A student calculates the acceleration of an object to be $2.476\text{ m/s}^2$ with an estimated absolute uncertainty of $\pm 0.063\text{ m/s}^2$. According to standard experimental reporting conventions, how should this measurement and its uncertainty be recorded?

A) $(2.476 \pm 0.063)\text{ m/s}^2$

B) $(2.5 \pm 0.1)\text{ m/s}^2$

C) $(2.48 \pm 0.06)\text{ m/s}^2$

D) $(2.476 \pm 0.06)\text{ m/s}^2$

An instrument has a fixed absolute reading uncertainty. Which of the following actions reduces the percentage uncertainty of a measurement made with this instrument?

A) Increasing the magnitude of the measured quantity

B) Decreasing the magnitude of the measured quantity

C) Rounding the recorded measurement to fewer significant figures

D) Introducing a constant zero offset to the instrument readings

When experimental data for two directly proportional physical quantities are plotted on a graph, how does a constant zero error in the dependent variable affect the line of best fit?

A) It increases the random scatter of the plotted data points around the line.

B) It shifts the line to produce a non-zero vertical intercept without altering its slope.

C) It changes the slope of the line while maintaining an intercept at the origin.

D) It introduces a curvature that causes the linear relationship to appear non-linear.

Which of the following conditions causes a parallax error when reading a measurement on an analog instrument?

A) The zero mark of the instrument being shifted before the measurement is taken

B) The line of sight not being perpendicular to the scale markings

C) Random fluctuations in ambient temperature during the experiment

D) Inherent limitations imposed by the spacing of the smallest scale division

Which of the following statements correctly distinguishes between the accuracy and the precision of an experimental measurement?

A) Accuracy refers to the degree of agreement among repeated measurements, whereas precision indicates how close a measured value is to the accepted true value.

B) Accuracy indicates how close a measured value is to the accepted true value, whereas precision refers to the agreement or reproducibility among repeated measurements.

C) Accuracy depends entirely on the resolution of the measuring device, whereas precision is determined exclusively by the presence of systematic error.

D) Accuracy can always be improved simply by averaging repeated trials, whereas precision is independent of the number of trials conducted.

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

A) An incorrectly calibrated digital scale that consistently records 0.50 g above the actual mass for every trial.

B) Unpredictable drafts in the room that cause consecutive readings on an open balance to fluctuate randomly.

C) Slight variations in an observer's reaction time when starting and stopping a manual stopwatch across repeated runs.

D) Random electrical noise in a detector circuit causing scattered readings both above and below the true voltage.

Which of the following procedures is effective in reducing the effect of random errors in an experiment?

A) Calibrating the measuring instrument against a known standard

B) Subtracting a predetermined zero offset from each recorded value

C) Maintaining identical laboratory conditions while taking only a single measurement

D) Repeating the measurement multiple times and calculating the average value

Measurement uncertainty and error Knowledge-Based Practice

Physics · Introduction to Physics · Physics · Measurement & Units

19 Physics practice questions on Measurement uncertainty and error. Questions that assess core concepts and understanding.

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1.
A student calculates the acceleration of an object to be $2.476\text{ m/s}^2$ with an estimated absolute uncertainty of $\pm 0.063\text{ m/s}^2$ . According to standard experimental reporting conventions, how should this measurement and its uncertainty be recorded?
- A) $(2.476 \pm 0.063)\text{ m/s}^2$
- B) $(2.5 \pm 0.1)\text{ m/s}^2$
- C) $(2.48 \pm 0.06)\text{ m/s}^2$
- D) $(2.476 \pm 0.06)\text{ m/s}^2$
2.
When analyzing experimental data on a graph, a student determines that the steepest line of best fit has a gradient of $1.85\text{ m/s}$ and the shallowest line of best fit has a gradient of $1.55\text{ m/s}$ . What is the absolute uncertainty in the gradient?
- A) $0.05\text{ m/s}$
- B) $0.30\text{ m/s}$
- C) $1.70\text{ m/s}$
- D) $0.15\text{ m/s}$
3.
An instrument has a fixed absolute reading uncertainty. Which of the following actions reduces the percentage uncertainty of a measurement made with this instrument?
- A) Increasing the magnitude of the measured quantity
- B) Decreasing the magnitude of the measured quantity
- C) Rounding the recorded measurement to fewer significant figures
- D) Introducing a constant zero offset to the instrument readings
4.
The frequency $f$ of a wave is determined from its measured period $T$ using the relationship $f = 1/T$ . If the period is measured with a percentage uncertainty of 4%, what is the percentage uncertainty in the calculated frequency?
- A) 0.25%
- B) 2.0%
- C) 8.0%
- D) 4.0%
5.
The side length of a square is measured as $(15.0 \pm 0.2)\text{ cm}$ . What is the absolute uncertainty in the calculated perimeter of the square?
- A) $\pm 0.8\text{ cm}$
- B) $\pm 0.2\text{ cm}$
- C) $\pm 0.4\text{ cm}$
- D) $\pm 1.6\text{ cm}$
6.
An experiment yields a measured aluminium density of 2.43 g/cm³, while the accepted theoretical value is 2.70 g/cm³. What is the percentage error of this experimental measurement?
- A) 5.0%
- B) 10%
- C) 11.1%
- D) 27%
7.
When experimental data for two directly proportional physical quantities are plotted on a graph, how does a constant zero error in the dependent variable affect the line of best fit?
- A) It increases the random scatter of the plotted data points around the line.
- B) It shifts the line to produce a non-zero vertical intercept without altering its slope.
- C) It changes the slope of the line while maintaining an intercept at the origin.
- D) It introduces a curvature that causes the linear relationship to appear non-linear.
8.
The mass of an object is measured with an uncertainty of 1%, and its speed is measured with an uncertainty of 3%. What is the percentage uncertainty in the calculated kinetic energy of the object?
- A) 4%
- B) 7%
- C) 3.5%
- D) 10%
9.
An electronic balance displays a reading of +0.08 g when nothing is placed on the pan. If an object placed on the balance produces a reading of 24.52 g, what is the corrected mass of the object?
- A) 24.44 g
- B) 24.60 g
- C) 24.52 g
- D) 24.36 g
10.
A student records five repeated measurements for the diameter of a cylinder: 10.2 cm, 10.6 cm, 10.4 cm, 10.8 cm, and 10.5 cm. Using the range method, what is the absolute uncertainty of this measurement?
- A) $\pm 0.3\text{ cm}$
- B) $\pm 0.6\text{ cm}$
- C) $\pm 0.1\text{ cm}$
- D) $\pm 0.2\text{ cm}$
11.
Which of the following conditions causes a parallax error when reading a measurement on an analog instrument?
- A) The zero mark of the instrument being shifted before the measurement is taken
- B) The line of sight not being perpendicular to the scale markings
- C) Random fluctuations in ambient temperature during the experiment
- D) Inherent limitations imposed by the spacing of the smallest scale division
12.
A student measures the total time for 10 complete oscillations of a pendulum as 18.0 s with an absolute uncertainty of $\pm 0.4$ s. What is the absolute uncertainty in the calculated period of one oscillation?
- A) $\pm 4.0$ s
- B) $\pm 0.04$ s
- C) $\pm 0.4$ s
- D) $\pm 0.02$ s
13.
Which of the following statements correctly distinguishes between the accuracy and the precision of an experimental measurement?
- A) Accuracy refers to the degree of agreement among repeated measurements, whereas precision indicates how close a measured value is to the accepted true value.
- B) Accuracy indicates how close a measured value is to the accepted true value, whereas precision refers to the agreement or reproducibility among repeated measurements.
- C) Accuracy depends entirely on the resolution of the measuring device, whereas precision is determined exclusively by the presence of systematic error.
- D) Accuracy can always be improved simply by averaging repeated trials, whereas precision is independent of the number of trials conducted.
14.
The radius of a uniform sphere is measured with a percentage uncertainty of 1.5%. What is the percentage uncertainty in the calculated volume of the sphere?
- A) 1.5%
- B) 4.5%
- C) 3.4%
- D) 0.5%
15.
The length of a rectangular plate is measured with a percentage uncertainty of 2%, and its width is measured with a percentage uncertainty of 3%. What is the percentage uncertainty in the calculated surface area of the plate?
- A) 1%
- B) 1.5%
- C) 6%
- D) 5%
16.
Two lengths are measured as (15.4 ± 0.2) cm and (6.1 ± 0.3) cm. What is the absolute uncertainty in the calculated difference between these two measurements?
- A) 0.1 cm
- B) 0.25 cm
- C) 0.3 cm
- D) 0.5 cm
17.
A student measures the length of a metal block as 5.0 cm with an absolute uncertainty of 0.2 cm. What is the percentage uncertainty in this measurement?
- A) 0.04%
- B) 1.0%
- C) 2.5%
- D) 4.0%
18.
Which of the following scenarios is an example of a systematic error in an experimental measurement?
- A) An incorrectly calibrated digital scale that consistently records 0.50 g above the actual mass for every trial.
- B) Unpredictable drafts in the room that cause consecutive readings on an open balance to fluctuate randomly.
- C) Slight variations in an observer's reaction time when starting and stopping a manual stopwatch across repeated runs.
- D) Random electrical noise in a detector circuit causing scattered readings both above and below the true voltage.
19.
Which of the following procedures is effective in reducing the effect of random errors in an experiment?
- A) Calibrating the measuring instrument against a known standard
- B) Subtracting a predetermined zero offset from each recorded value
- C) Maintaining identical laboratory conditions while taking only a single measurement
- D) Repeating the measurement multiple times and calculating the average value

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Introduction to Physics · Physics

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