Least count, significant figures, errors in measurements - One Line Questions
1.
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? —
±0.1
2.
If the measured value of a length is 10.5 cm and the true value is 10.0 cm, what is the absolute error? —
±0.5 cm
3.
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? —
±0.005 mm
4.
Which of the following numbers has the most significant figures? —
5.00
5.
A measurement is recorded as 15.00 ± 0.02. What is the percentage error? —
0.13%
6.
If the absolute error in a measurement is ±0.2 cm and the true value is 5.0 cm, what is the relative error? —
0.04
7.
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? —
0.05 s
8.
What is the percentage error if the relative error is 0.05? —
5%
9.
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? —
0.1 mm
10.
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? —
0.005 mm
11.
How many significant figures are there in the number 0.0250? —
3
12.
How many significant figures are in the number 3.00 x 10^4? —
3
13.
Consider the measurement 5.000 m. How many significant figures does it have? —
4
14.
If a meter scale is divided into millimeters, what is its least count? —
1 mm
15.
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)? —
12.25 cm to 12.35 cm
16.
If a measurement is 12.345 cm and needs to be rounded to three significant figures, what is the result? —
12.4 cm
17.
The number of significant figures in 0.000000102 is: —
3
18.
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)? —
3 (Δr/r)
19.
Add 2.5 cm and 3.14 cm. Round the result to the correct number of significant figures. —
5.6 cm
20.
Multiply 2.5 cm by 3.14 cm. Round the result to the correct number of significant figures. —
7.9 cm^2
21.
What is a 'gross error' in measurements? —
An error due to improper use of the instrument or misreading
22.
If the true value of a quantity is 'a' and the measured value is 'a_m', the absolute error (Δa) is: —
±(a_m - a)
23.
The relative error in a measurement is the ratio of: —
Absolute error to the true value
24.
Which of the following is a way to minimize random errors? —
Taking a large number of readings and averaging them
25.
When adding two quantities with absolute errors, how is the resultant absolute error determined? —
It is the sum of the individual absolute errors
26.
When subtracting two quantities with absolute errors, how is the resultant absolute error determined? —
It is the sum of the individual absolute errors
27.
When multiplying two quantities with relative errors, how is the resultant relative error determined? —
It is the sum of the individual relative errors
28.
When dividing two quantities with relative errors, how is the resultant relative error determined? —
It is the sum of the individual relative errors
29.
What is the primary characteristic of a systematic error? —
It is always in the same direction (positive or negative).
30.
In addition and subtraction, the result should be rounded to the: —
Same number of decimal places as the quantity with the least number of decimal places
31.
In multiplication and division, the result should be rounded to the: —
Same number of significant figures as the quantity with the least number of significant figures
32.
Which of the following instruments typically has the smallest least count? —
Screw gauge
33.
Which of the following operations involving significant figures requires rounding to the same number of decimal places? —
Addition
34.
An error that arises due to the imperfection in the experimental technique or method is classified as: —
Systematic error
35.
If a measuring instrument consistently shows a reading that is higher or lower than the true value, it is likely due to: —
Systematic error
36.
If a voltmeter consistently reads 0.5 V higher than the actual voltage, this is an example of: —
Systematic error
37.
Percentage error is calculated as: —
Relative error × 100
38.
Which of the following is NOT a type of error in measurements? —
Absolute error
39.
What kind of error can be eliminated by taking multiple readings and averaging them? —
Random error
40.
Which type of error is often due to the limitations of the measuring instrument itself, like the smallest division? —
Least count error
41.
The absolute error in a measurement is defined as: —
The difference between the true value and the measured value
42.
Significant figures in a measurement indicate: —
The number of digits that are known with certainty plus one uncertain digit
43.
What does the least count of a measuring instrument represent? —
The smallest value that can be measured accurately with the instrument
44.
When expressing a measurement, the number of significant figures reflects: —
The precision of the instrument
45.
What is the primary purpose of using a Vernier caliper or screw gauge over a simple meter scale? —
To achieve higher precision and accuracy
46.
If quantity Z = A + B, and the absolute errors are ΔA and ΔB, then the absolute error in Z (ΔZ) is: —
ΔZ = ΔA + ΔB
47.
If quantity Z = A - B, and the absolute errors are ΔA and ΔB, then the absolute error in Z (ΔZ) is: —
ΔZ = ΔA + ΔB
48.
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: —
ΔZ/Z = n × (ΔA/A)
49.
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: —
ΔZ/Z = ΔA/A + ΔB/B
50.
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: —
ΔZ/Z = ΔA/A + ΔB/B