Units & Measurement
Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the relative uncertainty in the density?
A.
0.0125
B.
0.01
C.
0.005
D.
0.02
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Solution
Relative uncertainty = (absolute uncertainty / measured value) = 0.1 / 8.0 = 0.0125.
Correct Answer: B — 0.01
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Q. If the length of a side of a cube is doubled, how does its volume change?
A.
Increases by 2 times
B.
Increases by 4 times
C.
Increases by 8 times
D.
Remains the same
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Solution
The volume of a cube is given by V = a³. If the side length a is doubled, the new volume is (2a)³ = 8a³, which is 8 times the original volume.
Correct Answer: C — Increases by 8 times
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Q. If the length of a side of a cube is doubled, how does the volume change?
A.
Increases by 2 times
B.
Increases by 4 times
C.
Increases by 8 times
D.
Remains the same
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Solution
Volume of a cube is given by V = a³. If a is doubled, V becomes (2a)³ = 8a³, hence volume increases by 8 times.
Correct Answer: C — Increases by 8 times
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Q. If the length of a side of a cube is measured as 2.0 ± 0.1 m, what is the maximum possible error in the volume of the cube?
A.
0.8 m³
B.
0.4 m³
C.
0.2 m³
D.
0.1 m³
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Solution
Volume V = L³. The maximum error in volume can be calculated using the formula: ΔV = 3L²ΔL. Here, ΔL = 0.1 m, L = 2.0 m, so ΔV = 3(2.0)²(0.1) = 1.2 m³.
Correct Answer: B — 0.4 m³
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Q. If the length of a side of a cube is measured as 2.5 cm with an uncertainty of 0.1 cm, what is the volume of the cube?
A.
15.625 cm³
B.
16.0 cm³
C.
16.5 cm³
D.
17.0 cm³
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Solution
Volume = side³ = (2.5 cm)³ = 15.625 cm³. Considering significant figures, it is reported as 16.0 cm³.
Correct Answer: B — 16.0 cm³
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Q. If the length of a side of a cube is measured as 2.5 cm with an uncertainty of 0.1 cm, what is the volume of the cube with its uncertainty?
A.
15.625 ± 0.25 cm³
B.
15.625 ± 0.5 cm³
C.
12.5 ± 0.1 cm³
D.
10.0 ± 0.2 cm³
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Solution
Volume = (2.5 cm)³ = 15.625 cm³. The uncertainty in volume can be calculated using the formula for propagation of uncertainty.
Correct Answer: A — 15.625 ± 0.25 cm³
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Q. If the length of an object is doubled, what happens to its area?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
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Solution
If the length is doubled, the area increases by a factor of four (A = length²).
Correct Answer: D — It quadruples
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Q. If the length of an object is doubled, what happens to its volume?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It increases by a factor of eight
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Solution
If the length is doubled, the volume increases by a factor of 2^3 = 8, since volume is proportional to the cube of the length.
Correct Answer: D — It increases by a factor of eight
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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 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. If you add 12.11 and 0.3, how many decimal places should the answer have?
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Solution
The answer should have 1 decimal place, as 0.3 has the least decimal places.
Correct Answer: A — 1
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Q. If you multiply 2.5 (2 significant figures) by 3.42 (3 significant figures), how many significant figures should the result have?
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Solution
The result should have 2 significant figures, as the least number of significant figures in the factors is 2.
Correct Answer: A — 2
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Q. If you multiply 2.5 (2 significant figures) by 3.42 (3 significant figures), how many significant figures should the answer have?
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Solution
The answer should have 2 significant figures, as the least number of significant figures in the factors is 2.
Correct Answer: A — 2
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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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