Define dimensional formula and dimensional equation by using suitable example.

Dimensional formulae : The expression which shows how and which of the base quantity represent the dimensions of a physical quantity.

Example :

Dimensional formulae of volume is $\left[\mathrm{M}^{0} \mathrm{~L}^{3} \mathrm{~T}^{0}\right]$

Dimensional formula of speed (or velocity) is $\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}$

Dimensional formulae of acceleration is $\left[\mathrm{M}^{0} \mathrm{LT}^{-2}\right]$

Dimensional formula of density is $\left[\mathrm{M}^{0} \mathrm{~L}^{-3} \mathrm{~T}^{0}\right]$

Dimensional equation : An equation obtained by equating a physical quantity with its dimensional formula is called dimensional equation of the physical quantity.

Example :

Volume $[\mathrm{V}]=\left[\mathrm{M}^{0} \mathrm{~L}^{3} \mathrm{~T}^{0}\right]$

Speed or Velocity $[v]=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\right]$

Force $[\mathrm{F}]=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$

Density $[\rho]$ (Density) $[d]=\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{0}\right]$