Q: If the measured value of $$q = 0.0050 \pm 0.0001 C $$and $$d = 50.0 \pm 0.2 m$$, what is the percentage uncertainty in $$E = \frac{q}{d^2$}$$?

$$0.02 + 2 \times 0.004 = 0.028 or$$ $$2.8\%$$

Question 1

A student measures the length of a metal rod five times and obtains the following values (in cm): 12.1, 12.3, 12.2, 12.4, and 12.0. What is the average length and the random uncertainty (range error) in the measurement?

Accepted Answer

$$12.2 \pm 0.1 cm$$

Question 2

Which of the following best describes a parallax error?

Accepted Answer

An error caused by not viewing a scale directly in line with the pointer or measurement mark.

Question 3

A student measures the mass of a sample as $$m = 2.50 \pm 0.05 g. $$What is the percentage uncertainty in the measurement?

Accepted Answer

$$2\%$$

Question 4

If the radius of a sphere is measured as $$r = 3.00 \pm 0.02 cm$$, what is the absolute uncertainty in the calculated diameter?

Accepted Answer

$$0.04 cm$$

Question 5

A voltage $$V = 12.0 \pm 0.2 V is $$measured across a resistor, and the current is $$I = 2.0 \pm 0.1 A. $$What is the resistance $$R$$ and its absolute uncertainty?

Accepted Answer

$$R = 6.0 \pm 0.4\ \Omega$$

Question 6

Which of the following statements about random and systematic uncertainties is correct?

Accepted Answer

Random uncertainties can be reduced by repeating measurements, while systematic uncertainties cannot.

Question 7

A student calculates the area $$A of a $$rectangle using $$A = l 	imes w$$, where $$l = 5.0 \pm 0.1 cm $$and $$w = 2.0 \pm 0.1 cm. $$What is the percentage uncertainty in $$A$$?

Accepted Answer

$$7\%$$

Question 8

If a value is reported as $$x = 8.0 \pm 0.2 m$$, what is the fractional uncertainty?

Accepted Answer

$$0.025$$

Question 9

A student measures the time for a chemical reaction as $$t = 45.0 \pm 0.5 s. If $$the rate is calculated as $$r = \frac{1}{t}$$, what is the percentage uncertainty in $$r$$?

Accepted Answer

$$1.1\%$$

Question 10

Which of the following is the correct way to combine uncertainties when adding two measured quantities $$a$$ and $$b$$?

Accepted Answer

Add the absolute uncertainties: $$\Delta c = \Delta a + \Delta b$$

Question 11

A student measures the length of a table as $$l = 1.20 \pm 0.01 m $$and the width as $$w = 0.80 \pm 0.02 m. $$What is the area and its absolute uncertainty?

Accepted Answer

$$0.96 \pm 0.03 m$^2$$

Question 12

If a measured value is $$x = 4.00 \pm 0.10 m$$, what is the value and uncertainty of $$y = 3x$$?

Accepted Answer

$$y = 12.00 \pm 0.30 m$$

Question 13

A student calculates the volume of a cube using $$V = a^3$, where a = 2.00$$ \pm 0.05$$ cm. What is the percentage uncertainty in V$?

Accepted Answer

$$7.5\%$$

Question 14

Which of the following is NOT a source of personal uncertainty in measurement?

Accepted Answer

Instrument calibration error

Question 15

A student records the following measurements for the focal length of a lens: 10.2 cm, 10.4 cm, 10.1 cm, and 10.3 cm. What is the average focal length and its range error?

Accepted Answer

$$10.25 \pm 0.08 cm$$

Question 16

If the measured value of $$q = 0.0050 \pm 0.0001 C $$and $$d = 50.0 \pm 0.2 m$$, what is the percentage uncertainty in $$E = \frac{q}{d^2$}$$?

Accepted Answer

$$0.02 + 2 	imes 0.004 = 0.028 or$$ $$2.8\%$$

Question 17

Which of the following best describes an anomaly in a set of measurements?

Accepted Answer

A value that is well outside the average of most values due to a known error.

Question 18

A student measures the period of a pendulum as $$T = 2.00 \pm 0.02 s. If $$the frequency is $$f = \frac{1}{T}$$, what is the absolute uncertainty in $$f$$?

Accepted Answer

$$0.005 Hz$$

Question 19

Which of the following is true about absolute, fractional, and percentage uncertainties?

Accepted Answer

Absolute uncertainties have units, while fractional and percentage uncertainties do not.

Uncertainty Analysis in Experimental Measurements

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