Question

if force volume and density are taken as the fundamental units the dimensional formula of pressure is

Answer 1

"The Dimensional formula for pressure is [$M^{1} L^{-1} T^{-2}$] ".

Explanation:

Normally, Pressure and density cannot be taken as fundamental quantities as they are related to each other by the relation .

But force and volume can taken as fundamental units of the dimensional formula of pressure is [$M^{1} L^{-1}T-^{2}$]

Dimensional Formula of Pressure :

Formula for Pressure = force/time.

The dimensional formula of pressure is given by,

[$M^{1}L^{-1} T^{-2}$]

Where,

M = Mass

L = Length

T = Time

Derivation

Pressure (P) = Force × $Area^{-1}$  --(1)

Since, Force = Mass × Acceleration

And, acceleration = velocity × $Time^{-1}$ = [L $T^{-1}$] [$T^{-1}$] =[L $T^{-2}$]

Therefore the dimensional formula of force = [M] × [L $T^{-2}$] So, Force = $M^{1} L^{1} T^{-2}$  --(2)

The dimensional formula of area = $M^{0} L^{2} T^{0}$ --(3)

On substituting equation (2) and (3) in equation (1) we get,

Pressure (P) = Force × $Area^{-1}$

Or, P = [$M^{1} L^{1} T^{-2}$] × [$L^{2}$]-1 = $M^{1} L^{-1} T^{-2}$.

Therefore, the dimensional formula of pressure is represented as $M^{1} L^{-1} T^{-2}$