What is Dimensional Equation?

Dimensional Equation

When a dimensional formula is equated to its physical quantity then the equation is called Dimensional Equation.

Ex. Dimensional equation of Force :

By $F=$ ma $\quad \Rightarrow \quad$ Dimension Equation of $F=\left[M^{1}\right]\left[L^{1} T^{-2}\right]=\left[M L T^{-2}\right]$

Ex. Dimensional equation of Energy : By $E=W=$ Force $\times$ Displacement Dimensional equation of ' $E$ ' $=\left[M^{1} L^{1} T^{-2}\right]\left[L^{1}\right]=\left[M^{1} L^{2} T^{-2}\right]$

Important view related to Dimension

1. Pure number and pure ratio are dimension less. Ex. $1,2, \pi, e^{x}, \log x, \sin \theta, \cos \theta$ etc. and refractive index.

2. Dimensionless quantity may have the unit. Ex. Angle and solid angle.

3. The method of dimensions can not be applied to derive the formula if a physical quantity depends on more than three physical quantities.

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