Error Analysis
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?
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Solution
Percentage uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.
Correct Answer: A — 5%
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Q. A physical quantity is measured as 50.0 units with an uncertainty of ±1.0 units. If this quantity is multiplied by 3, what is the new uncertainty?
A.
3.0 units
B.
1.0 units
C.
2.0 units
D.
4.0 units
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Solution
New uncertainty = 3 * (uncertainty) = 3 * 1.0 = 3.0 units.
Correct Answer: A — 3.0 units
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Q. A speed is measured as 20 m/s with an uncertainty of ±0.5 m/s. If this speed is used to calculate kinetic energy, what is the percentage error in kinetic energy?
A.
5%
B.
2.5%
C.
1%
D.
10%
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Solution
K.E. = 0.5 * m * v², percentage error = 2 * (Δv/v) = 2 * (0.5/20) = 0.05 or 5%.
Correct Answer: B — 2.5%
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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
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Solution
The absolute error is given directly as ±0.5 m/s.
Correct Answer: A — 0.5 m/s
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Q. A speed is recorded as 60 km/h with an error of 2 km/h. What is the percentage error?
A.
3.33%
B.
2.5%
C.
1.67%
D.
4%
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Solution
Percentage error = (Absolute error / Measured value) * 100 = (2 / 60) * 100 = 3.33%
Correct Answer: A — 3.33%
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Q. A speed of 30 m/s is measured with an uncertainty of ±0.5 m/s. What is the total uncertainty if this speed is used to calculate kinetic energy?
A.
0.25 J
B.
0.5 J
C.
1 J
D.
2 J
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Solution
Kinetic energy = 0.5 * m * v²; uncertainty in KE = 2 * v * uncertainty in v = 2 * 30 * 0.5 = 30 J.
Correct Answer: C — 1 J
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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
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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
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Q. A student measures a length as 30.2 m, but the actual length is 30 m. What is the error in measurement?
A.
0.2 m
B.
0.1 m
C.
0.3 m
D.
0.5 m
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Solution
Error = Measured value - True value = 30.2 m - 30 m = 0.2 m.
Correct Answer: A — 0.2 m
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Q. A student measures the length of a rod as 15.3 cm. If the true length is 15 cm, what is the error in measurement?
A.
0.3 cm
B.
0.2 cm
C.
0.1 cm
D.
0.5 cm
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Solution
Error in measurement = Measured value - True value = 15.3 - 15 = 0.3 cm.
Correct Answer: A — 0.3 cm
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Q. A student measures the length of a rod as 150 cm with a possible error of 2 cm. What is the range of the true length?
A.
148 cm to 152 cm
B.
149 cm to 151 cm
C.
150 cm to 152 cm
D.
150 cm to 154 cm
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Solution
True length can vary from 150 - 2 to 150 + 2, which is 148 cm to 152 cm.
Correct Answer: A — 148 cm to 152 cm
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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
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Solution
Average length = (10.1 + 10.2 + 10.0 + 10.3) / 4 = 10.15 cm.
Correct Answer: B — 10.1 cm
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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
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Solution
Average length = (10.1 + 10.2 + 10.0) / 3 = 10.1 cm.
Correct Answer: B — 10.1 cm
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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%
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Solution
Relative uncertainty = (Uncertainty / Measured value) * 100 = (2 / 200) * 100 = 1%.
Correct Answer: B — 0.5%
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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%
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Solution
Percentage uncertainty = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.
Correct Answer: A — 3.33%
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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%
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Solution
Percentage error = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.
Correct Answer: A — 3.33%
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Q. A student measures the speed of a car as 60.0 km/h with an uncertainty of ±2.0 km/h. What is the percentage uncertainty in the speed measurement?
A.
3.33%
B.
2.0%
C.
1.67%
D.
5.0%
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Solution
Percentage uncertainty = (absolute uncertainty / measured value) * 100 = (2.0 / 60.0) * 100 = 3.33%.
Correct Answer: A — 3.33%
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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
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Solution
Minimum temperature = Measured value - Uncertainty = 25.0 - 0.5 = 24.5°C.
Correct Answer: A — 24.5°C
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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%
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Solution
Percentage uncertainty = (Uncertainty / Measured value) * 100 = (0.1 / 2.0) * 100 = 5%.
Correct Answer: C — 2.5%
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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
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Solution
The absolute error is given directly as ±0.1 s.
Correct Answer: A — 0.1 s
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Q. A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the fractional error in the time period?
A.
0.05
B.
0.1
C.
0.02
D.
0.1
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Solution
Fractional error = (absolute error / measured value) = 0.1 / 2.0 = 0.05.
Correct Answer: A — 0.05
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Q. A student measures the width of a table as 1.2 m with a possible error of 0.02 m. What is the range of the true width?
A.
1.18 m to 1.22 m
B.
1.20 m to 1.22 m
C.
1.20 m to 1.24 m
D.
1.18 m to 1.20 m
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Solution
True width = Measured value ± Absolute error = 1.2 ± 0.02 gives the range 1.18 m to 1.22 m.
Correct Answer: A — 1.18 m to 1.22 m
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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
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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
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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
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Solution
Maximum possible error = Least count = 1°C.
Correct Answer: B — 1°C
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Q. A thermometer reads 100.0 °C with an uncertainty of ±0.5 °C. What is the range of possible temperatures?
A.
99.5 °C to 100.5 °C
B.
99.0 °C to 100.0 °C
C.
100.0 °C to 101.0 °C
D.
100.5 °C to 101.5 °C
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Solution
Range = 100.0 ± 0.5 °C gives 99.5 °C to 100.5 °C.
Correct Answer: A — 99.5 °C to 100.5 °C
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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%
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Solution
Percentage error = (Absolute error / True value) * 100 = (0.5 / 100.0) * 100 = 0.5%.
Correct Answer: B — 1.0%
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Q. A thermometer reads 25.0 °C with an uncertainty of ±0.2 °C. What is the range of possible temperatures?
A.
24.8 °C to 25.2 °C
B.
24.5 °C to 25.5 °C
C.
25.0 °C to 25.4 °C
D.
24.0 °C to 26.0 °C
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Solution
Range = 25.0 ± 0.2 gives 24.8 °C to 25.2 °C.
Correct Answer: A — 24.8 °C to 25.2 °C
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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
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Solution
When multiplying, the relative uncertainty doubles: 2 * 0.5 °C = 1 °C.
Correct Answer: A — 1 °C
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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
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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
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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
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Solution
Range = 25.0 ± 0.5 °C = 24.5 °C to 25.5 °C.
Correct Answer: A — 24.5 °C to 25.5 °C
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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
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Solution
Absolute error is the same as the uncertainty, which is ±0.1 V.
Correct Answer: A — 0.1 V
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