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Q1. What is the uncertainty in a measurement of 50.0 ± 0.5 g when converted to kilograms?
Solution:
To convert grams to kilograms, divide by 1000. The uncertainty in kilograms is 0.5 g / 1000 = 0.0005 kg.
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Q2. If the length of an object is doubled, what happens to its area?
Solution:
If the length is doubled, the area increases by a factor of four (A = length²).
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Q3. If you add 12.11 and 0.3, how many decimal places should the answer have?
Solution:
The answer should have 1 decimal place, as 0.3 has the least decimal places.
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Q4. What is the uncertainty in the measurement of a length of 5.00 cm ± 0.02 cm when calculating the area?
Solution:
Area = length² = (5.00 cm)² = 25.00 cm². The uncertainty in area is calculated using the formula: ΔA = 2LΔL = 2(5.00 cm)(0.02 cm) = 0.20 cm².
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Q5. If a measurement is recorded as 0.004560, how many significant figures does it have?
Solution:
Leading zeros are not significant. The significant figures are 4, 5, 6, which gives a total of 4 significant figures.
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Q6. 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?
Solution:
New uncertainty = 3 * (uncertainty) = 3 * 1.0 = 3.0 units.
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Q7. The weight of an object is measured as 10 kg with a 0.1 kg error. What is the maximum possible weight?
Solution:
Maximum possible weight = Measured weight + Absolute error = 10 + 0.1 = 10.1 kg.
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Q8. 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?
Solution:
The maximum possible error is the absolute uncertainty, which is ±0.5 V.
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Q9. Which of the following quantities has the dimension of [M^0L^2T^-2]?
Solution:
Energy and work both have the same dimensions of [M^1L^2T^-2]. Power has dimensions of [M^1L^2T^-3].
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Q10. A length is measured as 50.1 cm with an error of 0.1 cm. What is the minimum possible true length?
Solution:
Minimum true length = Measured value - Error = 50.1 cm - 0.1 cm = 50 cm.
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