Question

The dimensions of strain is:
A. ${L}$
B. ${{L}^{2}}$
C. It is dimensionless
D. $M{{L}^{2}}{{T}^{-2}}$

Answer 1

Hint: Strain is the measure of how much the object has changed its shape because of an external force. Strain is useful to determine the change in dimensions. It is also a relative change of length/area/volume.
Formula Used:
The strain is expressed as,

$\dfrac{L}{\Delta L}$
Where,
L is the original length in the absence of external force.
$\Delta L$ is the change in length after we apply any force.

Complete step by step answer:
First, we need to understand the definition of strain.
In simpler terms, strain is the quantity which determines the relative change in length of an object when it is subjected to a stress/force. It is an important aspect of determining the stress of an object when we apply a force.
Mathematically, strain is quantified as,

$\dfrac{L}{\Delta L}$

Where,
${\Delta L}$is the change in length
L is the original length.

Change in the length has the dimension ,

${{M}^{0}}{{L}^{1}}{{T}^{0}}$

Original Length has the dimension,

${{M}^{0}}{{L}^{1}}{{T}^{0}}$

So, the dimension of the strain is,

$\dfrac{{{M}^{0}}{{L}^{1}}{{T}^{0}}}{{{M}^{0}}{{L}^{1}}{{T}^{0}}}={{M}^{0}}{{L}^{0}}{{T}^{0}}$

Hence, strain is a dimensionless quantity.
So, the correct answer is (C).

Note:
Strain is an important tool in determining the change in shape of an object due to an external force or pressure. Depending on the type of force, there are three kinds of strains:

(I)Longitudinal Strain
(II)Shearing Strain
(III)Volume Strain

If we can find the stress on the object, the expansion coefficients can be used to determine the strain on the object. Using equation (1), we can determine the change in the length, area, or volume easily.
You need to know the definition of strain to answer this question. Pay attention to the definitions, and you can simply derive the dimensions of the quantity from it. You can break it down into simple quantities and then put the dimensions of those simple terms to avoid mistakes.