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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Define relative error.

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प्रश्न

Define relative error.

व्याख्या
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उत्तर

The ratio of the mean absolute error in the measurement of a physical quantity to its arithmetic mean value is called relative error.

Relative error = `(triangle "a"_"mean")/"a"_"mean"`

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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) 3. | पृष्ठ १४

संबंधित प्रश्‍न

Define absolute error.


Define Mean absolute 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"`


Answer the following question.

Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "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?


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.


Solve the numerical example.

If the length of a cylinder is l = (4.00 ± 0.001) cm, radius r = (0.0250 ± 0.001) cm and mass m = (6.25 ± 0.01) g. Calculate the percentage error in the determination of density.


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.


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.


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 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 ______.


The least count of the main scale of a screw gauge is 1 mm. The minimun number of divisions on its circular scale required to measure 5 µm diameter of a wire 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 ______.


A laboratory balance shows a mass reading even when no object is placed on the pan. What is the main cause of this error?


What are random errors?


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


If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.


Instrumental error can be minimised by ______.


The reason behind holding thermometer in the mouth instead of the armpit is to reduce ______.


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