2 marks

Question 1(b)(ii)

1(b)(ii)

the percentage uncertainty in the radius of the sphere.

Mediumstructured2 marks

Answer

percentage uncertainty in \(V=(0.5 / 28) \times 100\) ( = 1.79\%) C1 percentage uncertainty in r=1.79 / 3 = 0.6\% A1

Question 1

1

A well has a depth of 36 m from ground level to the surface of the water in the well, as shown in Fig. 1.1. A student wishes to find the depth of the well. The student plans to drop a stone down the well and record the time taken from releasing the stone to hearing the splash made by the stone as it enters the water.

structured7 marks

Question 1(b)

1(b)

The time recorded by the student using a stop-watch is not equal to the time in (a). Suggest three possible reasons, other than the effect of air resistance, for this difference. 1 2 3

Mediumstructured3 marks

Answer

reaction time between hearing the splash and stopping the stop-watch - the sound (of the splash) takes time to reach the student or the stone hits the water at a different time to the sound being heard or the sound (of the splash) has to travel to the student - the student might not let go of the stone from ground level - the student might not let go of the stone and start the stop-watch at the same time - stop-watch may not be properly calibrated / has a zero error - (local value of) g is not (exactly) \(9.81\left(\mathrm{~m} \mathrm{~s}^{-2}\right)\) - stone given initial velocity / initial velocity not zero - stone does not fall (exactly) vertically / in a straight line Any three points, 1 mark each B3

Question 1(c)

1(c)

The student repeats the experiment three times and uses the results to calculate the depth of the well. The values are shown in Table 1.1. The true depth of the well is 36.0 m . Explain why these results may be described as precise but not accurate.

Mediumstructured2 marks

Answer

precise: results are close together / have little scatter B1 not accurate: the values are not close to / 50\% different / (very) different from the true value B1

Question 1

1

1 marks

Question 1(c)

1(c)

An experiment is performed to determine the value of k by measuring the values of the other quantities in the equation in (b). The values of L and R each have a percentage uncertainty of 2\%. State and explain, quantitatively, which of these two quantities contributes more to the percentage uncertainty in the calculated value of k.

Mediumstructured1 marks

Answer

R contributes \(4 \times 2 \%\) or 8 % (and L contributes 2 % ) so R contributes more (to the percentage uncertainty in k ) B1

Question 1

1

1 marks

Question 1(c)

1(c)

An experiment is performed to determine the acceleration of the car in (b). The following measurements are obtained:

structured1 marks

Question 1(c)(ii)

1(c)(ii)

Determine the percentage uncertainty, to two significant figures, in a. percentage uncertainty =

Mediumstructured0 marks

Answer

percentage uncertainty \(=(2 \times 0.8)+0.5\) C1 = 2.1\% A1

Question 1(c)(iii)

1(c)(iii)

Use your answers in (c)(i) and (c)(ii) to determine the absolute uncertainty in the calculated value of a. absolute uncertainty = \(\mathrm{ms}^{-2}\)

Mediumstructured1 marks

Answer

absolute uncertainty \(=(2.1 / 100) \times 0.97\) \[ =0.02 \mathrm{~m} \mathrm{~s}^{-2} \] A1

Question 1

1

The rate of flow Q of a liquid along a narrow pipe of length L and radius r is given by where \(\alpha\) is a constant. An experiment is carried out to determine the value of \(\alpha\). The data from the experiment are shown in Table 1.1.

structured5 marks

Question 1(b)

1(b)

Show that the percentage uncertainty in \(\alpha\) is 15 %.

Mediumstructured1 marks

Answer

(percentage uncertainty = ) \(3+4+2 \times 4=15\) (\%) A1

Question 1(c)

1(c)

Calculate \(\alpha\) with its absolute uncertainty. Give your answer to an appropriate number of significant figures.

Mediumstructured3 marks

Answer

\[ \begin{aligned} \alpha =Q L / r^{4} =2.72 \times 10^{-8} \times 2.5 \times 10^{-2} /\left(7.1 \times 10^{-5}\right)^{4} =2.7 \times 10^{7} \end{aligned} \] C1 absolute uncertainty \(=0.15 \times\left[2.7 \times 10^{7}\right]\) \[ =0.4 \times 10^{7} \] C1 \(\alpha=(2.7 \pm 0.4) \times 10^{7} \mathrm{~s}^{-1}\) A1