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A steel wire of uniform cross- section of $2\;mm^2$ is heated upto $50^{\circ}$ and clamped rigidly at two ends. If the temperature of wire falls to $30^{\circ}$ then change in tension in wire will be , if coefficient of linear expansion of steel is $1.1 \times 10^{-5}/ ^{\circ} C$ and $Y=2 \times 10^{11} N/m^2$

$\begin {array} {1 1} (a)\;44\;N \\ (b)\;88\;N \\ (c)\;132\;N\\ (d)\;22\;N \end {array}$

Force $F=Y \alpha \Delta t\;A$
$F= 2 \times 10 ^{11} \times 1.1 \times 10^{-5} \times 20 \times 2 \times 10^{-6}$
$\qquad=88N$
Hence b is the correct answer.

edited Feb 18, 2014 by meena.p