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%
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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%
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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%
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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
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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?
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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?
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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
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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?
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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
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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
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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%
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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%
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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%
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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%
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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
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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%
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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
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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
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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
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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
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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
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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
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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
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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 absolute error in the voltage measurement?
A.
0.5 V
B.
0.05 V
C.
5 V
D.
1 V
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Solution
The absolute error is given directly as ±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 maximum possible error in the voltage measurement?
A.
0.5 V
B.
0.25 V
C.
1 V
D.
0.1 V
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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. 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
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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
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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
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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
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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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