Measurement Uncertainty in Physics: Master Accuracy and Precision

Question 1

Which of the following is a characteristic of a systematic error?

Accepted Answer

The measuring instrument consistently gives higher or lower readings than the true value.

Answer

The measurement is affected by random fluctuations, such as changes in temperature or humidity.

Answer

The measurement is not precise enough to accurately determine the true value.

Answer

The measurement is estimated instead of being accurately measured.

Question 2

Which of the following is a systematic error in measurement?

Accepted Answer

Using a poorly calibrated measuring device

Answer

Taking a measurement multiple times and getting different results

Answer

Estimating the last digit of a measurement

Answer

Making a mistake in reading the measuring scale

Question 3

How many significant figures are in the number 0.00250?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 4

Which of the following is NOT a way to reduce random errors in measurements?

Accepted Answer

Ignoring the outliers in the data set

Answer

Taking multiple measurements and averaging the results

Answer

Using a more precise measuring device

Answer

Eliminating sources of error, such as vibrations or temperature fluctuations

Question 5

Which of the following is a source of systematic error in a digital thermometer?

Accepted Answer

The thermometer has not been calibrated recently

Answer

Sticking the thermometer in the liquid too quickly

Answer

Reading the thermometer at an angle

Answer

Using a thermometer that is too small for the container

Question 6

A student measures the mass of an object to be 2.34 g. The balance has an accuracy of 0.02 g. What is the range of possible values for the true mass of the object?

Accepted Answer

2.32 g to 2.36 g

Answer

2.33 g to 2.35 g

Answer

2.34 g to 2.36 g

Answer

2.35 g to 2.37 g

Question 7

Which of the following is **not** a characteristic of systematic errors?

Accepted Answer

Arise from random fluctuations in the measuring process

Answer

Constant in magnitude and direction

Answer

Can be eliminated by repeating measurements

Answer

Affect the accuracy of measurements

Question 8

Precision refers to the:

Accepted Answer

Degree of consistency among repeated measurements

Answer

Closeness of measurements to the true value

Answer

Number of significant figures used

Answer

Range of possible errors

Question 9

Which of the following is a common method of reducing random errors?

Accepted Answer

Repeating measurements multiple times and averaging the results

Answer

Using more precise measuring instruments

Answer

Eliminating external factors that may affect the measurement

Answer

Applying error analysis techniques

Question 10

The resolution of a measuring instrument refers to the:

Accepted Answer

Smallest change in the measurand that can be detected

Answer

Range of values over which the instrument can measure

Answer

Accuracy of the instrument

Answer

Precision of the instrument

Question 11

The percentage uncertainty of a measurement is calculated using the formula:

Accepted Answer

(Absolute error / Measurement) * 100%

Answer

(Measurement / Absolute error) * 100%

Answer

Absolute error + Measurement * 100%

Answer

Measurement - Absolute error * 100%

Question 12

What is the term used to describe the closeness of a measurement to its true value?

Accepted Answer

Accuracy

Answer

Precision

Answer

Resolution

Answer

Uncertainty

Question 13

What is the propagation of errors?

Accepted Answer

The process of combining uncertainties from multiple measurements

Answer

The increase in uncertainty as measurements are combined

Answer

The reduction in uncertainty as measurements are combined

Answer

The calculation of the exact value of a derived quantity

Question 14

Explain the key difference between precision and accuracy in the context of scientific measurements:

Accepted Answer

Precision refers to the consistency of measurements, while accuracy measures their closeness to the true value

Answer

Accuracy refers to the consistency of measurements, while precision measures their closeness to the true value

Answer

Precision and accuracy are synonymous terms in scientific measurements

Answer

Neither precision nor accuracy is a relevant concept in measurement science

Question 15

Which of these methods is most effective in minimizing the impact of random errors in measurements?

Accepted Answer

Repeating measurements and averaging the results

Answer

Using a measuring device with higher precision

Answer

Controlling environmental conditions during measurement

Answer

Eliminating systematic errors

Question 16

In an experiment, the measured values of a physical quantity are consistently higher than the true value. This observation suggests the presence of a:

Accepted Answer

Positive systematic error

Answer

Negative systematic error

Answer

Positive random error

Answer

Negative random error

Question 17

How do significant figures affect the accuracy and precision of a measurement?

Accepted Answer

More significant figures indicate higher accuracy but not necessarily higher precision.

Answer

More significant figures indicate higher accuracy and precision.

Answer

More significant figures indicate higher precision but not necessarily higher accuracy.

Answer

The number of significant figures does not affect the accuracy or precision of the measurement.

Question 18

What is the purpose of a zero error correction?

Accepted Answer

To eliminate the systematic error caused by a non-zero reading on a measuring device when the true value is zero.

Answer

To reduce the random error in a measurement.

Answer

To increase the accuracy of a measurement.

Answer

To make it easier to perform calculations with measured values.

Question 19

Which of the following is a way to minimize random errors in a measurement?

Accepted Answer

Repeating the measurement multiple times and averaging the results.

Answer

Using a more expensive measuring instrument.

Answer

Calibrating the measuring instrument regularly.

Answer

Eliminating all sources of systematic error.

Question 20

How are accuracy and precision different in the context of measurements?

Accepted Answer

Accuracy refers to the closeness of a measurement to the true value, while precision refers to the closeness of repeated measurements to each other.

Answer

Precision refers to the closeness of a measurement to the true value, while accuracy refers to the closeness of repeated measurements to each other.

Answer

Accuracy and precision are the same thing.

Answer

Neither accuracy nor precision is relevant to measurement.

Question 21

What is a defining characteristic of a systematic error?

Accepted Answer

It consistently affects all measurements in the same way.

Answer

It can be eliminated by repeating measurements.

Answer

It arises from random fluctuations.

Question 22

Identify the type of measurement error associated with consistent deviations from the true value:

Accepted Answer

Systematic error

Answer

Random error

Answer

Gross error

Answer

Instrumental error

Question 23

Explain the difference between accuracy and precision in scientific measurements:

Accepted Answer

Accuracy refers to the closeness of a measurement to the true value, while precision refers to the consistency of repeated measurements.

Answer

Precision refers to the closeness of a measurement to the true value, while accuracy refers to the consistency of repeated measurements.

Answer

Accuracy and precision are the same concept.

Answer

Precision is more important than accuracy in scientific measurements.

Question 24

Which of the following scenarios describes a random error in a measurement?

Accepted Answer

Temperature fluctuations in an experiment

Answer

A measuring scale that consistently reads 2 grams lower than the true value

Answer

Incorrectly recording the number of trials

Answer

Using an outdated instrument

Question 25

State the primary purpose of error propagation in scientific calculations:

Accepted Answer

To determine the overall uncertainty in the calculated result

Answer

To minimize the impact of individual measurement errors

Answer

To eliminate systematic errors

Answer

To increase the reliability of the result

Question 26

Which type of error is caused by a consistent bias in the measurement process?

Accepted Answer

Systematic error

Answer

Random error

Answer

Absolute error

Answer

Percentage error

Question 27

Which method can effectively minimize the impact of random errors?

Accepted Answer

Taking multiple measurements and averaging the results

Answer

Using high-quality measurement equipment

Answer

Eliminating personal biases

Answer

Calibrating instruments regularly

Question 28

How can random and systematic errors be distinguished?

Accepted Answer

Random errors fluctuate while systematic errors remain constant.

Answer

Systematic errors are easier to correct than random errors.

Answer

Random errors affect precision while systematic errors affect accuracy.

Answer

Systematic errors are always larger than random errors.

Question 29

Which of the following is an example of a random error?

Accepted Answer

Fluctuations in the readings of a digital multimeter.

Answer

Calibration error of a measuring tape.

Answer

Incorrect zeroing of a balance.

Question 30

Which of the following is a recommended technique for reducing measurement errors?

Accepted Answer

Using calibrated instruments.

Answer

Repeating measurements multiple times without averaging.

Answer

Guessing the correct value.

Answer

Ignoring outliers.

Question 31

What is the uncertainty in a measurement that is reported as 25.00 ± 0.05 g?

Accepted Answer

0.05 g

Answer

25.00 g

Answer

0.10 g

Question 32

Which of the following is NOT a characteristic of random error?

Accepted Answer

It affects the accuracy of the measurements.

Answer

It occurs when the measuring equipment is unstable.

Answer

It is unpredictable.

Answer

It can be minimized by repeating the experiment.

Question 33

What's the purpose of using significant figures in the measurement?

Accepted Answer

To indicate the precision of the measurement.

Answer

To make the measurement easier to read.

Answer

To ensure that the measurement is accurate.

Answer

To convert the measurement to a different unit.

Question 34

Which of the following is a systematic error?

Accepted Answer

Using a measuring tape that is slightly stretched.

Answer

Measuring the length of an object multiple times with different results.

Answer

Taking measurements in a windy environment.

Answer

Making a mistake in reading the scale of a measuring instrument.

Question 35

What is the purpose of propagating errors?

Accepted Answer

To compute the uncertainty associated with the result of a calculation.

Answer

To remove errors from the result of a calculation.

Answer

To reduce the error associated with the result of a calculation.

Question 36

Which of the following is NOT a way to minimize measurement errors?

Accepted Answer

Using a measuring instrument that is not calibrated.

Answer

Using a measuring instrument with high precision.

Answer

Taking multiple measurements and averaging the results.

Question 37

Which of the following is NOT a characteristic of systematic errors?

Accepted Answer

Random fluctuations in the measuring instrument

Answer

Can affect the accuracy of measurements

Answer

Can be eliminated by calibration

Answer

Consistent bias in measurements

Question 38

What is the term used to describe the degree to which repeated measurements of the same quantity give consistent results?

Accepted Answer

Precision

Answer

Resolution

Answer

Accuracy

Answer

Sensitivity

Question 39

What is the purpose of propagating errors in measurements?

Accepted Answer

To determine the overall uncertainty of a calculated result

Answer

To identify the sources of measurement errors

Answer

To reduce the number of significant figures in a measurement

Question 40

Which of the following equations represents the propagation of errors for multiplication or division of measurements?

Accepted Answer

Δy = |x|Δx/y + |y|Δy/x

Answer

Δy = xΔx + yΔy

Answer

Δy = (Δx + Δy)/2

Answer

Δy = Δx - Δy

Question 41

What is the effect of increasing the precision of a measuring instrument on the uncertainty of a measurement?

Accepted Answer

The uncertainty is reduced

Answer

The uncertainty is increased

Answer

The uncertainty remains the same

Answer

The uncertainty cannot be determined

Question 42

Which of the following is a method to minimize systematic errors in measurements?

Accepted Answer

Calibration of the measuring instrument

Answer

Repeating measurements multiple times

Answer

Using a different measuring instrument

Answer

Estimating the error and applying a correction factor

Question 43

What is the fundamental difference between accuracy and precision in measurements?

Accepted Answer

Accuracy refers to the closeness of a measurement to the true value, while precision refers to the consistency of a set of measurements.

Answer

Accuracy is more important than precision

Answer

Precision is more important than accuracy