Measurement uncertainty and error Knowledge-Based Download PDF

Questions

1. 1.

   Which of the following procedures is effective in identifying and eliminating a systematic error in an experimental measurement?

   • A) Repeating the trials multiple times and calculating the mean value
   • B) Increasing the number of decimal places recorded for each observation
   • C) Calculating the range between the maximum and minimum recorded values
   • D) Calibrating the measuring instrument against an accepted reference standard
2. 2.

   On a graph of experimental data, what is represented by a vertical error bar drawn through a data point?

   • A) The percentage discrepancy between the measured value and the accepted theoretical value
   • B) The constant systematic calibration error present in the experimental apparatus
   • C) The absolute uncertainty associated with the independent variable
   • D) The uncertainty associated with the measurement of the dependent variable
3. 3.

   When experimental data are plotted to determine a linear relationship, how does a constant systematic error in the measured dependent variable affect the line of best fit?

   • A) It shifts the vertical intercept while the gradient remains unchanged.
   • B) It alters the gradient while the vertical intercept remains unchanged.
   • C) It increases the random scatter of the data points around the best-fit line.
   • D) It curves the best-fit line so that the relationship is no longer linear.
4. 4.

   Which of the following is an example of a random error in an experimental measurement?

   • A) A voltmeter that consistently reads 0.5 V higher than the true potential difference
   • B) A micrometer screw gauge that has an uncorrected zero offset
   • C) Unpredictable air currents causing small, irregular fluctuations in the readings of a sensitive balance
   • D) A wooden meter stick whose zero end has been worn away by 2 mm
5. 5.

   The side length of an equilateral triangle is measured as $s = (8.0 \pm 0.3)$ cm. What is the perimeter of the triangle expressed with its absolute uncertainty?

   • A) $(24.0 \pm 0.1)$ cm
   • B) $(24.0 \pm 0.3)$ cm
   • C) $(24.0 \pm 0.6)$ cm
   • D) $(24.0 \pm 0.9)$ cm
6. 6.

   The kinetic energy of an object is given by $E_{\text{k}} = \frac{1}{2}mv^2$. If the percentage uncertainty in the mass $m$ is 4% and the percentage uncertainty in the speed $v$ is 3%, what is the percentage uncertainty in the calculated kinetic energy?

   • A) 7%
   • B) 10%
   • C) 11%
   • D) 14%
7. 7.

   Which of the following measurements has the smallest percentage uncertainty?

   • A) $5.0 \pm 0.2\text{ cm}$
   • B) $20.0 \pm 0.6\text{ cm}$
   • C) $50.0 \pm 0.5\text{ cm}$
   • D) $2.0 \pm 0.1\text{ cm}$
8. 8.

   A micrometer screw gauge has a zero error of $+0.03\text{ mm}$. If the measured reading for the thickness of a glass slide is $1.85\text{ mm}$, what is the corrected thickness of the slide?

   • A) $1.88\text{ mm}$
   • B) $1.82\text{ mm}$
   • C) $1.85\text{ mm}$
   • D) $1.79\text{ mm}$
9. 9.

   A student measures a length as $12.438\text{ cm}$ with an absolute uncertainty of $0.06\text{ cm}$. How should this measurement be properly reported with its uncertainty?

   • A) $(12.44 \pm 0.06)\text{ cm}$
   • B) $(12.438 \pm 0.06)\text{ cm}$
   • C) $(12.4 \pm 0.06)\text{ cm}$
   • D) $(12.44 \pm 0.1)\text{ cm}$
10. 10.

    A student uses a digital balance whose display reads to the nearest 0.01 g. What is the instrumental reading uncertainty associated with a single measurement from this balance?

    • A) ±0.01 g
    • B) ±0.005 g
    • C) ±0.02 g
    • D) ±0.1 g
11. 11.

    An electric current is measured as 4.0 A with a percentage uncertainty of 5%. What is the absolute uncertainty of this measurement?

    • A) ±0.05 A
    • B) ±0.20 A
    • C) ±0.80 A
    • D) ±1.25 A
12. 12.

    A student repeats a timing measurement five times and records values of 1.24 s, 1.28 s, 1.22 s, 1.25 s, and 1.30 s. Using half the range of the data set, what is the estimated absolute uncertainty in the measured time?

    • A) 0.08 s
    • B) 0.04 s
    • C) 0.02 s
    • D) 0.01 s
13. 13.

    A student measures the total thickness of a stack of 50 identical index cards as $25.0 \pm 1.0$ mm. What is the thickness of a single card expressed with its absolute uncertainty?

    • A) $(0.50 \pm 0.02)$ mm
    • B) $(0.50 \pm 1.00)$ mm
    • C) $(0.50 \pm 0.10)$ mm
    • D) $(0.50 \pm 0.05)$ mm
14. 14.

    A runner travels a distance of $d = (100 \pm 2)\text{ m}$ in a time of $t = (20.0 \pm 0.6)\text{ s}$. What is the absolute uncertainty in the calculated speed of the runner?

    • A) $0.25\text{ m/s}$
    • B) $0.05\text{ m/s}$
    • C) $2.60\text{ m/s}$
    • D) $0.10\text{ m/s}$
15. 15.

    The radius of a sphere is measured with a percentage uncertainty of 2%. What is the percentage uncertainty in the calculated volume of the sphere?

    • A) 6%
    • B) 8%
    • C) 4%
    • D) 2%
16. 16.

    Which of the following procedures is effective in reducing the uncertainty caused by random errors in an experiment?

    • A) Calibrating the measuring instrument against an accepted reference standard
    • B) Taking multiple independent readings and calculating their arithmetic mean
    • C) Identifying and subtracting the zero offset of the instrument from every reading
    • D) Replacing the apparatus with an instrument that has a larger full-scale range
17. 17.

    When determining the change in temperature $\Delta T = T_2 - T_1$, a student records $T_1 = (18.4 \pm 0.2)\text{ }^\circ\text{C}$ and $T_2 = (29.7 \pm 0.3)\text{ }^\circ\text{C}$. What is the calculated change in temperature expressed with its absolute uncertainty?

    • A) $(11.3 \pm 0.1)\text{ }^\circ\text{C}$
    • B) $(11.3 \pm 0.25)\text{ }^\circ\text{C}$
    • C) $(11.3 \pm 0.3)\text{ }^\circ\text{C}$
    • D) $(11.3 \pm 0.5)\text{ }^\circ\text{C}$
18. 18.

    A researcher measures the boiling point of pure water at standard atmospheric pressure four times, obtaining values of 104.1 °C, 104.2 °C, 104.0 °C, and 104.1 °C. If the accepted true boiling point is 100.0 °C, which statement best characterizes this experimental data set?

    • A) High precision and low accuracy
    • B) High accuracy and low precision
    • C) Low precision and low accuracy
    • D) High precision and high accuracy
19. 19.

    Which of the following statements correctly describes a systematic error in physical measurements?

    • A) It produces unpredictable fluctuations that cancel out when repeated measurements are averaged.
    • B) It can be minimized by increasing the sample size and calculating the mean value.
    • C) It shifts measured values by a consistent magnitude or in a constant direction away from the true value.
    • D) It is eliminated by using an instrument with finer scale markings to record more decimal places.
20. 20.

    The length and width of a rectangular plate are measured as $20.0 \pm 0.4$ cm and $10.0 \pm 0.1$ cm, respectively. What is the percentage uncertainty in the calculated area of the plate?

    • A) 1.0%
    • B) 2.0%
    • C) 2.5%
    • D) 3.0%