Measurements and Uncertainties: Master the Fundamentals of Physics

Question 1

How should you measure the diameter of a thin wire using a digital vernier caliper?

Accepted Answer

Read the diameter using the zero mark on the main scale and the mark on the vernier scale that aligns exactly.

Answer

Read the diameter directly from the main scale.

Answer

Read the diameter using only the vernier scale.

Answer

Read the diameter using the zero mark on the main scale and then add up the number of divisions on the main scale and the vernier scale.

Question 2

Which of the following best describes the precision of a measuring instrument?

Accepted Answer

A. How close repeated measurements are to each other

Answer

B. How close a measurement is to the true value

Answer

C. The range of values that can be measured

Answer

D. The smallest change in the quantity being measured that can be detected

Question 3

In measurements, which of the following is NOT a potential source of error?

Accepted Answer

Perfectly executed measurement

Answer

Instrument error

Answer

Human error

Answer

Environmental error

Question 4

Which of the following is NOT a source of uncertainty in measurements?

Accepted Answer

Theoretical limitations

Answer

Calibration errors

Answer

Environmental factors

Answer

Human error

Question 5

Which of the following actions will NOT improve the accuracy of a measurement?

Accepted Answer

Changing the units of measurement

Answer

Using a more precise instrument

Answer

Taking multiple measurements and averaging the results

Answer

Calibrating the instrument regularly

Question 6

When aiming for precise measurements, which characteristic is undesirable in a measuring instrument?

Accepted Answer

Low Sensitivity

Answer

High Accuracy

Answer

Good Precision

Answer

Wide Measurement Range

Question 7

Which instrument offers the highest precision for measuring time intervals?

Accepted Answer

A digital stopwatch with a resolution of 0.01 seconds

Answer

A ruler with a smallest division of 0.1 cm

Answer

A graduated cylinder with a smallest division of 1 mL

Answer

A vernier caliper with a least count of 0.05 mm

Question 8

To determine the zero error of a measuring instrument, which method is most appropriate?

Accepted Answer

Measure a standard value with a known value using the instrument.

Answer

Take multiple measurements and calculate their average.

Answer

Refer to the instrument's manual for the specified zero error.

Answer

Estimate the zero error by observing the instrument's scale.

Question 9

Which of the following does **not** influence the resolution of a measuring instrument?

Accepted Answer

The type of quantity being measured

Answer

The smallest division on the instrument's scale

Answer

The precision of the instrument's readout

Question 10

Describe two practical methods that can be used to minimize uncertainty in experimental measurements.

Accepted Answer

Use measuring instruments with high precision and accuracy.

Accepted Answer

Take multiple measurements and calculate the average value.

Answer

Estimate the measurement instead of getting an exact reading.

Answer

Round the measurement to the nearest whole number.

Question 11

When using a vernier caliper, aligning the zero marks of the main and vernier scales is crucial. Failure to do so can cause a specific type of error. What is this error called?

Accepted Answer

Zero error

Answer

Random error

Answer

Parallax error

Answer

Rounding error

Question 12

Which of the following is an advantage of using digital instruments over analog instruments for precise measurements?

Accepted Answer

Digital instruments have a higher resolution.

Accepted Answer

Digital instruments are less susceptible to human error.

Accepted Answer

Digital instruments provide a direct digital readout.

Answer

Digital instruments are more durable than analog instruments.

Question 13

How does calibration enhance the accuracy of measuring instruments and minimize systematic errors?

Accepted Answer

Calibration aligns the instrument's readings with a known standard, correcting systematic errors due to its construction or past use.

Answer

Calibration solely improves the instrument's precision by reducing random errors.

Answer

Calibration only reduces uncertainty in digital instruments, not analog instruments.

Answer

Calibration is unnecessary for instruments with already high levels of precision.

Question 14

Express the uncertainty of 0.005 grams correctly.

Accepted Answer

(0.005 ± 0.0005) g

Answer

(0.005 ± 0.005) g

Answer

0.005 g (5%)

Answer

0.0005 g (5%)

Question 15

A length is measured to be 2.50 ± 0.02 cm. Calculate the maximum possible percentage error in this measurement.

Accepted Answer

0.8%

Answer

0.08%

Answer

8%

Answer

80%

Question 16

During uncertainty propagation in a calculation, which operation requires the uncertainties to be added?

Accepted Answer

Addition

Answer

Subtraction

Answer

Multiplication

Answer

Division

Question 17

What is the primary purpose of error bars when representing measurement uncertainties graphically?

Accepted Answer

To visually represent the range of possible values within which the true value of the measured quantity is likely to lie.

Answer

To indicate the precision of a measurement.

Answer

To enable comparisons of the uncertainties of different measurements.

Answer

To be used exclusively in highly precise measurements.

Question 18

When performing calculations with significant figures, the best practice is to:

Accepted Answer

Round the final answer to the least number of significant figures used

Answer

Retain all significant figures throughout the calculation

Answer

Add the uncertainties of all measurements before performing the calculation

Answer

Ignore significant figures when adding and subtracting

Question 19

A measurement is recorded as 25.0 ± 0.5 cm. The relative uncertainty in this measurement is:

Accepted Answer

2.0%

Answer

0.02

Answer

0.05

Answer

5.0%

Question 20

A student measures the length of a table using a ruler graduated in 0.1 cm and obtains a reading of 120.5 cm. What is the uncertainty in this measurement?

Accepted Answer

0.1 cm

Answer

0.05 cm

Answer

0.2 cm

Answer

0.5 cm

Question 21

What is the purpose of propagating uncertainties through calculations?

Accepted Answer

To ensure accurate reporting of uncertainties

Answer

To minimize uncertainty

Answer

To maximize precision

Answer

To eliminate uncertainty

Question 22

What is the significance of significant figures in reporting measurements?

Accepted Answer

To convey the precision of the measurement

Answer

To prevent confusion in calculations

Answer

To ensure the accuracy of the measurement

Answer

To conform to scientific conventions

Question 23

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

Accepted Answer

It is consistent and affects all measurements in the same way.

Answer

It is random and unpredictable.

Answer

It can be eliminated by taking multiple readings.

Answer

It is caused by environmental factors.

Question 24

What is the uncertainty in a measurement of 12.50 ± 0.05 cm?

Accepted Answer

0.05 cm

Answer

0.01 cm

Answer

0.10 cm

Answer

0.50 cm

Question 25

A student measures the length of a rod five times and obtains the following readings: 24.2 cm, 24.4 cm, 24.3 cm, 24.5 cm, 24.6 cm. What is the mean length of the rod?

Accepted Answer

24.5 cm

Answer

24.2 cm

Answer

24.4 cm

Answer

24.6 cm

Question 26

Which of the following is the correct way to express a measurement with an uncertainty?

Accepted Answer

25.4 cm ± 0.1 cm

Answer

25.4 cm (0.1 cm)

Answer

25.4 cm +/- 0.1 cm

Answer

25.4 +/- 0.1 cm

Question 27

A student measures the mass of an object three times and obtains the following readings: 101.2 g, 101.1 g, 101.3 g. What is the range of the measurements?

Accepted Answer

0.2 g

Answer

0.1 g

Answer

101.1 g - 101.3 g

Answer

101.2 g - 101.3 g

Question 28

A measurement has a value of 5.00 ± 0.05. How many significant figures should be reported in the final result of a calculation using this measurement?

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 29

Which of the following correctly describes the propagation of uncertainties when adding or subtracting measured values?

Accepted Answer

Add the uncertainties

Answer

Subtract the uncertainties

Answer

Multiply the uncertainties

Answer

Divide the uncertainties

Question 30

A student plots a graph of their experimental data and finds that the slope of the line of best fit is 2.00 ± 0.05. What does this uncertainty represent?

Accepted Answer

The uncertainty in the slope measurement

Answer

The uncertainty in the y-intercept measurement

Answer

The uncertainty in the independent variable measurement

Answer

The uncertainty in the dependent variable measurement

Question 31

Why is measurement traceability essential for ensuring consistent and reliable measurement practices across different laboratories and organizations?

Accepted Answer

It ensures that measurements are comparable and verifiable.

Answer

It eliminates the need for regular calibration.

Answer

It reduces the uncertainty associated with measurements.

Question 32

Which instrument is most suitable for accurately measuring the thickness of a thin sheet of paper?

Accepted Answer

Micrometer screw gauge

Answer

Vernier calipers

Answer

Ruler

Answer

Protractor

Question 33

The measurement 2.30 ± 0.05 cm indicates that the absolute uncertainty is:

Accepted Answer

0.05 cm

Answer

0.01 cm

Answer

0.02 cm

Answer

0.10 cm

Question 34

The number of significant figures in the uncertainty of a measurement should be:

Accepted Answer

One less than the number of significant figures in the measured value

Answer

Equal to the number of significant figures in the measured value

Answer

Two less than the number of significant figures in the measured value

Answer

Three less than the number of significant figures in the measured value

Question 35

Which of the following is a common source of systematic error?

Accepted Answer

miscalibration of equipment

Answer

parallax error

Answer

random fluctuations

Answer

rounding errors

Question 36

The uncertainty in a measurement is typically represented by which symbol?

Accepted Answer

±

Answer

/

Answer

+

Answer

-

Question 37

A student measures the length of a rod to be 10.2 ± 0.1 cm. What is the percentage uncertainty in this measurement?

Accepted Answer

Approximately 1%

Answer

Exactly 100%

Answer

0.1%

Answer

Exactly 10%

Question 38

A student takes two measurements of the same quantity, obtaining values of 5.2 cm and 5.4 cm. What is the most accurate estimate for the true value of the quantity?

Accepted Answer

5.3 cm

Answer

5.2 cm

Answer

10.6 cm

Answer

5.4 cm

Question 39

A student measures the mass of an object using a digital scale and obtains a reading of 100.0 g. If the scale has a resolution of 0.1 g, what is the appropriate uncertainty in this measurement?

Accepted Answer

± 0.1 g

Answer

± 0.01 g

Answer

± 0.05 g

Answer

± 1 g

Question 40

Which of the following units is NOT a valid unit of length?

Accepted Answer

Minute

Answer

Inch

Answer

Meter

Answer

Centimeter

Question 41

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

Accepted Answer

Consistent and repeatable error

Answer

Random and unpredictable error

Answer

Caused by equipment malfunction

Answer

Easily identified and corrected

Question 42

Calculate the percentage uncertainty in a measurement of 25.6 ± 0.2 cm:

Accepted Answer

0.8%

Answer

5%

Answer

50%

Answer

20%

Question 43

Which factor is NOT relevant when selecting an appropriate measuring instrument?

Accepted Answer

Cost of the instrument

Answer

Range of the instrument

Answer

Accuracy of the instrument

Answer

Precision of the instrument

Question 44

What is the standard unit of length in the International System of Units (SI)?

Accepted Answer

Meter

Answer

Mile

Answer

Inch

Answer

Foot

Question 45

If a measured value is 10.2 ± 0.3 cm, what is the maximum possible value of the true quantity?

Accepted Answer

10.5 cm

Answer

10.0 cm

Answer

10.3 cm

Answer

9.9 cm

Question 46

Which of the following is a dimensionless quantity?

Accepted Answer

Relative uncertainty

Answer

Time

Answer

Mass

Answer

Length

Question 47

How is the percentage uncertainty in a quantity calculated?

Accepted Answer

(Uncertainty / Quantity) x 100%

Answer

(Quantity - Uncertainty) x 100%

Answer

Uncertainty / (Quantity x 100%)

Answer

Quantity / Uncertainty

Question 48

What is the correct expression for the uncertainty in the sum of two measurements, A and B?

Accepted Answer

√(Uncertainty in A)^2 + (Uncertainty in B)^2

Answer

Uncertainty in A + Uncertainty in B

Answer

(Uncertainty in A) x (Uncertainty in B)

Answer

(Uncertainty in A) - (Uncertainty in B)

Question 49

Which unit is NOT a fundamental base unit in the SI system?

Accepted Answer

Newton

Answer

Ampere

Answer

Kilogram

Answer

Second

Question 50

Which method is most effective for reducing uncertainties in measurements?

Accepted Answer

Taking multiple measurements and calculating the average

Answer

Using a different measuring technique for each measurement

Answer

Using an instrument with a lower resolution

Answer

Estimating the value without a measuring instrument

Question 51

A digital voltmeter displays '10.5 V ± 0.2 V'. What does '± 0.2 V' represent?

Accepted Answer

The uncertainty of the measurement

Answer

The average voltage over time

Answer

The calibration error of the voltmeter

Answer

The range of possible voltage readings

Question 52

When multiplying quantities with percentage uncertainties, how is the percentage uncertainty of the result calculated?

Accepted Answer

Add the percentage uncertainties of the individual quantities

Answer

Average the percentage uncertainties of the individual quantities

Answer

Subtract the smallest percentage uncertainty from the largest one

Answer

Square the percentage uncertainties, add them, then take the square root

Question 53

Which of these examples describes a systematic error in an experiment?

Accepted Answer

Consistently using a ruler that is slightly too short

Answer

Misreading a value on a measuring scale

Answer

Accidentally bumping the experiment setup during measurement

Answer

Fluctuations in the room temperature affecting the experiment

Question 54

Which scenario best exemplifies a random error in an experiment?

Accepted Answer

Slight variations in repeated time measurements of a pendulum's swing

Answer

Using a thermometer with a known offset in its readings

Answer

Incorrectly noting down the measurements in a lab notebook

Answer

External vibrations consistently affecting a sensitive balance

Question 55

What is the main purpose of using significant figures when reporting scientific measurements?

Accepted Answer

To reflect the precision of the measurement taken

Answer

To ensure all measurements have the same number of decimal places

Answer

To simplify the numbers and make them easier to handle

Answer

To avoid rounding errors in subsequent calculations

Question 56

Which of the following measurements contains the highest number of significant figures?

Accepted Answer

0.02500 m

Answer

2.50 m

Answer

2500 m

Answer

250 m

Question 57

What type of error consistently causes measurements to be either higher or lower than the true value?

Accepted Answer

Systematic Error

Answer

Human Error

Answer

Parallax Error

Answer

Random Error

Question 58

A student measures the time for a pendulum to complete 20 oscillations. This is repeated five times. Why is it better to calculate the average time for 20 oscillations than to time one oscillation directly?

Accepted Answer

It reduces the percentage uncertainty in the measurement of the time period.

Answer

Increases the systematic error in the measurement

Answer

Eliminates the need to consider reaction time

Question 59

A measurement of the velocity of an object is recorded as 10 ± 0.5 m/s. What does this notation indicate?

Accepted Answer

The true value of the velocity is likely to be between 9.5 m/s and 10.5 m/s.

Answer

The velocity is exactly 10 m/s.

Answer

The error in the measurement is 50%.

Question 60

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

Accepted Answer

Accuracy describes how close a measurement is to the true value, while precision reflects how close repeated measurements are to each other.

Answer

Accuracy and precision are essentially the same concept.

Question 61

When plotting experimental data and drawing a line of best fit, what is the primary objective?

Accepted Answer

To represent the overall trend of the data and minimize the influence of random errors.

Answer

To connect all the data points on the graph.

Answer

To make the graph look more visually appealing.

Question 62

When measuring the length of an object, which action most likely introduces a parallax error?

Accepted Answer

Viewing the measurement scale from an angle rather than directly above.

Answer

Using a ruler with worn-out markings.

Answer

Not zeroing the instrument before taking the measurement.

Question 63

Why is it crucial to consider and report uncertainties in scientific measurements?

Accepted Answer

To indicate the reliability of the results and allow for meaningful comparisons with other data.

Answer

To make the experiment seem more complex and impressive.

Question 64

Which of the following is the standard unit for measuring length in the International System of Units (SI)?

Accepted Answer

Meter

Answer

Ampere

Answer

Kilogram

Answer

Second