Question

Within the elastic limit, which of the following graphs correctly represents the variation of extension in the length of a wire with the external load?
\[\left( a \right)\]

$\left( b \right)$

$\left( c \right)$

$\left( d \right)$

Answer 1

Hint: For knowing the variation of extension in the length of a wire with the external load we will use the concept of Hooke’s law. And as we know that, according to hooke's law the strain of material will be proportional to the stress applied. And it will be within the elastic limit of the material.

Complete step by step answer:
As we know that the elastic wire follows the hooke's law. And according to hooke's law
$ \Rightarrow F = Kx$
And here, $F$ will be the force which will act as load and $x$ will be the load.
From the above formula we can see that with load, the extension is making the linear graph. So from the option, our main will be to check the linear graph now.
So from the option, we can see that the option $\left( b \right)$ is making the linear graph.

Hence, the option $\left( b \right)$ is correct.

Note: From solving this type of question where we have to choose one from the given options of the graph then by using some basic information about the topic we can answer such a question. Here in this question, we can see that by using the evaluation of hooke's law we had easily solved it.