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) $[d]=\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{0}\right]$
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) $[d]=\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{0}\right]$
Similar Questions
The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $\mathrm{h} / \sqrt{2 m E}$ The dimensional formula for Planck's constant is:
- [JEE MAIN 2024]
Which of the following pair does not have similar dimensions
- [AIIMS 2001]
The dimensions of solar constant (energy falling on earth per second per unit area) are
Give an example of
$(a)$ a physical quantity which has a unit but no dimensions
$(b)$ a physical quantity which has neither unit nor dimensions
$(c)$ a constant which has a unit
$(d)$ a constant which has no unit
$(a)$ a physical quantity which has a unit but no dimensions
$(b)$ a physical quantity which has neither unit nor dimensions
$(c)$ a constant which has a unit
$(d)$ a constant which has no unit