Question

A rod of length \[2m\] rests on a smooth horizontal floor. If the rod is heated from \[0^\circ \;C\;\] to \[30\;^\circ C\] . Find the longitudinal strain developed? \[(\alpha \; = {\text{ }}5 \times {10^{ - 5}}/^\circ C)\]
\[(A){10^{ - 3}}\]
\[(B)2 \times {10^{ - 3}}\]
\[(C){\text{Zero}}\]
\[(D){\text{None}}\]

Answer 1

Hint: The longitudinal strain is defined as the ratio of the change in length to the original length. It is caused by the longitudinal stress acts on the object. The strain is the force that is inclined to stretch the object to an extreme.
Note that the longitudinal strain occurs if there exists an external force that will try not to stretch the object.

Complete step by step answer:
There are two types of strain: Longitudinal strain and Lateral strain.
The ratio of the given original length to the change in length is known as the longitudinal strain. If we consider a rod when the longitudinal stress acts on it the length of the rod increases. Then the increased portion is divided by its original length; this will be called the longitudinal strain.
Here in the problem, the rod of the original length $l = 2m$. It is heated from \[0^\circ \;C\;\] to \[30\;^\circ C\].
Given that the rod is kept on a smooth surface, so there is no frictional force. Hence it seems that the length will increase without any limit since no frictional force exists to resist it.
We know that longitudinal strain occurs if there exists an external force that will try not to stretch the object.
Here is no external force as well as no longitudinal strain exists. i.e the longitudinal strain is zero.

Hence the right answer is in option C.

Note: If the surface would be rough, it will make the rod increase its length due to the rise in temperature to a certain limit. Then we can easily find the longitudinal strain by dividing the change in length by its original length.