Question

SI unit of strain is
$\begin{align}
  & a)N/{{m}^{2}} \\
 & b)m \\
 & c)N-m \\
 & d)\text{no unit} \\
\end{align}$

Answer 1

Hint: The physical quantity strain is defined as the ratio change in length of the substance on application of stress to its original length before the application of the substance. The units of any physical quantity can be obtained by expressing the quantity in its fundamental dimensions and then obtain the required unit. The ratio of the same physical quantity has no units. From this information we can determine the unit of the strain.

Complete answer:
Let us first write the strain in a body mathematically.

$Strain=\dfrac{\Delta L}{L}$ where $\Delta L$ is the change in length of a body on application of stress and L is the length of the body before application of stress. The change in the length of the body and the actual length of the body have the same fundamental dimension of meters. Hence if we take the ratio of the change in length i.e. $\Delta L$ and the actual length of the body i.e. L, the fundamental dimension meters will cancel each other. Hence we can conclude that the physical quantity strain will have no unit.

So, the correct answer is “Option D”.

Note:
In the above solution we have only written strain across the length of a body. But the strain can be changed in the area of a body or the change in volume of the body. But still strain in general will have no units as the ratio of the a quantity having the same fundamental dimension has no dimension. The change in a physical quantity and the actual physical quantity always has the same dimension.