A steel rod of length 1   m and cross-sectional area 10 - 4   m 2 is heated from 0 ° C to 200…

The formula to calculate the Young's modulus of the material of the wire is given by

$Y=\frac{FL}{A∆L} ...\left(1\right)$

The increase in length of the wire due to increase in temperature is given by

$∆L=L\alpha \left(T_2-T_1\right) ...\left(2\right)$

Substitute the expression for the extension in length from equation (2) into equation (1) and simplify to obtain the required compressive tension.

$\begin{array}{rcl}Y& =& \frac{FL}{AL\alpha \left(T_2-T_1\right)}\\ & \Rightarrow & F=A\alpha Y\left(T_2-T_1\right) ...\left(3\right)\end{array}$

Substitute the values of the known parameters into equation (3) to calculate the required compressive tension in the wire.

$\begin{array}{rcl}F& =& {10}^{-4} m^2\times {10}^{-5} {\mathrm{K}}^{-1}\times 2\times {10}^{11} {\mathrm{Nm}}^{-2}\times \left(200° \mathrm{C}-0° \mathrm{C}\right)\\ & =& 4\times {10}^4 \mathrm{N}\end{array}$