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Unit-1: Chp-1:Measurement And Dimensional Analysis

PHYSICXION: Measurement, Dimensional analysis, and Error analysis are unavoidable tools for any branch of science. Actually, there is a long history

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Measurement, Dimensional analysis, and Error analysis are unavoidable tools for any branch of science. Actually, there is a long history of the evolution of these things in the form they take nowadays. Today, we use the word measurement in every step of life. Most of us are unaware of the fact, from where it came actually.


A brief view of its history:
  • The term "measurement" was first introduced by the ancient Greeks. The Greek word "metron" means "limited proportion". The Greeks were the first to develop a systematic approach to measurement, and they used a variety of units of measurement, including the cubit, the foot, and the mile.
  • The word "measurement" was first used in English in the 14th century. It is derived from the Old French word "measure", which also means "limited proportion".
  • Joseph Fourier (1768-1830) is credited with making the first important contributions to dimensional analysis. He was a French mathematician and physicist.
  • James Clerk Maxwell (1831-1879) played a major role in establishing the modern use of dimensional analysis. He was a Scottish physicist and mathematician.
  • Lord Rayleigh (1842-1919) was an English physicist and mathematician.
  • Richard von Mises (1883-1953) was an Austrian-American mathematician and statistician who is best known for his work on probability theory and statistics. Von Mises developed a rigorous mathematical framework for dimensional analysis and error analysis.
  • The Vernier caliper and screw gauge were both invented by Pierre Vernier in the 17th century. Vernier was a French mathematician and instrument maker. He is also credited with inventing the vernier scale, which is a special scale used to make precise measurements.

Interesting Facts that will be posted on website Physicxion



Interesting Facts:
➤ PLANCK UNITS
The Planck units are fundamental quantities in physics, and it is essential to understanding the universe at its smallest scales. It is a challenging and fascinating concept, and it is one that physicists are still trying to understand. 

Some Planck units:
  • The Planck length is the smallest possible length that can be measured. It is equal to 1.616 × 10^-35 meters.
  • The Planck mass is the smallest possible mass that can be measured. It is equal to 2.176 × 10^-8 kilograms.
  • The Planck energy is the smallest possible energy that can be measured. It is equal to 1.956 × 10^9 joules.
  • The Planck temperature is the highest possible temperature that can be measured. It is equal to 1.416 × 10^32 Kelvin.
  • The Planck force is the strongest possible force that can be measured. It is equal to 1.2 × 10^44 Newton.
  • The smallest unit of time that can be measured is the Planck time, which is equal to 5.4 × 10^-44 seconds. This is the smallest unit of time that has any physical significance.

These quantities are all derived from the fundamental constants of physics, and they represent the limits of what we can currently measure. They are a reminder of the vastness of the universe and the limits of our understanding of it.
➤ THE BUCKINGHAM Ï€ THEOREM
The Buckingham π theorem states that any physical equation with n independent variables can be expressed in terms of n - m dimensionless groups, where m is the number of fundamental dimensions in the problem.

The Buckingham π theorem can be used to identify the dimensionless groups that are important for a particular physical system.
➤ VERNIER AND SCREW GAUGE
  • The vernier caliper was originally called the "nonius" after the Roman astronomer and mathematician Marcus Nonius Marcellus.
  • The screw gauge was originally called the "micrometer" after the Greek word for "small measure".
  • The vernier caliper was first used to measure the thickness of the gold leaf.
  • The screw gauge was first used to measure the diameter of wires.


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CLASS NOTES :

Here full Class Notes PDFs are attached which will help you to score well in the exam.

NOTE-1: Theory of Measurement and Dimensional Analysis.

NOTE-2: Solved Numerical (Easy and moderate level descriptive problems)

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NOTE-1
   

                                                                                                                                                                     

NOTE-2




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NOTE-2

NOTE-1