Units & Measurement: Dimensional formula

Dimensional Formula

When a physical quantity is expressed in terms of fundamental quantities (using M, L, T, A, K, mol, cd), the expression obtained is called dimensional formula of that physical quantity.

Thus, "the dimensional formula of a physical quantity is an expression which shows on which of the fundamental quantities and how, the given physical quantity depends."

Example: The dimensional formulae of density and acceleration are ML^-3 and  MLT^-2 

From dimensional formula of density, we come to know that density depends on 1 & -3 powers of M & L respectively.  It does not depend on time.

Dimensional Equation

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

Example: Dimensional equations of force (F) and Density (D) are as follows;

[F] = [MLT^-2]

[D] = [MLT^-3]

Note: When we represent a physical quantity in terms of M, L, T etc. (i.e., in terms of base quantitative), the magnitudes are not considered.  We consider only the quality or the type of physical quantity.

Thus, all the following physical quantities will have same dimensional formula [LT^-1]:

• a change in velocity
• initial velocity
• average velocity
• final velocity
• speed
• change in speed etc.