Q: A student measures the mass of a sample as $$m = 50.0 \pm 0.2\, \mathrm{g}. $$What is the percentage uncertainty?

$$0.5\%$$ (\frac{0.2}{50.0} \times 100)$

Question 1

A student uses a digital thermometer with a resolution of 0.1°C to measure the temperature of a solution. The reading fluctuates between 25.2°C and 25.6°C. What is the absolute uncertainty in the measurement?

Accepted Answer

$$\pm 0.2\, ^\circ\mathrm{C} ($$half the range: $$\frac{25.6-25.2}{2})$$

Question 2

Which of the following best describes a measurement that is precise but not accurate?

Accepted Answer

Repeated measurements are close to each other but far from the true value.

Question 3

A voltmeter consistently reads 0.05 V when not connected to a circuit. What type of error does this represent?

Accepted Answer

Zero error (systematic error)

Question 4

A student measures the mass of a sample as $$m = 50.0 \pm 0.2\, \mathrm{g}. $$What is the percentage uncertainty?

Accepted Answer

$$0.5\%$$ (\frac{0.2}{50.0} 	imes 100)$

Question 5

When adding two measured lengths $$l_1 = 12.0$$ \pm 0.1\, \mathrm{cm}$$ and l_2$ = 8.0 \pm 0.2\, \mathrm{cm}$$, what is the combined uncertainty?

Accepted Answer

$$\pm 0.3\, \mathrm{cm}$$

Question 6

A student calculates the area $$A of a $$rectangle using $$A = l 	imes w$$, where $$l = 10.0 \pm 0.1\, \mathrm{cm}$$ and $$w = 5.0 \pm 0.1\, \mathrm{cm}. $$What is the percentage uncertainty in $$A$$?

Accepted Answer

$$3\%$$

Question 7

Which instrument would be most appropriate to measure the diameter of a thin copper wire with the highest precision?

Accepted Answer

Micrometer screw gauge

Question 8

A stopwatch has a resolution of $$0.01\, \mathrm{s}. $$What does this mean?

Accepted Answer

It can measure time intervals as small as $$0.01\, \mathrm{s}.$$

Question 9

A measurement is recorded as $$l = 2.67\, \mathrm{mm}$$ using a micrometer. If the main scale reads $$2.5\, \mathrm{mm}$$ and the thimble scale reads $$0.17\, \mathrm{mm}$$, how is the final value obtained?

Accepted Answer

By adding the main scale and thimble scale readings: $$2.5 + 0.17 = 2.67\, \mathrm{mm}$$

Question 10

A student uses a vernier caliper and gets a main scale reading of $$1.0\, \mathrm{cm}$$ and a vernier scale reading of $$0.33\, \mathrm{cm}. $$What is the total measurement?

Accepted Answer

$$1.33\, \mathrm{cm}$$

Question 11

If the uncertainty in a measurement is $$\pm 0.05\, \mathrm{cm}$$ and the measured value is $$2.00\, \mathrm{cm}$$, what is the fractional uncertainty?

Accepted Answer

$$0.025$$ (\frac{0.05}{2.00})

Question 12

Which of the following is a method to reduce random errors in an experiment?

Accepted Answer

Repeating measurements and averaging

Question 13

A student calculates the volume $$V of a $$sphere using $$V = \frac{4}{3}\pi r^3$, where r = 2.00$$ \pm 0.05\, \mathrm{cm}$$. What is the percentage uncertainty in V$?

Accepted Answer

$$7.5\% ($$multiply percentage uncertainty in $$r by 3$$: $$\frac{0.05}{2.00} 	imes 100 	imes 3)$$

Question 14

Which of the following statements about systematic errors is correct?

Accepted Answer

They affect the accuracy but not the precision of measurements.

Question 15

A balance gives a reading of $$300.23\, \mathrm{g}$$ for a standard $$300.00\, \mathrm{g}$$ mass. What is the absolute error?

Accepted Answer

$$0.23\, \mathrm{g}$$

Question 16

Which instrument would you use to measure the potential difference across a resistor with the highest resolution?

Accepted Answer

Voltmeter

Question 17

A student records the following times for a reaction: $$12.3\, \mathrm{s}$$, $$12.5\, \mathrm{s}$$, $$12.1\, \mathrm{s}$$, $$12.4\, \mathrm{s}. $$What is the uncertainty in the mean time?

Accepted Answer

$$\pm 0.2\, \mathrm{s} ($$half the range: $$\frac{12.5-12.1}{2})$$

Physics with Calculus: Measurements, Errors, and Uncertainties

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