Error Analysis for Competitive Exam Success

Error Analysis

Q. If the mass of an object is measured as 10.0 kg with an uncertainty of ±0.2 kg, what is the percentage error in the mass measurement?

A. 2%
B. 0.2%
C. 0.5%
D. 1%

Solution

Percentage error = (absolute error / measured value) * 100 = (0.2 / 10.0) * 100 = 2%.

Correct Answer: D — 1%

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Q. If the mass of an object is measured as 10.0 kg with an uncertainty of ±0.2 kg, what is the percentage error?

A. 2%
B. 0.2%
C. 0.02%
D. 0.5%

Solution

Percentage error = (absolute error / measured value) * 100 = (0.2 / 10.0) * 100 = 2%.

Correct Answer: A — 2%

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Q. If the mass of an object is measured as 50 kg with an uncertainty of ±0.5 kg, what is the percentage error in the mass measurement?

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

Solution

Percentage error = (absolute error / measured value) * 100 = (0.5 / 50) * 100 = 1%.

Correct Answer: A — 1%

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Q. If the measured length of a rod is 20 cm with an error of 0.5 cm, what is the relative error in the measurement?

A. 0.025
B. 0.05
C. 0.0025
D. 0.005

Solution

Relative error = (Absolute error / Measured value) = 0.5 / 20 = 0.025 or 2.5%

Correct Answer: B — 0.05

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Q. If the measured value of a quantity is 100 with a relative error of 0.02, what is the absolute error?

A. 2
B. 0.02
C. 0.5
D. 1

Solution

Absolute error = Relative error * Measured value = 0.02 * 100 = 2.

Correct Answer: A — 2

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Q. If the measured value of a quantity is 75 with a relative error of 0.04, what is the true value?

A. 72
B. 78
C. 75
D. 80

Solution

Relative error = Absolute error / True value. Let true value be x. 0.04 = |75 - x| / x. Solving gives x = 78.

Correct Answer: B — 78

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Q. If the temperature is recorded as 30°C with an error of 0.5°C, what is the maximum possible temperature?

A. 30.5°C
B. 29.5°C
C. 31°C
D. 30°C

Solution

Maximum possible temperature = Measured value + Error = 30 + 0.5 = 30.5°C

Correct Answer: A — 30.5°C

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Q. If the true value of a measurement is 50 and the measured value is 48, what is the absolute error?

A. 2
B. 48
C. 50
D. 52

Solution

Absolute error = |True value - Measured value| = |50 - 48| = 2.

Correct Answer: A — 2

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Q. If the true value of a measurement is 50.0 cm and a student records a value of 49.5 cm, what is the absolute error?

A. 0.5 cm
B. 0.0 cm
C. 0.5 m
D. 1.0 cm

Solution

Absolute error = |True value - Measured value| = |50.0 - 49.5| = 0.5 cm.

Correct Answer: A — 0.5 cm

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Q. If the true value of a measurement is 50.0 cm and the measured value is 49.5 cm, what is the absolute error?

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

Solution

Absolute error = |True value - Measured value| = |50.0 - 49.5| = 0.5 cm.

Correct Answer: A — 0.5 cm

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Q. If the true value of a measurement is 50.0 units and the measured value is 48.0 units, what is the percentage error?

A. 4.0%
B. 2.0%
C. 5.0%
D. 3.0%

Solution

Percentage error = |(True value - Measured value) / True value| * 100 = |(50.0 - 48.0) / 50.0| * 100 = 4.0%.

Correct Answer: A — 4.0%

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Q. If the true value of a quantity is 100 and the measured value is 98, what is the percentage error?

A. 2%
B. 1%
C. 3%
D. 0.5%

Solution

Percentage error = (|True value - Measured value| / True value) * 100 = (|100 - 98| / 100) * 100 = 2%.

Correct Answer: A — 2%

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Q. If the true value of a quantity is 200 and the measured value is 198, what is the percentage error?

A. 1%
B. 0.5%
C. 2%
D. 0.25%

Solution

Percentage error = (|True value - Measured value| / True value) * 100 = (|200 - 198| / 200) * 100 = 1%.

Correct Answer: A — 1%

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Q. In a lab experiment, the density of a liquid is measured as 1.2 g/cm³ with an uncertainty of ±0.05 g/cm³. What is the relative error?

A. 4.17%
B. 3.33%
C. 5.00%
D. 2.50%

Solution

Relative error = (Uncertainty / Measured value) * 100 = (0.05 / 1.2) * 100 = 4.17%.

Correct Answer: A — 4.17%

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Q. In a lab experiment, the speed of sound is measured as 340 m/s with an uncertainty of ±2 m/s. What is the total uncertainty if the speed is used in a calculation involving division by 2?

A. ±1 m/s
B. ±2 m/s
C. ±0.5 m/s
D. ±0.25 m/s

Solution

Total uncertainty = (2 m/s) / 2 = ±1 m/s.

Correct Answer: A — ±1 m/s

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Q. In a lab experiment, the speed of sound is measured as 340 m/s with an uncertainty of ±5 m/s. What is the percentage uncertainty in this measurement?

A. 1.47%
B. 1.5%
C. 2%
D. 0.5%

Solution

Percentage uncertainty = (absolute uncertainty / measured value) * 100 = (5 / 340) * 100 ≈ 1.47%.

Correct Answer: B — 1.5%

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Q. In a physics experiment, the force applied is measured as 50 N with an uncertainty of ±1 N. What is the relative uncertainty in the force measurement?

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

Solution

Relative uncertainty = (absolute uncertainty / measured value) = 1 / 50 = 0.02.

Correct Answer: B — 0.01

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Q. In a physics experiment, the speed of an object is measured as 20.0 m/s with an uncertainty of ±0.4 m/s. What is the maximum possible error in the kinetic energy calculated from this speed?

A. 8 J
B. 4 J
C. 2 J
D. 1 J

Solution

Kinetic energy = 0.5 * m * v²; maximum error = m * v * uncertainty in v = m * 20.0 * 0.4 = 8 J (assuming m = 1 kg).

Correct Answer: A — 8 J

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Q. In an experiment, a student measures the mass of an object as 200 g with an uncertainty of ±5 g. What is the range of possible values for the mass?

A. 195 g to 205 g
B. 200 g to 210 g
C. 195 g to 210 g
D. 200 g to 205 g

Solution

Range = Measured value ± Uncertainty = 200 g ± 5 g = 195 g to 205 g.

Correct Answer: A — 195 g to 205 g

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Q. In an experiment, the length of a rod is measured as 12.0 m with an uncertainty of ±0.5 m. What is the total uncertainty if the length is used in a calculation involving multiplication by 3?

A. ±1.5 m
B. ±0.5 m
C. ±0.75 m
D. ±0.25 m

Solution

Total uncertainty = 3 * (0.5 m) = ±1.5 m.

Correct Answer: A — ±1.5 m

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Q. In an experiment, the mass of an object is measured as 5.0 kg with an uncertainty of ±0.2 kg. What is the absolute error?

A. 0.2 kg
B. 0.5 kg
C. 0.1 kg
D. 0.3 kg

Solution

Absolute error is the uncertainty in the measurement, which is ±0.2 kg.

Correct Answer: A — 0.2 kg

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Q. In an experiment, the measured value of a voltage is 12.0 V with an uncertainty of ±0.2 V. What is the maximum possible error?

A. 0.2 V
B. 0.1 V
C. 0.5 V
D. 0.0 V

Solution

Maximum possible error is equal to the uncertainty, which is ±0.2 V.

Correct Answer: A — 0.2 V

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Q. In an experiment, the voltage is measured as 12.0 V with an uncertainty of ±0.3 V. What is the absolute error in the voltage measurement?

A. 0.3 V
B. 0.25 V
C. 0.5 V
D. 0.1 V

Solution

The absolute error is given as ±0.3 V.

Correct Answer: A — 0.3 V

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Q. In an experiment, the voltage is measured as 12.0 V with an uncertainty of ±0.5 V. What is the maximum possible error in the voltage measurement?

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

Solution

The maximum possible error is the absolute uncertainty, which is ±0.5 V.

Correct Answer: A — 0.5 V

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Q. In an experiment, the voltage is measured as 12.0 V with an uncertainty of ±0.5 V. What is the absolute error in the voltage measurement?

A. 0.5 V
B. 0.05 V
C. 5 V
D. 1 V

Solution

The absolute error is given directly as ±0.5 V.

Correct Answer: A — 0.5 V

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Q. The length of a rod is measured as 50 cm with an error of 1 cm. What is the minimum possible length?

A. 49 cm
B. 50 cm
C. 51 cm
D. 48 cm

Solution

Minimum possible length = Measured value - Error = 50 - 1 = 49 cm.

Correct Answer: A — 49 cm

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Q. The temperature is measured as 25°C with an error of 1°C. What is the range of possible true values?

A. 24°C to 26°C
B. 25°C to 27°C
C. 23°C to 25°C
D. 26°C to 28°C

Solution

True value can be in the range of (Measured value - Error) to (Measured value + Error) = 25°C ± 1°C = 24°C to 26°C.

Correct Answer: A — 24°C to 26°C

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Q. The weight of an object is measured as 10 kg with a 0.1 kg error. What is the maximum possible weight?

A. 10.1 kg
B. 10.2 kg
C. 10 kg
D. 9.9 kg

Solution

Maximum possible weight = Measured weight + Absolute error = 10 + 0.1 = 10.1 kg.

Correct Answer: A — 10.1 kg

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Q. The weight of an object is measured as 200 g with a possible error of 5 g. What is the range of the true weight?

A. 195 g to 205 g
B. 200 g to 205 g
C. 195 g to 200 g
D. 200 g to 210 g

Solution

True weight range = Measured value ± Absolute error = 200 ± 5 = 195 g to 205 g.

Correct Answer: A — 195 g to 205 g

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Error Analysis

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