Q: When dividing two measured values $$a = 341 \pm 5$$ and $$b = 17 \pm 2$$, what is the formula for the uncertainty in $$h = \frac{a}{b}$$?

$$\Delta h = \frac{\text{max value} - \text{min value}}{2}$$

Q: If you repeat a measurement $$N$$ times and calculate the average, what is the formula for the uncertainty in the mean ($$\sigma_{\text{mean}}$$)?

$$\sigma_{\text{mean}} = \frac{\sigma}{\sqrt{N}}$$

Q: If the measured value of a quantity is $$x = 5.67 \pm 0.12$$ and the expected value is $$5.80$$, what is the percent difference between the experimental and expected values?

$$\frac{|5.67 - 5.80|}{5.80} \times 100\% = 2.24\%$$

Question 1

Which of the following best describes measurement uncertainty when using a measuring tool such as a meter stick or digital caliper?

Accepted Answer

It is the range within which the true value is expected to lie, based on the precision of the measuring device.

Question 2

Given a measurement reported as $$x \pm \Delta x$$, what does $$\Delta x$$ represent?

Accepted Answer

The uncertainty or possible error in the measurement.

Question 3

If you measure the length of a block as $$12.3 \pm 0.1 cm $$and the width as $$4.5 \pm 0.1 cm$$, what is the uncertainty in the sum of these two measurements?

Accepted Answer

$$0.2 cm$$

Question 4

When dividing two measured values $$a = 341 \pm 5$$ and $$b = 17 \pm 2$$, what is the formula for the uncertainty in $$h = \frac{a}{b}$$?

Accepted Answer

$$\Delta h = \frac{	ext{max value} - 	ext{min value}}{2}$$

Question 5

A digital caliper has an uncertainty of $$\pm 0.01 mm. If $$you measure a length as $$25.34 mm$$, what is the correct way to report this measurement?

Accepted Answer

$$25.34 \pm 0.01 mm$$

Question 6

If you repeat a measurement $$N$$ times and calculate the average, what is the formula for the uncertainty in the mean ($$\sigma_{	ext{mean}}$$)?

Accepted Answer

$$\sigma_{	ext{mean}} = \frac{\sigma}{\sqrt{N}}$$

Question 7

Which of the following best explains why significant figures are important in reporting measurements?

Accepted Answer

They indicate the precision of the measuring device and the reliability of the measurement.

Question 8

A student measures the period of a pendulum 20 times and calculates the average and standard deviation. What is the best way to report the period and its uncertainty?

Accepted Answer

Report the average period and the standard deviation of the mean.

Question 9

If the measured value of a quantity is $$x = 5.67 \pm 0.12$$ and the expected value is $$5.80$$, what is the percent difference between the experimental and expected values?

Accepted Answer

$$\frac{|5.67 - 5.80|}{5.80} 	imes 100\% = 2.24\%$$

Question 10

Which of the following is NOT a correct way to propagate uncertainty when multiplying two measured values $$x \pm \Delta x$$ and $$y \pm \Delta y$$?

Accepted Answer

$$\Delta (xy) = \Delta x + \Delta y$$

Question 11

A student uses a meter stick (uncertainty $$\pm 1 mm) to $$measure the length of a table as $$1.234 m. $$What is the correct way to express this measurement?

Accepted Answer

$$1.234 \pm 0.001$$ 	ext{ m}$

Question 12

Which of the following statements about the uncertainty range is correct?

Accepted Answer

The uncertainty range is the interval within which the true value is expected to lie.

Question 13

When calculating the density of a block, which of the following best describes how to propagate uncertainties in mass and volume?

Accepted Answer

Add the relative uncertainties of mass and volume, then multiply by the calculated density.

Question 14

If you measure the circumference $$C$$ and diameter $$D of a $$cylinder to calculate $$\pi = \frac{C}{D}$$, how do you determine the uncertainty in $$\pi$$?

Accepted Answer

By propagating the uncertainties in $$C$$ and $$D$$ using the formula $$\Delta \pi = \pi \left( \frac{\Delta C}{C} + \frac{\Delta D}{D} \right)$$

Question 15

Which of the following is a correct statement about the use of Excel or Vernier Graphical Analysis in laboratory data analysis?

Accepted Answer

They can be used to fit data, calculate averages, and determine uncertainties.

Question 16

A student measures the period of a pendulum and finds $$T = 2.00 \pm 0.05 s. $$The expected value is $$2.03 s. Do $$the uncertainty ranges overlap?

Accepted Answer

Yes, because $$2.03 s is $$within the range $$1.95 s to$$ $$2.05 s.$$

Laboratory 1: Measurements and Analysis – Study Notes for College Physics

Study Guide - Practice Questions

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