Advertisements
Advertisements
प्रश्न
In a workshop, a worker measures the length of a steel plate with Vernier calipers having a least count 0.01 cm. Four such measurements of the length yielded the following values: 3.11 cm, 3.13 cm, 3.14 cm, 3.14 cm. Find the mean length, the mean absolute error, and the percentage error in the measured value of the length.
Advertisements
उत्तर
Given:
a1 = 3.11 cm, a2 = 3.13 cm,
a3 = 3.14 cm, a4 = 3.14 cm
Least count L.C. = 0.01 cm.
To find:
i. Mean length `("a"_"mean")`
ii. Mean absolute error `(triangle "a"_"mean")`
iii. Percentage error.
Formulae:
1. `"a"_"mean" = ("a"_1 + "a"_2 + "a"_3 + "a"_4)/4`
2. `triangle "a"_"n" = |"a"_"mean" - "a"_"n"|`
3. `triangle "a"_"mean" = (triangle"a"_1 + triangle"a"_2 + triangle"a"_3 + triangle"a"_4)/4`
4. Percentage error = `(triangle "a"_"mean")/("a"_"mean") xx 100`
Calculation:
From formula (i),
`"a"_"mean" = (3.11 + 3.13 + 3.14 + 3.14)/4`
= 3.13 cm
From formula (ii),
`triangle"a"_1 = |3.13 - 3.11| = 0.02` cm
`triangle"a"_2 = |3.13 - 3.13| = 0`
`triangle"a"_3 = |3.13 - 3.14| = 0.01` cm
`triangle"a"_4 = |3.13 - 3.14| = 0.01` cm
From formula (iii),
`triangle"a"_"mean" = (0.02 + 0 + 0.01 + 0.01)/4` = 0.01 cm
From formula (iii),
% error = `0.01/3.13 xx 100`
`= 1/3.13`
= 0.3196 .....(using reciprocal table)
= 0.32 %
Ans:
- Mean length is 3.13 cm.
- Mean absolute error is 0.01 cm.
- Percentage error is 0.32 %.
APPEARS IN
संबंधित प्रश्न
The error in the measurement of the sides of a rectangle is 1%. The error in the measurement of its area is ______.
Define percentage error.
If the measured values of the two quantities are A ± ΔA and B ± ΔB, ΔA and ΔB being the mean absolute errors. What is the maximum possible error in A ± B? Show that if Z = `"A"/"B"`
`(Delta "Z")/"Z" = (Delta "A")/"A" + (Delta "B")/"B"`
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = `(A^2B^(1/2))/(C^(1/3)D^3)`, will be:
The relative density of a metal may be found by hanging a block of the metal from a spring balance and nothing that in air, the balance reads (5 .00 ± 0.05)N while in water, it reads (4.00 ± 0.05)N. The relative density would be quoted as ______.
Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms–1 ± 0.5 ms–1 B = 0.10 s ± 0.01 s. The value of A B will be ______.
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for `sqrt(AB)` as ______.
The mean length of an object is 5 cm. Which of the following measurements is most accurate?
The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccuracy in the measurement of distance.
Time for 20 oscillations of a pendulum is measured as t1 = 39.6 s; t2 = 39.9 s; t3 = 39.5 s. What is the precision in the measurements? What is the accuracy of the measurement?
A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a2 b3 c5/2d–2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.
The dependence of g on geographical latitude at sea level is given by `g = g_0(1 + betasin^2Phi)` where Φ is the latitude angle and β is a dimensionless constant. If Δg is the error in the measurement of g then the error in measurement of latitude angle is ______.
If the zero of the vernier lies on the right-hand side and the fourth division coincides with the main scale division when the jaws are in contact so the correction will be ______.
What is an error in measurement?
Systematic errors cause all measurements to shift in the same direction. What does this primarily affect?
What are random errors?
Which of the following is an environmental error?
Which strategy would best reduce an instrumental error caused by a faulty weighing scale?
Instrumental error can be minimised by ______.
Error due to non-removal of parallax between pointer and its image in case of magnetic compass needle causes ______.
Constant error can be caused due to ______.
