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# If $Y_{Steel}=2\times 10^{11}N/m^2$ ,what force must be applied to steel rod of $l=2m$ and $r=2mm$ to stretch it by 1mm

$\begin{array}{1 1}(A)\;11.35\times 10^2N\\(B)\;23.34\times 10^2N\\(C)\;12.56\times 10^2N\\(D)\;\text{None of these}\end{array}$

As $Y=(\large\frac{F}{a})\frac{l}{\Delta l}$
$\Rightarrow F=\large\frac{Y\times a\times \Delta l}{l}$
$\Rightarrow \large\frac{2\times 106{11}\times \pi\times (2\times 10^{-3})^2\times 1\times 10^{-3}}{2}$
$\Rightarrow 4\pi\times 10^2$
$\Rightarrow 12.56\times 10^2N$
Hence (C) is the correct answer.