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# Units and dimensions pdf

With progress in technology, the measuring techniques get improved leading to measurements with greater precision. The definitions of base units are revised to . PHYSICS. UNIT & DIMENSION PHYSICAL QUANTITIES: The quantities which can be measured by an instrument and by means of which we can describe the. UNITS AND DIMENSIONS. 1. Physical Quantities. 1. 2. Set of fundamental quantities. 1. 3. Derived physical quantities. 2. 4. Dimensions and dimensional.

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chapter we will have an over view of different units of different Physical quantities. We will learn the dimension and dependence of the unit of any Physical. Chapter 2 Units, Dimensional Analysis, Problem Solving, and. Estimation. But we must not forget that all things in the world are connected with one another. It is fairly easy to confuse the physical dimensions of a quantity with the units used to dimensions of other quantities like speed, which is length/time, in terms of.

SI units of derived Quantities: A complete set of units both fundamental and derived units are called a system of units. Here [ M1 L1 T — 1 ] is called dimensional formula of momentum , and we can say that momentum has 1 Dimension in M mass 1 Dimension in L length and —1 Dimension in T time The representation of any quantity in terms of basic quantities M,L,T So in order to express the very large magnitude as well as very small magnitude more compactly. From similar logic we can say that all the numbers are dimensionless. Mechanical Properties Of Fluids.

If velocity V. In CGS system. F and T Solution: Suppose we want to find the unit of force. Example The dimensional constant.. L and T hence we get only three equations. So we can have only three variable only three dependent quantities So dimensional analysis will work only if the quantity depends only on three parameters.

Can Pressure P.

## UNIT & DIMENSION.pdf

The method works only if the dependence is by power functions.. In many cases. So these three terms are dependent. Instead of this. These units are called SI units International system of units In Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic standard called unit. General Conference on weight and Measure decided the standard units. In this system. If a quantity involves only length.

Two supplementar y units were also defined: It comes under SI system. SI Units of Basic Quantities: In this system Length. Suppose distance between kota to Jaipur is m. So in order to express the very large magnitude as well as very small magnitude more compactly.

SI units of derived Quantities: N Physical Quantity Unit name Symbol of the unit Expression in terms of other units Expression in terms of base units 1. Electric Potential Emf. SI Derived units. Activity of radioactive material becquerel Bq Di sin tegration sec ond s SI Units S.

Some SI units expressed in terms of the special names and also in terms of base units: If unit of length and time are doubled and unit of mass is halved than the numerical value of the force in the new unit will be.

So the numerical value of Area will became one fourth As unit of length is doubled.. Flag for inappropriate content.

Related titles. Atomic Structure 1 Jump to Page. Search inside document. Physical quantities are of three types Fundamental or Basic quantities 1. Abera Mamo. Nitin Das. Aakash Kedia. Roberto De La Paz.

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Lye Xinquan. Fu Hong. Acer Master. Dimensional analysis can be used to check the dimensional consistency of equations, deducing relations among physical quantities etc. A dimensionally consistent equation need not be actually an exact equation, but a dimensionally wrong or inconsistent equation must be wrong. These are the errors that tend to be either positive or negative. Sources of systematic errors are i Instrumental errors ii Imperfection in experimental technique or procedure iii Personal errors.

Those errors which occur irregularly. These errors arise due to unpredictable fluctuations in experimental conditions. The magnitude of the difference between the individual measurement and the true value of the quantity is called the absolute error of the measurement. The arithmetic mean of all the absolute errors is taken as the final or mean absolute error of the value of the physical quantity a.

It is represented by?

Percentage Error: When the relative error is expressed in per cent, it is called the percentage error? When two quantities are added or subtracted, the absolute error in the final result is thesums of the absolute errors in the individual quantities. The relative error in a physical quantity raised to the power k is the k times the relative error in the individual quantity. The significant figures are normally those digits in a measured quantity which are known reliably plus one additional digit that is uncertain.

For counting of the significant figure rule are as: But such zeros are significant if they come from a measurement. Single zero conventionally placed to the left of the decimal point is not significant.

In addition or subtraction , the result should be reported to the same number of decimal places as that of the number with minimum number of decimal places. For ex: In multiplication or division, the result should be reported to the same number of significant figures as that of the number with minimum of significant figures.

Accuracy refers to the closeness of a measurement to the true value of the physical quantity and precision refers to the resolution or the limit to which the quantity is measured. The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. While rounding off measurements the following rules are applied Rule I: If the digit to be dropped is smaller than 5,then the preceding digit should be left unchanged.

If the digit to be dropped is greater than 5, then the preceding digit should be raised by 1 For ex: If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit should be raised by 1 For ex: If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is not changed if it is even, is raised by 1 if it is odd. M 1 L 1 T -2 is the dimensional formula of Force. Dimensional Costants: These are the quantities which possess dimensions and have a fixed value.

Gravitational Constant.

Dimensional Variables: These are the quantities which possess dimensions and do not have a fixed value For ex: Dimensionless Constants: Dimensionless Variables: