Question

A wire of length $L$ and radius $r$ fixed at one end and a force $F$ applied to the other end produces an extension $l$.The extension produced in another wire of the same material of length $2L$ and radius $2r$ by a force $2F$, is :

• A. $l$
• B. $2l$
• C. $4l$
• D. $\frac{l}{2}$

Answer 1

The correct option is A $l$

Given

Extention in the first rod is $l$ due to application of force $F$, Let extention in another wire is $e$ with given condition.

$\begin{array}{c}Y=\frac{Fl}{Ae}\\ \Rightarrow \frac{FL}{r^2\times l}=\frac{2F\times 2L}{{\left(2r\right)}^2\times e}\\ \Rightarrow e=l\end{array}$

Hence,

option $\left(A\right)$ is correct answer.