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Define absolute error. - Physics

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प्रश्न

Define absolute error.

व्याख्या
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उत्तर

  1. For a given set of measurements of a quantity, the magnitude of the difference between mean value (Most probable value) and each individual value is called absolute error (Δa) in the measurement of that quantity.
  2. absolute error = |mean value - measured value|
    Δa1 = |amean - a1|
    Similarly,
    Δa2 = |amean - a2|,
              `\vdots           \vdots             \vdots`
    Δan = |amean - an|
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पाठ 1: Units and Measurements - Exercises [पृष्ठ १४]

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बालभारती Physics [English] Standard 11 Maharashtra State Board
पाठ 1 Units and Measurements
Exercises | Q 2. (iii) 1. | पृष्ठ १४

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 Mean absolute error.


Define relative error.


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"`


The masses of two bodies are measured to be 15.7 ± 0.2 kg and 27.3 ± 0.3 kg. What is the total mass of the two and the error in it?


The distance travelled by an object in time (100 ± 1)s is (5.2 ± 0.1) m. What are the speed and its maximum relative error?


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.


Find the percentage error in kinetic energy of a body having mass 60.0 ± 0.3 g moving with a velocity of 25.0 ± 0.1 cm/s.


In Ohm’s experiments, the values of the unknown resistances were found to be 6.12 Ω, 6.09 Ω, 6.22 Ω, 6.15 Ω. Calculate the (mean) absolute error, relative error, and percentage error in these measurements.


Solve the numerical example.

If the formula for a physical quantity is X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))` and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.


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 ______.


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?


The resistance R = `"V"/"I"`, where V = (50 ± 2) V and I = (20 ± 0.2)A. The percentage error in R is 'x' %. 

The value of x to the nearest integer is ______.


In a Screw Gauge, the fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation, the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with the reference line. Calculate the true reading.


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 ______.


A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ______ × 10-6 m. 


What is an error in measurement?


Reading a graduated cylinder at an angle (parallax error) is a specific example of which type of systematic error?


Systematic errors cause all measurements to shift in the same direction. What does this primarily affect?

 

A weighing scale that always reads a constant +0.2 kg because its zero mark is misaligned is a clear example of a(n):


Which of the following is an environmental error?


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