The concept of Units and Dimensions :
This is also known as the dimensional analysis and this encompasses the analysis of the different kinds of relationships between the physical quantities. This is done by first identifying the base quantities and these are mass, time or length or electric current. We also consider the units of measurements here and thus this is the very first step. The conversion from one unit to another is often done which is the easier method within the SI system and not with the others. The dimensional analysis which is the known method is also known as the unit factor method and this method is widely used for all the algebra rules. We can say that physical quantities which are of same dimension and can be compared to each other although their method of measurement in the initial place was different. For example if we take metre and yard and also seconds and year. When we talk of those physical quantities which are of different kinds and have different dimensions and thus they can be compared or measured against each other they are known as incommensurable physical quantities. For example- IF we take kilogram against years then it is not possible to measure them.
If we take any equation then the right side of the equation needs to be same to the left side of the equation to induce equality and so to say meaning. This property is known as dimensional homogeneity. This process is very common for dimensional analysis. Because the crux of the process is for it to be equal. This process also serves as a guide for the equations which are derived as a physical system where there is no rigorous derivation. When we talk of measurable and commensurable physical quantities then it can be said to follow the functions of addition, substation and also it can compared and also equated. However for those physical quantities which can not be measured or compared we may take the ratios of such and multiply or divide them. Let us see an example-
It will not make sense if we say that one hour is same or less than one kilometre as these are different dimensions. However it makes perfect sense if we say an object travels 200 kms in 2 hours and thus we can divide these quantities to come of the conclusion that the objects average speed is 100 km/hr. Here we simply divide these quantities and derive at the conclusion.
TO ACE THIS TOPIC:
To ace this topic one needs to be really be confident and sure of the basic physical quantities concept and these concepts will help one to understand the measurement cannot be compared between two physical quantities which are different. To get good result for this topic the base concept needs to be very clear and thus this can really help to get answers to the questions. Most of the topics under this topic will come from class 11 and class 12 also so a thorough reading is necessary for this subject. NCERT book can be the guide for this exam also. Students can go through the sample papers given in this book and also the multiple choice questions in the book.
Also it is important to know that the units and dimensions applications in the real world is very useful to know.
Applications: This is very often used for physics and chemistry and also mathematics but it is not confined to these only.
Application in Mathematics: It is used for computing and also the area of the surface of any given object. When we determine the constants then it takes more advanced mathematics and it can e also checked by dimensional analysis alone. It is also used widely in Finance and Accounting and Economic. This is commonly referred to in terms of stocks and others. This is used for Measuring the different economic ratios and financial ratios.
In the field of Fluid Dynamics the dimensional analysis is done to get the dimensions for the terms and groups. According to the rules of dimensional analysis there can be measurements for the system behaviour and thus it can be described as the model for the same dimensional relationship.
Can you answer the question:A pressure of 10^(6)” dyne”//cm^(2) is equivalent to :
In the field of dimensional analysis we can take concrete numbers and base units. If we take a set of base units of measurements and this is a chosen set then we cannot define any of them with the combination of the other and thus the remaining units of the system will be expressed.
