Write down the units and dimensional formulae of following physical quantities:
$S t r a i n = \frac{e l o n g a t i o n}{a c t u a l l e n g t h}$

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Solution

Units and dimensional formula of strain:
Strain can be defined as the change in the size or shape of an object caused due to a deforming force.
Mathematically, it can be given as $S t r a i n = \frac{e l o n g a t i o n}{a c t u a l l e n g t h}$ .
So, the unit of the strain $= \frac{m}{m}$ , i.e., the strain does not have any units.
It is due to the fact that it is a ratio of two lengths.
Since strain has no units, it has no dimensions as well.
In other words, it is a dimensionless quantity.
$S t r a i n = [M^{0} L^{0} T^{0}]$
Thus, there is no unit of strain and thus it is a dimensionless quantity.

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