Question

A wire of length $2.5m$ has a percentage strain of $0.012\% $ under a tensile force. The extension produced in the wire will be
(A) $0.03mm$
(B) $0.3mm$
(C) $0.3m$
(D) $0.03m$

Answer 1

Hint: The strain produced in the wire is given by the ratio of the small extension that is produced in the wire and the original length of the wire. Here we are given the value of the train and the length of the wire. So from there we can find the extension produced in the wire.

Formula Used In this solution we will be using the following formula,
$Strain = \dfrac{{\Delta L}}{L}$
where $\Delta L$ is the extension produced and
$L$ is the original length of the wire.

Complete Step by Step Solution: The strain on any object is the measure of how much that object is stretched or deformed from its original shape due to the effect of any force on that object. It is mostly used to describe the change in the length of an object.
Now, in this problem we are given that the strain is produced on a wire due to the effect of a tensile force on the wire. This strain is given to be $0.012\% $.
So we can write $strain = \dfrac{{0.012}}{{100}}$
Now according to the formula, strain is the ratio of the change in length to the original length. That is,
$Strain = \dfrac{{\Delta L}}{L}$
In the problem we are said that the wire was initially of the length $L = 2.5m$
So substituting the value of the strain and the length of the wire, we get,
$\dfrac{{0.012}}{{100}} = \dfrac{{\Delta L}}{{2.5}}$
On taking the $2.5$ to the LHS we get,
$\Delta L = \dfrac{{0.012}}{{100}} \times 2.5$
So on calculating this we get,
$\Delta L = 3 \times {10^{ - 4}}m$
So to convert this into mm, we multiply by 1000 and get,
$\Delta L = 0.3mm$
So the extension in the length of the wire is $0.3mm$

Therefore, the correct answer is option B.

Note: The magnitude of the strain on the wire is independent of the force that is applied to it. Since it is the ratio of two similar quantities, it does not have any unit. There are mainly 3 types of strain. They are: longitudinal strain, volume strain and shearing strain.