10. State “Principle of Homogeneity”. Check the correctness of the relation
, where T is the time period, l is the length of pendulum and g
is acceleration due to gravity. 2
Answers
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.
I think you can understand it now..