explain the principle of homogeneity?with example
Answers
Answer:
Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same. This principle is helpful because it helps us convert the units from one form to another.
Explanation:
Example 1: Check the correctness of physical equation s = ut + ½ at2.
Answer and Explanation:
Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same. This principle is helpful because it helps us convert the units from one form to another. To better understand the principle, let us consider the following example:
Example 1: Check the correctness of physical equation s = ut + ½ at2. In the equation, s is the displacement, u is the initial velocity, v is the final velocity, a is the acceleration and t is the time in which change occurs.
Solution:
We know that L.H.S = s and R.H.S = ut + 1/2at²
The dimensional formula for the L.H.S can be written as s = [L¹M⁰T⁰] ...… (1)
We know that R.H.S is ut + ½ at² , simplifying we can write R.H.S as [u][t] + [a] [t]²
[L¹M⁰T⁻¹][L⁰M⁰T⁻¹] + [L¹M⁰T⁻²][L⁰M⁰T⁰]
=[L¹M⁰T⁰]………..(2)
From (1) and (2), we have [L.H.S] = [R.H.S]
Hence, by the principle of homogeneity, the given equation is dimensionally correct.
Applications of Dimensional Analysis
Dimensional analysis is a fundamental aspect of measurement and is applied in real-life physics. We make use of dimensional analysis for three prominent reasons:
- To 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
Limitations of Dimensional Analysis
Some limitations of dimensional analysis are:
- It doesn’t give information about the dimensional constant.
- The formula containing trigonometric function, exponential functions, logarithmic function, etc. cannot be derived.
- It gives no information about whether a physical quantity is a scalar or vector.