Question

SI unit of strain is
(A). $N{m}^{-2}$
(B). $m$
(C). $N-m$
(D). no unit

Answer 1

Hint: Strain is the measure of deformations taking place in a body when a stress or deforming force is applied to it. Strain is the ratio between the changed shape of a body to the original shape. It is of different types and also depends on the type of stress acting on the body.

Complete answer:
When a deforming force is applied on a body, its shape and dimensions change. Strain is the measure of how much the shape of a body changes in the direction of force applied. Strain can also be defined as the ratio of change in dimension to the initial dimension. Strain in terms of deformation in length is given by-
$S={\displaystyle \frac{\mathrm{\Delta }l}{l}}$
Here, $S$ is the strain
$\mathrm{\Delta }l$ is the change in length
$l$ is the original length
Strain is of different types-
Normal strain- it is the ratio of change in dimension to the original dimension.
Shear strain- It is the ratio of change in angle between two perpendicular to the original angle.
Volumetric strain- It is the ratio of volume change to the original volume.
Therefore, we can see that strain is the ratio between two quantities of the same unit. So, strain is a unitless quantity.
Therefore, the strain does not have a unit.

Hence, the correct option is (D).

Note:
Usually strain is calculated by taking the ratio between change in area to original area or by taking the ratio of change in length to the original length. Deformations in a body occur when a stress is applied. The stress strain curve gives us the behavior of a body when stress is applied to it and it undergoes strain. Practically, some strain is always left in the body.