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

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Solution

Units and dimensional formula of pressure:
Stress can be defined as the internal restoring force developed per unit area inside a body on the application of some external force.
Mathematically, it can be given as $S t r e s s = \frac{f o r c e}{a r e a}$ .
So, the unit of stress $= \frac{N}{m^{2}} = N m^{- 2}$ , i.e., Newton per meter square which is nothing but Pascal $(P a)$ in SI system.
Use its unit to find the dimensional formula of stress:
$S t r e s s = N \times m^{- 2} [S] = [M L T^{- 2}] \times [L^{- 2}] = [M L^{1 - 2} T^{- 2}] = [M L^{- 1} T^{- 2}]$
Thus, the unit of stress 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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