Least count, significant figures, errors in measurements - Question Bank

1. The number of significant figures in 0.000000102 is:
A) 2
B) 3
C) 7
D) 9
2. A measurement is recorded as 15.00 ± 0.02. What is the percentage error?
A) 0.02%
B) 0.13%
C) 1.3%
D) 2%
3. Which of the following operations involving significant figures requires rounding to the same number of decimal places?
A) Multiplication
B) Division
C) Addition
D) Exponentiation
4. A student measures the diameter of a wire as 1.00 mm using a screw gauge. If the least count of the screw gauge is 0.01 mm, what is the absolute error in this measurement?
A) ±0.01 mm
B) ±0.005 mm
C) ±1.00 mm
D) ±0.1 mm
5. In the calculation of the volume of a sphere (V = 4/3 πr³), if the radius 'r' has a relative error Δr/r, what is the relative error in the volume (ΔV/V)?
A) 3 (Δr/r)
B) 4/3 (Δr/r)
C) π (Δr/r)
D) (Δr/r)³
6. If the length of an object is measured as 12.3 cm, what is the possible range of the true length considering the least count of a meter scale (0.1 cm)?
A) 12.2 cm to 12.4 cm
B) 12.25 cm to 12.35 cm
C) 12.3 cm to 12.4 cm
D) 12.0 cm to 12.6 cm
7. Consider the measurement 5.000 m. How many significant figures does it have?
A) 1
B) 2
C) 3
D) 4
8. When expressing a measurement, the number of significant figures reflects:
A) The precision of the instrument
B) The accuracy of the measurement
C) Both precision and accuracy
D) The exactness of the measurement
9. Which of the following is a way to minimize random errors?
A) Calibrating the instrument
B) Using a more precise instrument
C) Taking a large number of readings and averaging them
D) Ensuring consistent experimental conditions
10. If a voltmeter consistently reads 0.5 V higher than the actual voltage, this is an example of:
A) Random error
B) Gross error
C) Systematic error
D) Least count error
11. What is the primary characteristic of a systematic error?
A) It varies randomly with each measurement.
B) It is always in the same direction (positive or negative).
C) It can be eliminated by averaging.
D) It is due to chance fluctuations.
12. Which type of error is often due to the limitations of the measuring instrument itself, like the smallest division?
A) Systematic error
B) Random error
C) Least count error
D) Gross error
13. If the true value of a quantity is 10.0 and the measured values are 9.8, 10.1, 10.3, what is the absolute error for the measurement 10.1?
A) +0.1
B) -0.1
C) ±0.1
D) 0.01
14. A student measures the time period of a pendulum as 2.50 s, 2.55 s, and 2.45 s. What is the mean absolute error?
A) 0.05 s
B) 0.02 s
C) 0.01 s
D) 0.03 s
15. Multiply 2.5 cm by 3.14 cm. Round the result to the correct number of significant figures.
A) 7.85 cm^2
B) 7.9 cm^2
C) 7.850 cm^2
D) 8 cm^2
16. Add 2.5 cm and 3.14 cm. Round the result to the correct number of significant figures.
A) 5.64 cm
B) 5.6 cm
C) 5.7 cm
D) 5.640 cm
17. If a measurement is 12.345 cm and needs to be rounded to three significant figures, what is the result?
A) 12.3 cm
B) 12.4 cm
C) 12.35 cm
D) 12 cm
18. In multiplication and division, the result should be rounded to the:
A) Least number of significant figures
B) Same number of decimal places as the quantity with the least number of decimal places
C) Same number of significant figures as the quantity with the least number of significant figures
D) Same number of decimal places as the quantity with the most decimal places
19. In addition and subtraction, the result should be rounded to the:
A) Least number of significant figures
B) Same number of decimal places as the quantity with the least number of decimal places
C) Same number of significant figures as the quantity with the most significant figures
D) Same number of decimal places as the quantity with the most decimal places
20. How many significant figures are in the number 3.00 x 10^4?
A) 1
B) 2
C) 3
D) 4
21. How many significant figures are there in the number 0.0250?
A) 1
B) 2
C) 3
D) 4
22. Which of the following numbers has the most significant figures?
A) 0.005
B) 5.00
C) 50
D) 500
23. Significant figures in a measurement indicate:
A) The exact value of the measurement
B) The number of digits that are known with certainty plus one uncertain digit
C) The total number of digits in the measurement
D) The precision of the instrument used
24. For a quantity raised to a power, Z = A^n, the relative error in Z (ΔZ/Z) is related to the relative error in A (ΔA/A) by:
A) ΔZ/Z = n × (ΔA/A)
B) ΔZ/Z = (ΔA/A) / n
C) ΔZ/Z = ΔA/A + n
D) ΔZ/Z = n + ΔA/A
25. If quantity Z = A / B, and the relative errors are ΔA/A and ΔB/B, then the relative error in Z (ΔZ/Z) is approximately:
A) ΔZ/Z = ΔA/A + ΔB/B
B) ΔZ/Z = |ΔA/A - ΔB/B|
C) ΔZ/Z = (ΔA/A) × (ΔB/B)
D) ΔZ/Z = max(ΔA/A, ΔB/B)
26. If quantity Z = A × B, and the relative errors are ΔA/A and ΔB/B, then the relative error in Z (ΔZ/Z) is approximately:
A) ΔZ/Z = ΔA/A + ΔB/B
B) ΔZ/Z = |ΔA/A - ΔB/B|
C) ΔZ/Z = (ΔA/A) × (ΔB/B)
D) ΔZ/Z = max(ΔA/A, ΔB/B)
27. When dividing two quantities with relative errors, how is the resultant relative error determined?
A) It is the difference of the individual relative errors
B) It is the sum of the individual relative errors
C) It is the product of the individual relative errors
D) It is the maximum of the individual relative errors
28. When multiplying two quantities with relative errors, how is the resultant relative error determined?
A) It is the difference of the individual relative errors
B) It is the sum of the individual relative errors
C) It is the product of the individual relative errors
D) It is the maximum of the individual relative errors
29. If quantity Z = A - B, and the absolute errors are ΔA and ΔB, then the absolute error in Z (ΔZ) is:
A) ΔZ = ΔA + ΔB
B) ΔZ = |ΔA - ΔB|
C) ΔZ = max(ΔA, ΔB)
D) ΔZ = (ΔA + ΔB)/2
30. If quantity Z = A + B, and the absolute errors are ΔA and ΔB, then the absolute error in Z (ΔZ) is:
A) ΔZ = ΔA + ΔB
B) ΔZ = |ΔA - ΔB|
C) ΔZ = max(ΔA, ΔB)
D) ΔZ = (ΔA + ΔB)/2
31. When subtracting two quantities with absolute errors, how is the resultant absolute error determined?
A) It is the difference of the individual absolute errors
B) It is the sum of the individual absolute errors
C) It is the maximum of the individual absolute errors
D) It is the average of the individual absolute errors
32. When adding two quantities with absolute errors, how is the resultant absolute error determined?
A) It is the difference of the individual absolute errors
B) It is the sum of the individual absolute errors
C) It is the maximum of the individual absolute errors
D) It is the average of the individual absolute errors
33. What is the percentage error if the relative error is 0.05?
A) 0.05%
B) 5%
C) 50%
D) 0.5%
34. If the absolute error in a measurement is ±0.2 cm and the true value is 5.0 cm, what is the relative error?
A) 0.04
B) 0.2
C) 5
D) 0.02
35. If the measured value of a length is 10.5 cm and the true value is 10.0 cm, what is the absolute error?
A) +0.5 cm
B) -0.5 cm
C) ±0.5 cm
D) 5%
36. Percentage error is calculated as:
A) Relative error × 100
B) Absolute error × 100
C) True value × 100
D) Measured value × 100
37. The relative error in a measurement is the ratio of:
A) Absolute error to the true value
B) True value to the absolute error
C) Measured value to the absolute error
D) Absolute error to the measured value
38. If the true value of a quantity is 'a' and the measured value is 'a_m', the absolute error (Δa) is:
A) a_m - a
B) a - a_m
C) ±(a - a_m)
D) ±(a_m - a)
39. The absolute error in a measurement is defined as:
A) The average of all errors
B) The difference between the true value and the measured value
C) The ratio of the true value to the measured value
D) The smallest division on the measuring scale
40. What is a 'gross error' in measurements?
A) A small, unavoidable error
B) An error due to improper use of the instrument or misreading
C) An error due to the limitations of the instrument's least count
D) An error that consistently affects all measurements in the same way
41. If a measuring instrument consistently shows a reading that is higher or lower than the true value, it is likely due to:
A) Random error
B) Gross error
C) Systematic error
D) Least count error
42. An error that arises due to the imperfection in the experimental technique or method is classified as:
A) Random error
B) Personal error
C) Systematic error
D) Gross error
43. What kind of error can be eliminated by taking multiple readings and averaging them?
A) Systematic error
B) Random error
C) Zero error
D) Instrumental error
44. Which of the following is NOT a type of error in measurements?
A) Systematic error
B) Random error
C) Personal error
D) Absolute error
45. What is the primary purpose of using a Vernier caliper or screw gauge over a simple meter scale?
A) To measure larger distances
B) To achieve higher precision and accuracy
C) To measure volume
D) To measure temperature
46. In a screw gauge, if the pitch is 0.5 mm and there are 100 divisions on the circular scale, what is the least count?
A) 0.5 mm
B) 0.05 mm
C) 0.005 mm
D) 0.01 mm
47. What is the least count of a Vernier caliper where 10 Vernier scale divisions (VSD) coincide with 9 main scale divisions (MSD) and 1 MSD is equal to 1 mm?
A) 0.1 mm
B) 0.01 mm
C) 0.02 mm
D) 0.1 cm
48. If a meter scale is divided into millimeters, what is its least count?
A) 1 cm
B) 1 mm
C) 0.1 mm
D) 0.01 mm
49. Which of the following instruments typically has the smallest least count?
A) Meter scale
B) Vernier caliper
C) Screw gauge
D) Measuring tape
50. What does the least count of a measuring instrument represent?
A) The maximum possible error in a measurement
B) The smallest value that can be measured accurately with the instrument
C) The total range of the instrument
D) The precision of the instrument
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