# Chapter-2(Units and Measurement) ## Dimensional Analysis and It’s Applications

The dimensional analysis helps us in reducing the relations among different physical quantities and checking the accuracy, derivation and dimensional consistency or its homogeneity of various numerical expressions. It’s applications are as given below 1. Checking The Dimensional Consistency Of Equations To check the dimensional correctness of a physical equation. For this purpose we make … ## Dimensions Of A Physical Quantity

All the derived physical quantity can be expressed in the terms of some combination of the seven fundamental or base quantities. We call these fundamental quantities as the seven dimensions of the world, which are denoted with square or big brackets [ ]. These 7 Dimensions are as under- Dimension of Length = [L] Dimension … ## Rules For Arithmetical Operations With Significant Figures

The following rules for Arithmetical operations with significant figures that make final result more consistent with the Precision of the measured value. For Addition and Subtraction In both addition and subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places. Example:- We have three … ## Rounding Off

The result of computation with approximate numbers, which contain more than one uncertain digit should be rounded off. Rules For Rounding Off 1. If the digit to be dropped is less than 5, then the preceding digit is left changed. Example:- X = 7.82 is rounded off 7.8 2. If the digit to be dropped … ## Significant Figures

The significant figures are normally the measurement of a number that includes all digits in the number that is known reliably plus first digit that is uncertain. The digit that are known reliably plus the first uncertain digit are known as significant figures or digits. Example:- let a measured distance is reported as 374.5 m. … ## Combination Of Errors

When we perform the mathematical operations, such as addition, subtraction, division, multiplication etc, the error combination depends on the type of mathematical operation performed on physical quantities. 1. Error In Sum Of Two Quantities Let ∆A and ∆B be the absolute errors in the two quantities A and B respectively, then Hence, The maximum possible … ## Errors In Measurement

To measure any physical quantity, we compare it with a standard unit of that quantity. No measurement is perfect as the error involved in the process, can not be removed completely. So the difference in the true value and the measured value of a quantity is called error of measurement. Error = True Value – … ## Accuracy And Precision Of Instruments

Accuracy The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. It refers to the closeness of a measurement to the true value of the physical quantity. As we reduce the errors, the measurement becomes more accurate. Precision Precision tells us to what … ## Measurement Of Time

A clock is used to measure time interval. An atomic standard of time is based on periodic vibration produced in a cesium atom. This is the basis of the cesium clock, sometimes called as atomic clock, used in the national standard. In the cesium atomic clock, the second is taken as the time needed for … ## Measurement Of Mass

Mass of a body is the quantity of matter in the body which does not depend on the temperature, pressure or location of the body in space. The prototypes of the international bureau of weights and measures (BIPM) are available in many other laboratories of different countries. In India, this is available at the national …

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