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Fundamental Units And Error

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Published in: Physics
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It contains some of the key facts of intermediate physics first chapter - Units and Measurements and Error

Shubham K / Kanpur

5 years of teaching experience

Qualification: B.Tech/B.E. (Associate member of institute of engineers - 2017)

Teaches: Algebra, Chemistry, Mathematics, Physics, UGC Exams, Mechanical

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  1. LJNITS MEASUREMENT AND ERROR ANALYSIS First of all, the word came UNIT. So, what is unit? In answer, we get that units are used to measure physical quantities. Now, what are these physical quantities? Physics is a subject of physical quantities and each physical quantity is measured and UNITS are used to measure these physical quantities. For measuring any of physical quantity two basic things are required. The unit The numerical value For example, if your mom has to say to bring you some grocery from market, then she will say that go and buy 2 kg. of potatoes, 1 litre of milk etc. In these 2 and 1 are numerical values and kg. and litre are units. Now, the thing comes that what is the relation between the unit and the numerical value. In whole of physics there are two types of basic relationships. First is Directly proportional and second is inversely proportional. For better understanding let us take an example of yours friend. If someone is your good friend then you will also be happy by his/her goodness and if he is in list of yours bad ones then you will get on little lower side in his/her happiness. Similarly, in Physics if one of physical quantity get increased by increase in other quantity or get decreased by decrease in other quantity, then they are in directly proportional relation. The other one is just opposite of it. FUNDAMENTAL OUANTITIES Before SI system, many of units are used for single physical quantity. For example, some people used to use Square Meters for the measurement of area while some used Square Inches.
  2. So a Worldwide System for the measurement of physical quantities was bring into force. It was called "SI System". This system contains seven basic physical quantities. These are called basic because all other physical quantities can be derived from these seven physical quantities. That's why they are called derived quantities. So, Basic physical quantities are as follows PHYSICAL QUANTITY LENGTH MASS TIME ELECTRIC CURRENT TEMPERATURE AMOUNT OF SUBSTANCE LUMINOUS INTENSITY UNIT METRE KILOGRAM SECOND AMPERE KELVIN MOLE CANDELA SYMBOL m kg s mol cd There are two supplementary Units for angle measurements. QUANTITY PLANE ANGLE SOLID ANGLE UNIT RADIAN STERADIAN SYMBOL Rad Sr There are three important definitions which you must know. I metre is defined as the distance containing 1.) Metre . 1 wavelengths of the orange-red light emitted by pure Krypton-86.'
  3. Or 1 metre has been defined as length of the path travelled by light in vacuum in 1/299,792,458 part of a second. 2.) Kilogram : 1 kilogram is defined as the mass of a platinum- iridium cylinder kept in Paris. Or 1/ 12th mass of an atom of carbon-12 isotope. 3.) Second : 1 second is defined as the time-interval in which cesium-133 atom completes 9,192,631,770 vibrations in an atomic clock. You can find many others definitions in your text book. Least count - Least count of any measuring instrument is defined as the minimum accurate observation that it can take without any error. Error ? Now what is error? So, Uncertainty in measurement is called Error. Error can be of two types By observer and by instrument For example if someone asked you for the time by your watch. You observed and told him it is 9: 14 pm. But it is possible that the time was 9:14 pm but you told him 9:15 pm so it is error by observer. On the other hand it is also possible that your watch will be telling you wrong data. So it is error by instruments. Now basically it is of three types. 1. Fractional Error : It is defined as Aa/a. Where Aa is the least count and a is the measurement taken. 2. Percentage Error :- It is defined as (Aa/a)* 100. 3. Experimental Percentage Error :- It is defined as- = (Difference b/w standard value and observed value/standard value)*100
  4. For example, The value of g is 9.8 m/sec2 and someone observed it 10 m/sec2 . The difference of both is 0.2 so now EPP becomes Key fact is that Error is always added.

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