Question

find find out the expression for error in difference of physical quantities​

Answer 1

Answer:

Definition:

The relative error expressed in percentage (i.e. multiplied by 100) is called percentage error.

∴Percentage error=amΔam×100%

Problem: 

In an experiment, the values of refractive indices of glass were found to be 1.54, 1.53, 1.44, 1.54,1.56 and 1.45 in successive measurements. 

Find the Percentage error.

Solution:

Mean=61.54+1.53+1.44+1.54+1.56+1.45 =1.51

∣Mean absolute error∣=61∑(x1ˉ−xˉ)2=0.04

Relative error=MeanAbsolute error=1.510.04=0.026≈0.03

% error= Relative error×100=3%  

ERRORS IN MEASUREMENT OF PHYSICAL QUANTITIES - DEFINITION

Any measurement made with a measuring device is approximate. If you measure the same object two different times, the two measurements may not be exactly the same. The difference between two measurements is called an error. The error in measurement is a mathematical way to show the uncertainty in the measurement. It is the difference between the result of the measurement and the true value.

Types of errors:

Systematic errors: The systematic errors are those errors that tend to be in one direction, either positive or negative.

Instrumental errors

Imperfection in experimental technique or procedure

Personal Errors

Random errors: These are the errors which occur irregularly and hence are random with respect to sign and size. These can arise due to random and unpredictable fluctuations in experimental conditions.

Least count error: The least count error is the error associated with the resolution of the instrument.

Example: If the dimension of the diameter of a circular cross-sectional rod is 5cm. In the laboratory experiment, while measuring with vernier caliper it is found as 5.05 cm. So the error in measurement is 0.05 cm here.

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