Units & Measurement for Competitive Exam Success

Units & Measurement

Error Analysis Significant Figures Units & Dimensions

Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the range of possible densities?

A. 7.8 to 8.2 g/cm³
B. 7.5 to 8.5 g/cm³
C. 8.0 to 8.4 g/cm³
D. 8.0 to 8.2 g/cm³

Solution

Range = 8.0 ± 0.2 gives 7.8 to 8.2 g/cm³.

Correct Answer: A — 7.8 to 8.2 g/cm³

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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

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

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

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

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

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

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

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?

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 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 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. If you add 12.11 and 0.3, how many decimal places should the answer have?

A. 1
B. 2
C. 3
D. 4

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 answer have?

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

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. If you multiply 2.5 (2 significant figures) by 3.42 (3 significant figures), how many significant figures should the result have?

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

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. 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 ±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 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 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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Units & Measurement

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