Write down the units and dimensional formulae of following physical quantities:
$Y o u n g' s m o d u l u s = \frac{s t r e s s}{s t r a i n}$

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Solution

Units and dimensional formula of Young's modulus of elasticity:
Young's modulus of elasticity can be defined as the ratio of stress and strain.
Mathematically, it can be given as $Y o u n g' s m o d u l u s = \frac{s t r e s s}{s t r a i n}$ .
So, the unit of Young's modulus $= N m^{- 2}$ , i.e., Newton per metre square which is nothing but Pascal $(P a)$ in SI system of units.
Its unit is the same as that of stress as strain does not have any units.
Use its unit to find the dimensional formula of stress:
$Y o u n g' s m o d u l u s = N \times m^{- 2} [E] = [M L T^{- 2}] \times [L^{- 2}] = [M L^{1 - 2} T^{- 2}] = [M L^{- 1} T^{- 2}]$
Thus, the unit of Young's modulus of elasticity 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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