write the applications for dimentional formulas?
Answers
Applications of Dimensional Analysis
Applications of Dimensional AnalysisTo check the consistency of a dimensional equation. To derive the relation between physical quantities in physical phenomena. To change units from one system to another.
Answer:
Dimensional Analysis
We quantify the size and shape of things using Dimensional Analysis. It helps us study the nature of objects mathematically. It involves lengths and angles as well as geometrical properties such as flatness and straightness. The basic concept of dimension is that we can add and subtract only those quantities that have the same dimensions. Similarly, two physical quantities are equal if they have the same dimensions.
Dimensional Analysis Explained
The study of the relationship between physical quantities with the help of dimensions and units of measurement is termed as dimensional analysis. Dimensional analysis is essential because it keeps the units the same, helping us perform mathematical calculations smoothly.
Unit Conversion and Dimensional Analysis
Dimensional analysis is also called Factor Label Method or Unit Factor Method because we use conversion factors to get the same units. To help you understand the stated better, let’s say you want to know how many meters make 3 km?
We know that 1000 meters make 1 km,
Therefore,
3 km = 3 × 1000 meters = 3000 meters
Here, the conversion factor is 1000 meters.
Using Dimensional Analysis to Check the Correctness of Physical Equation
Let’s say that you don’t remember whether
time = speed/distance, or
time = distance/speed
We can check this by making sure the dimensions on each side of the equations match.
Reducing both the equations to its fundamental units on each side of the equation, we get
\([T]=\frac{[L][T]^-1}{L}=[T]^-1\) (Wrong)
\([T]=\frac{[L]}{[L][T]^-1}=[T]\) (Right)
However, it should be kept in mind that dimensional analysis cannot help you determine any dimensionless constants in the equation.