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The chapter on errors is part of Measurement. We all know that for doing some measurements we need tools but sometimes these measuring instruments result in some uncertainty. This uncertainty is known as Error. Accuracy and precision are two important factors that need to be considered while taking measurements. Both of them indicate how close a measurement is to a known or accepted value.
To score positive marks from this chapter of JEE Main candidates can go through the important formulas, solved questions and some tips to prepare this chapter.
The measurement is the most important requirement of almost every science experiment and theory. Whether you study the units and dimensions of a body or do theories of electricity and magnetism, accurate measurement is required to understand the basic concepts behind it. Every measurement involves some kind of uncertainty in the experiment.
The uncertainties that happen while experimenting are referred to as errors. Errors mostly occur due to experiments, as every measured value can have some errors in it. Thus eradicating the errors from our results is much important so that it won’t create problems in the future. Based on the nature of the errors, they are divided into two terms, namely Accuracy and Precision.
Question: If the percentage of errors in the measurement of mass and speed is 2% and 3% respectively. Then calculate the maximum error in the estimation of the K.E by calculating the mass and speed?
Accuracy means the closeness of measured value to a standard value.
Example - Suppose you weigh a packet and its weight is 3.1 kg but its known value is 9 kg, then your measurement will not be reliable. The ability of any instrument to judge the accurate value is known as its accuracy. In easier words, the closeness of the measured value to a standard or true value.
Accuracy is calculated by considering small readings as small reading can lower the chances of error of the calculation. The accuracy of the system is classified into three types mentioned below:
Point Accuracy- The accuracy of the instrument at a particular point on its scale is known as the point accuracy. This accuracy doesn’t offer any information about the general accuracy of the instrument.
Accuracy as Percentage of Scale Range- The uniform scale range helps in calculating the accuracy of a measurement. For instance, a thermometer that hasve the scale range up to 500ºC, the thermometer has an accuracy of plus or minus 0.5, which means an increase or decrease by this much value in the instrument is negligible. But in case the reading shows changes of more or less than 0.5, then it might result in a high-value error.
Accuracy as Percentage of True Value- This kind of accuracy of the instruments is explained by considering the measured value regarding their true value. The accuracy of the instruments can be neglected up to plus/minus 0.5 percent from the true value.
Question: Let us consider that the random error in the arithmetic mean of 100 observations is x then calculate that what would be the random error in the arithmetic mean of 400 observations?
Precision means closeness between two or more measured values to each other.
Example - Suppose you weigh the same packet four times and get close results like 4.1, 4.2, 4.22, and 4.0 then your measurements are accurate. Always remember that Accuracy and Precision are two independent terms; you can be accurate in the measurements but non-precise, or vice-versa. Measurements of units revolve around accuracy and precision, therefore the experiment readings are mentioned in the decimal form.
Repeatability- The variations that arise when the conditions are kept identical and continuous measurements are taken after a short period.
Reproducibility- The variation that arises when the same measurement process among different instruments and operators, and measurements are taken after longer time periods.
Question: The significant figures in 0.310 x 103 are
|Accuracy means the level of agreement between the actual measurement and the absolute measurement.||Precision means any variations that lie in the values of several measurements of the same factor.|
|Accuracy means how closely the results agree with the standard value||It represents how closely results agree with one another|
|Single factor or measurement||Different measurements or factors are required|
|For any measurement to be accurate, it must precise.||Results can be precise without actually accurate. Alternatively, the results can be precise and accurate.|
The errors are divided into two types including:
Systematic Errors- The types of errors that arise only in one direction are referred to as Systematic Errors. Their direction might be positive or negative but will not be the same at the same time. Systematic errors are also referred to as Repetitive Error as they might occur due to some error in the machines and due to the selection of the wrong experiment apparatus. These errors take place in case the device used to take measurements is wrong.
Random Errors: The errors which happen due to lack of accuracy in an instrument are termed as instrumental errors. These kinds of errors happen due to beneath reasons:
The error in calculating the value of a physical quantity is divided as
Absolute error - The magnitude of variations between the measured and the true value of the quantity is called the absolute error of the measurement.
Percentage error - When the relative error is described in percentage, it is known as the percentage error.
Relative error- The ratio of absolute error to the true value in measuring a physical quantity is referred as relative error.
In case an experiment is not done as per the guidelines or physical conditions around are not favourable, then it will result in imperfection in technique errors. These kinds of errors arise due to:
In case we keep the thermometer under the armpit rather than under the tongue, the temperature will always come out to be lower than that of body, as the way of calculating the temperature is wrong.
Personal Errors: These errors happen due to improper setting of apparatus, of sometimes due to lack of observation skills as well. Personal errors depend on the user or student who is experimenting and don’t know much about the instrument settings.
Also, in some cases, while measuring the height of an object, if the student has not correctly placed his head, it might result to parallax and incorrect readings.
Systematic errors can be reduced greatly by:
Random Errors are not fixed on general perimeters and differ from measurements to measurements. Since these errors differ from measurement to measurement, they are being described as random errors as they are random in nature. Random errors are the variations in statistical readings due to limitations of precisions in the instrument. Random errors happen due to:
We can only lower the cases of random errors but can’t remove them completely as they are unpredictable and not fixed in nature unlike systematic errors.
The smallest value that can be measured in an instrument is referred to as the Least Count of the Instrument. Least count means the main part of a measurement and occurs in both random as well as systematic Errors. These errors are based on the resolution of the instrument and can be calculated in case we know the observations and the least count of instruments.
Question 1- The volume of a liquid is 26 mL. A college student calculates the volume and finds it to be 26.3 mL, 26.2 mL, 25.8 mL, and 26.3 mL in different rounds of measurements. Which of the beneath statements is true for his measurements?
Answer: The correct answer is good precision.
Question 2- The volume of a liquid is 20.5 mL. Which of the beneath sets of measurement has good accuracy?
Answer: The set 20.2 mL, 20.4 mL, 20.5 mL, 20.0 mL has good accuracy.
Question 3- A student uses a simple pendulum of 1m length to calculate G, the acceleration due to gravity. He preferred a stopwatch with minimum count of 1 sec for the same and recorded 40 seconds for 20 oscillation. For this observation, which of the beneath observations will be true?
Answer: Error, the time will be 0.05 seconds
We suggest JEE Main 2020 aspirants not to spend too much time reading the books; rather prefer reading some important books that can help in understanding more about the exact exam pattern, and help them in preparing a systematic strategy.
Some of the best and most recommended books for Physics include:
|Concepts of Physics (volumes 1 and 2)||H.C Verma|
|Guide to AIEEE Problems in General Physics||G. K Publishers I.E Irodov|
|D.C Pandey (Complete Set)||Arihant.|
|Problems in Physics||S. S Krotov|