A steel rod of length 1m and cross-sectional area 10 ^ - 4 m ^ 2 is...

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

$Y = \dfrac{FL}{A ∆ L} . . . \left(1\right)$

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.

$\begin{cases}Y & = & \dfrac{FL}{AL\alpha\left({T}_{2} - {T}_{1}\right)} \\ & ⇒ & F = A\alphaY\left({T}_{2} - {T}_{1}\right) . . . \left(3\right)\end{cases}$

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

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