The Strain is defined as the ratio of change in dimension of a body to the original dimension. So If you want to know the unit of strain then you have to take the ratio of units of change in dimension with the units of original dimension. Since it it is the ratio of quantities having same units so the strain is a unitless and dimensionless quantity. Lets understand it more clearly
The formula of stain is
e = Change in dimension/ Original dimension
Here we have taken the ratio of change in dimension with the original dimension and unit of both remains the same, so they cancel out each other and we get the answer 1. This shows that the unit of strain is unity i.e. it is a dimensionless quantity or unitless quantity.
To Understand it more clearly lets take an example. Consider there is a rod with lenght l and an external tensile force is applied on the rod. Due to the external force there is a increase in the length of the rod. Now new length of the rod is L. If we apply the formula of the strain then
Strain = change in length/ Original length = L-l/l = dl/l = unit of change in length/ unit of original length = meter/meter = m/m = 1.
The SI Unit of length is m, so the unit of change in length is also m and the unit of original length is also m. Now take the ratio of both
Unit of strain = unit of change in length/ unit of original length = meter/meter = m/m = 1
So the the Unit of strain is unity i.e it is unitless quantity. Or you can say that the strain is a dimensionless quantity and it is simply represented with decimal numbers.
Frequently Asked Questions
Q1. What will be the unit of strain with all types of strain.
Ans: The unit of strain remains same i.e. it will be unitless or dimensionless. It will not depend on the types of strain.
Q2. What we can conclude with the value of strain.
Ans: The value of strain indicates how much deformation has happened with the object. suppose we have three values of strain of three objects: 0.5, 0.6, 0.4 and now you have to tell which object has experienced more deformation. So the object with higher value of strain experiences more deformation.
