Dimensional formula is a
representation of a physical quantity in terms of fundamental quantities. When
we write a physics equation, it shall be in such a way that the dimensions of
left hand side of the equation has to be equal to the dimensions of all
physical quantities along the right hand side of the equation. This is possible
only when you add or subtract similar quantities at either left or right side
of the equation.
It is simple understanding that velocity can be added only
with velocity to get another velocity We can not add velocity with force and
the summation can not give either velocity or force and the summation is
meaning less.This principle is called principle of homogeneity. If any equation
is not satisfying the law, then it cannot be correct with respect to physics.
But we need to be careful that the dimensionally correct equation can not be
correct with respect to physics. Being satisfying the principle of homogeneity
is the fundamental condition to be accepted as a physics equation.
Limitations of Dimensional Analysis
Dimensional formulas helps us to understand the relation among the physical quantities and it helps us also in converting the physical quantity from one system of unit to other system of unit. But they have certain limitations. Trigonometric and exponential functions won’t have any dimensions and if they are involved in any equation, we can not solve them basing on dimensional analysis. If the equation on the right hand side is depending on more fundamental quantities than the left hand side, then we cannot solve the equation basing on dimensional analysis. We also won’t be able to find out the proportionality constants of a science equation using the dimensional analysis.
Dimensional formulas helps us to understand the relation among the physical quantities and it helps us also in converting the physical quantity from one system of unit to other system of unit. But they have certain limitations. Trigonometric and exponential functions won’t have any dimensions and if they are involved in any equation, we can not solve them basing on dimensional analysis. If the equation on the right hand side is depending on more fundamental quantities than the left hand side, then we cannot solve the equation basing on dimensional analysis. We also won’t be able to find out the proportionality constants of a science equation using the dimensional analysis.
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