Errors, uncertainties and error barsAQA A-Level Physics: Subtopic test

1. 1
   A student measures the diameter of a wire with a micrometer screw gauge that reads to the nearest 0.01 mm. With the jaws closed and nothing between them, the gauge reads 0.02 mm. The student then measures the diameter at five different places along the wire and the readings vary slightly, between 0.41 mm and 0.45 mm.

   (a)

   What type of error is shown by the reading of 0.02 mm when the jaws of the gauge are closed?

   [1 mark]

   • AA random error
   • BAn anomalous result
   • CA systematic error
   • DA lack of precision

   (b)

   What should the student do about the zero reading?

   [1 mark]

   • ASubtract 0.02 mm from every diameter reading
   • BTake more readings and calculate the mean
   • CAdd 0.02 mm to every diameter reading
   • DIgnore it, because the readings already vary

   (c)

   Explain why calculating the mean of the readings taken at the five places reduces the effect of random error but does not remove the zero error.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student determines the density of a metal cube. The mass of the cube is 85.0 ± 0.5 g and the length of each side is 2.00 ± 0.02 cm.

   (a)

   What is the percentage uncertainty in the length of a side?

   [1 mark]

   • A0.01%
   • B0.02%
   • C0.1%
   • D1.0%

   (b)

   What is the percentage uncertainty in the volume of the cube?

   [1 mark]

   • A1.0%
   • B3.0%
   • C2.0%
   • D0.03%

   (c)

   Calculate the percentage uncertainty in the density of the metal.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student times 20 complete oscillations of a simple pendulum of length 0.800 ± 0.002 m. The time for 20 oscillations is 35.9 ± 0.4 s. The acceleration of free fall can be found from g = 4π²L/T², where T is the period of the pendulum.

   (a)

   Calculate the period T of the pendulum and its absolute uncertainty.

   [3 marks]

   (b)

   Calculate g and its absolute uncertainty.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student hangs loads F of between 1.0 N and 6.0 N from a spring and measures the extension e for each load. The student plots e against F and draws error bars on each point. The best-fit line has a gradient of 0.0250 m N⁻¹ and cuts the e axis at 0.004 m. The steepest line that still passes through all the error bars has a gradient of 0.0265 m N⁻¹ and cuts the e axis at 0.002 m. The spring constant k is the reciprocal of the gradient, and the manufacturer quotes k = 42 N m⁻¹.

   (a)

   Describe how the uncertainty in the gradient and the uncertainty in the intercept of a straight-line graph are found, and how an intercept can reveal a systematic error.

   [6 marks]

   (b)

   Determine the spring constant with its absolute uncertainty. Evaluate whether the data are consistent with the manufacturer's value and with the extension being zero when the load is zero.

   [6 marks]

   Total for question 4: 12 marks

End of questions