Question

What is the unit of strain?

Answer 1

Hint: When we apply a force on the body it changes its shape or deforms from its existing shape. This deformation changes the existing dimensions of the body to which the force was applied. Thus stain is a property caused because of this deformation in the body.

Complete step-by-step solution:
Let us consider that we have a solid body. Initially it is at rest. Then after some time we apply force on the body and due to this force it is obvious that it experiences a change in itself and gets deformed to something else. Thus dimensions of the body change.
This is how we define strain: it is the ratio of change in dimension of the body to its original dimension.
Or the amount of deformation experienced by a body in the direction of force divided by the original dimension before the force was applied. Here to express in better words we will consider change in length of the body as an example:
Where S= longitudinal strain, is change in length, l- original length.
And if the volume was changing, it would be expressed as:
 Where: is the volumetric strain, is change in volume of the body and V is the original volume of the body.
By looking at the above definition and formula we can see that strain is expressed in ratio and hence it is unitless and also dimensionless.

Note: do not write the unit for strain by looking at the formula , its unit cannot be written as it is in the form of ratio. Hence it is stated that strain is a dimensionless and unitless quantity. It tells us about the relative change In the particular body as compared to its initial state.