Units & Measurement

Error Analysis Significant Figures Units & Dimensions

Q. A force is measured as 50 N with an uncertainty of ±1 N. What is the percentage uncertainty in the force measurement?

A. 2%
B. 1%
C. 0.5%
D. 0.1%

Solution

Percentage uncertainty = (absolute uncertainty / measured value) * 100 = (1 / 50) * 100 = 2%.

Correct Answer: B — 1%

Q. A force is measured as 50 N with an uncertainty of ±2 N. What is the relative uncertainty in this force measurement?

A. 0.04
B. 0.02
C. 0.01
D. 0.05

Solution

Relative uncertainty = (absolute uncertainty / measured value) = 2 / 50 = 0.04 or 4%.

Correct Answer: B — 0.02

Q. A length is measured as 100.0 m with an uncertainty of ±0.5 m. What is the significant figure of the measurement?

A. 2
B. 3
C. 4
D. 5

Solution

The measurement has 4 significant figures (100.0).

Correct Answer: C — 4

Q. A length is measured as 15.0 m with an uncertainty of ±0.2 m. What is the total uncertainty if this length is used in a calculation involving addition with another length of 10.0 m (±0.1 m)?

A. 0.3 m
B. 0.2 m
C. 0.1 m
D. 0.4 m

Solution

Total uncertainty = √((0.2)² + (0.1)²) = √(0.04 + 0.01) = √0.05 ≈ 0.224 m.

Correct Answer: A — 0.3 m

Q. A length is measured as 15.0 m with an uncertainty of ±0.3 m. What is the fractional error in this measurement?

A. 0.02
B. 0.03
C. 0.01
D. 0.005

Solution

Fractional error = (absolute error / measured value) = 0.3 / 15.0 = 0.02.

Correct Answer: B — 0.03

Q. A length is measured as 15.0 m with an uncertainty of ±0.3 m. What is the total length if two such lengths are added?

A. 29.4 m
B. 30.0 m
C. 30.6 m
D. 31.0 m

Solution

Total length = 15.0 + 15.0 = 30.0 m; Total uncertainty = ±0.3 + ±0.3 = ±0.6 m.

Correct Answer: C — 30.6 m

Q. A mass is measured as 5.0 kg with an uncertainty of ±0.1 kg. If this mass is used to calculate weight (W = mg), what is the uncertainty in weight if g = 9.8 m/s²?

A. ±0.2 N
B. ±0.5 N
C. ±0.1 N
D. ±0.4 N

Solution

Uncertainty in weight = g * (uncertainty in mass) = 9.8 * 0.1 = ±0.98 N, rounded to ±1 N.

Correct Answer: A — ±0.2 N

Q. A measurement of length is recorded as 5.0 cm with an uncertainty of ±0.1 cm. What is the relative error in this measurement?

A. 0.02
B. 0.01
C. 0.005
D. 0.1

Solution

Relative error = (absolute error / measured value) = 0.1 / 5.0 = 0.02 or 2%.

Correct Answer: B — 0.01

Q. A pendulum is measured to have a length of 2.0 m with an uncertainty of ±0.1 m. What is the relative uncertainty in the length?

A. 5%
B. 10%
C. 2.5%
D. 1%

Solution

Relative uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Correct Answer: C — 2.5%

Q. A pendulum's period is measured as 2.0 s with an uncertainty of ±0.1 s. What is the relative uncertainty?

A. 5%
B. 10%
C. 2%
D. 1%

Solution

Relative uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Correct Answer: A — 5%

Q. A pendulum's period is measured as 2.0 s with an uncertainty of ±0.1 s. What is the percentage uncertainty in the measurement?

A. 5%
B. 10%
C. 2%
D. 1%

Solution

Percentage uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Correct Answer: A — 5%

Q. A speed is measured as 20 m/s with an uncertainty of ±0.5 m/s. What is the absolute error in the speed measurement?

A. 0.5 m/s
B. 0.25 m/s
C. 1 m/s
D. 0.1 m/s

Solution

The absolute error is given directly as ±0.5 m/s.

Correct Answer: A — 0.5 m/s

Q. A student calculates the density of a substance as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³. What is the density range?

A. 7.9 g/cm³ to 8.1 g/cm³
B. 8.0 g/cm³ to 8.2 g/cm³
C. 8.0 g/cm³ to 8.1 g/cm³
D. 7.5 g/cm³ to 8.5 g/cm³

Solution

Density range = 8.0 ± 0.1 = 7.9 g/cm³ to 8.1 g/cm³.

Correct Answer: A — 7.9 g/cm³ to 8.1 g/cm³

Q. A student measures the length of a rod multiple times and records the values: 10.1 cm, 10.2 cm, 10.0 cm, 10.3 cm. What is the average length of the rod?

A. 10.0 cm
B. 10.1 cm
C. 10.2 cm
D. 10.3 cm

Solution

Average length = (10.1 + 10.2 + 10.0 + 10.3) / 4 = 10.15 cm.

Correct Answer: B — 10.1 cm

Q. A student measures the length of a rod multiple times and records values of 10.1 cm, 10.2 cm, and 10.0 cm. What is the average length of the rod?

A. 10.0 cm
B. 10.1 cm
C. 10.2 cm
D. 10.3 cm

Solution

Average length = (10.1 + 10.2 + 10.0) / 3 = 10.1 cm.

Correct Answer: B — 10.1 cm

Q. A student measures the mass of an object as 200 g with an uncertainty of ±2 g. What is the relative uncertainty?

A. 1%
B. 0.5%
C. 2%
D. 0.1%

Solution

Relative uncertainty = (Uncertainty / Measured value) * 100 = (2 / 200) * 100 = 1%.

Correct Answer: B — 0.5%

Q. A student measures the speed of a car as 60 km/h with an uncertainty of ±2 km/h. What is the percentage uncertainty?

A. 3.33%
B. 2.5%
C. 4.0%
D. 5.0%

Solution

Percentage uncertainty = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.

Correct Answer: A — 3.33%

Q. A student measures the speed of a car as 60 km/h with an uncertainty of ±2 km/h. What is the percentage error in the speed measurement?

A. 3.33%
B. 2.0%
C. 1.5%
D. 4.0%

Solution

Percentage error = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.

Correct Answer: A — 3.33%

Q. A student measures the temperature of water as 25°C with an uncertainty of ±0.5°C. What is the minimum temperature?

A. 24.5°C
B. 25.0°C
C. 25.5°C
D. 26.0°C

Solution

Minimum temperature = Measured value - Uncertainty = 25.0 - 0.5 = 24.5°C.

Correct Answer: A — 24.5°C

Q. A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the percentage uncertainty in the time period?

A. 5%
B. 10%
C. 2.5%
D. 1%

Solution

Percentage uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.

Correct Answer: C — 2.5%

Q. A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the absolute error in the time period?

A. 0.1 s
B. 0.05 s
C. 0.2 s
D. 0.01 s

Solution

The absolute error is given directly as ±0.1 s.

Correct Answer: A — 0.1 s

Q. A student records the time taken for a reaction as 15.0 s with an uncertainty of ±0.5 s. What is the total time range?

A. 14.5 s to 15.5 s
B. 15.0 s to 16.0 s
C. 14.0 s to 15.0 s
D. 15.0 s to 15.5 s

Solution

Total time range = 15.0 s ± 0.5 s = 14.5 s to 15.5 s.

Correct Answer: A — 14.5 s to 15.5 s

Q. A thermometer has a least count of 1°C. If the reading is 25°C, what is the maximum possible error in the measurement?

A. 0.5°C
B. 1°C
C. 0.1°C
D. 2°C

Solution

Maximum possible error = Least count = 1°C.

Correct Answer: B — 1°C

Q. A thermometer reads 100.5 °C when the actual temperature is 100.0 °C. What is the percentage error in the measurement?

A. 0.5%
B. 1.0%
C. 0.1%
D. 0.2%

Solution

Percentage error = (Absolute error / True value) * 100 = (0.5 / 100.0) * 100 = 0.5%.

Correct Answer: B — 1.0%

Q. A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. If this temperature is used in a calculation, what is the uncertainty in the result if the temperature is multiplied by 2?

A. 1 °C
B. 0.5 °C
C. 0.25 °C
D. 0.1 °C

Solution

When multiplying, the relative uncertainty doubles: 2 * 0.5 °C = 1 °C.

Correct Answer: A — 1 °C

Q. A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. What is the range of possible true temperatures?

A. 24.5 °C to 25.5 °C
B. 25.0 °C to 26.0 °C
C. 24.0 °C to 25.0 °C
D. 25.0 °C to 25.5 °C

Solution

Range = Measured value ± Uncertainty = 25.0 ± 0.5 = 24.5 °C to 25.5 °C.

Correct Answer: A — 24.5 °C to 25.5 °C

Q. A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. What is the range of possible temperatures?

A. 24.5 °C to 25.5 °C
B. 25.0 °C to 26.0 °C
C. 24.0 °C to 25.0 °C
D. 25.0 °C to 25.5 °C

Solution

Range = 25.0 ± 0.5 °C = 24.5 °C to 25.5 °C.

Correct Answer: A — 24.5 °C to 25.5 °C

Q. A voltage is measured as 12.0 V with an uncertainty of ±0.1 V. What is the absolute error?

A. 0.1 V
B. 0.2 V
C. 0.3 V
D. 0.4 V

Solution

Absolute error is the same as the uncertainty, which is ±0.1 V.

Correct Answer: A — 0.1 V

Q. A voltage is measured as 12.0 V with an uncertainty of ±0.2 V. What is the maximum possible voltage?

A. 11.8 V
B. 12.0 V
C. 12.2 V
D. 12.4 V

Solution

Maximum possible voltage = Measured value + Uncertainty = 12.0 + 0.2 = 12.2 V.

Correct Answer: C — 12.2 V

Q. A voltage is measured as 15.0 V with an uncertainty of ±0.3 V. What is the fractional error in the voltage measurement?

A. 0.02
B. 0.03
C. 0.01
D. 0.05

Solution

Fractional error = (absolute error / measured value) = 0.3 / 15.0 = 0.02.

Correct Answer: B — 0.03

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