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A steel wire 5mm in diameter is fixed between 2 clamps at $30^{\large\circ}C$.The temperature is increased to $30^{\large\circ}C$.Find the tension at $50^{\large\circ}C$ if linear expansion of steel is $11\times 10^{-6}/^{\large\circ}C$ and $Y_{steel}=2.1\times 10^{11}N/m^2$

$\begin{array}{1 1}(A)\;900N\\(B)\;897N\\(C)\;800N\\(D)\;\text{None of above}\end{array} $

1 Answer

$\large\frac{\Delta l}{l}$$=\alpha \Delta \theta$
$\Rightarrow 11\times 10^{-6}\times 20$
$\Rightarrow 2.2\times 10^{-4}$
$a=\pi r^2$
$\;\;\;=\pi(\large\frac{5}{2}$$\times 10^{-3})^2$
$F=Y\times \large\frac{\Delta l}{l}$$\times a$
$\;\;\;=2.1\times 10^{11}\times 2.2\times 10^{-4}\times \pi\times \large\frac{25}{4}$$\times 10^{-6}$
Hence (D) is the correct answer.
answered May 8, 2014 by sreemathi.v

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