Question

explain in detail the various types of errors (Physical world and measurement)

Answer 1

ERROR :

The uncertainty in a measurement is called an error.

Types of errors :

• $\text{\pink{Systemic Errors}}}$
• ${\text{\pink{Random Errors}}}$  

• $\text{Gross Errors}$

Systematic errors :

Systematic errors are reproducible inaccuracies that are consistently  in the same direction. These occur often due to a problem that persists throughout the experiment. Systematic errors can be classified as follows  

1. Instrumental errors : When an instrument is not calibrated properly at the time of manufacture, instrumental errors may arise. If a measurement is made with a meter scale whose end is worn out, the result obtained will have errors. These errors can be corrected by choosing the instrument carefully.
2.  Imperfections in experimental technique or procedure: These errors arise due to the limitations in the experimental arrangement. As an example, while performing experiments with a calorimeter, if there is no proper insulation, there will be radiation losses. This results in errors and to overcome these, necessary correction has to be applies
3.  Personal errors : These errors are due to individuals performing the experiment, may be due to incorrect initial setting up of the experiment or carelessness of the individual making the observation due to improper precaution.
4. Errors due to external causes : The change in the external conditions during an experiment can cause error in measurement. For example, changes in temperature, humidity, or pressure during measurements may affect the result of the measurement.
5.  Least count error : Least count is the smallest value that can be measured by the measuring instrument, and the error due to this measurement is least count error. The instrument’s  resolution hence is the cause of this error. Least count error can be reduced by using a high precision instrument for the measurement.

Random errors :

Random errors may arise due to random and unpredictable variations inexperimental conditions like pressure, temperature, voltage supply etc.

Errors may also be due to personal errors by the observer who performs the experiment. Random errors are sometimes called “chance error”. When different readings are obtained by a person every time he repeats the experiment, personal error occurs. For example, consider the case of the thickness of a wire measured using a screw gauge. The readings taken may be different for different trials. In this case, a large number of measurements are made and then the arithmetic mean is taken.

$\text{If n number of trial readings are taken in the experiement }\\\text{and the readings are }a_1,a_2,a_3 ..... a_n. \text{The arithematic mean is }$

$a_m = \frac{a_1+a_2+a_3 ... + a_n}{n}$

Answer 2

${\huge{\underbrace{\underline{\rm{Answer\checkmark}}}}}$

There are three types of error. They are as follows :

${\underline{\textit{\textbf{1.\:Systematic\:Errors:-}}}}$

The systematic errors are those errors that tend to be in one direction , either positive or negative. If the measured value is greater than the true value, the error is said to be positive. And, if the measured value is lesser than the true value, the error is said to negative.

Some of the sources of systematic errors are :

1. Instrumental Errors : These errors arise when the measuring instrument itself has some defect in it. The possible defects could be improper designing or calibration, zero error in the instrument, etc.
2. Imperfection in Experimental Technique or Procedure : The measurement may be systematically affected by external conditions such as changes in tempreture, humidity, wind velocity etc. For eg, the tempreture of a human body measured by a thermometer placed under armpit will always be less than actual tempreture.
3. Personal Errors : An experimentalist can introduce in his measurements sue to his carelessness or casual behavior, though such a behaviour is not expected from any serious experimentalist. If a person while reading the volume of water in a beaker, habitually keeps his eyes below the meniscus, he will introduce an error due to parallax.

${\underline{\textit{\textbf{2.\:Random\:Error:-}}}}$

The random errors are those errors, which occur irregularly and hence are random with respect to sign and size. They can arise due to random and unpredictable fluctuations in experimental condition (eg unpredictable fluctuations in tempreture, voltage supply, mechanical vibrations of experimental set-ups, etc.) , personal (unbiased) errors by the observer taking readings, etc.

For eg - When the same person repeats the same observation, it is very likely that he may get different readings everytime.

${\underline{\textit{\textbf{3.\:Least\:Count\:Error:-}}}}$

The smallest value of the measurement that can be directly taken from a measuring instrument is called it's least count. It is also called the resolution of the instrument. Thus a least count error is related to the precision provided by the measuring instrument. These errors can be reduced by using high precision instruments and improved experimental techniques.

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