Write down the units and dimensional formulae of following physical quantities:
$P r e s s u r e = \frac{f o r c e}{a r e a}$

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Solution

Units and dimensional formula of pressure:
Pressure on an object is defined as the force applied per unit area.
Mathematically, it can be given as $P r e s s u r e = \frac{f o r c e}{a r e a}$ .
So, the unit of pressure $= \frac{N}{m^{2}} = N m^{- 2}$ , i.e., Newton per metre square which is nothing but Pascal $(P a)$ in SI system.
Use its unit to find the dimensional formula of pressure:
$P r e s s u r e = N \times m^{- 2} [P] = [M L T^{- 2}] \times [L^{- 2}] = [M L^{1 - 2} T^{- 2}] = [M L^{- 1} T^{- 2}]$
Thus, the unit of pressure is $P a s c a l (P a), i . e ., N e w t o n p e r m e t r e s q u a r e (N m^{- 2})$ and its dimensional formula is $[M L^{- 1} T^{- 2}]$ .

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