A steel tape 1m long is correctly calibrated for a temperature of the length of a steel rod measured by this tape is found to be 63 cm an hot day when the temperature is ${45}^{0}c$  what is the actual length of the steel rod on that day ?  $\left[\alpha =1.2\times {10}^{-5}{K}^{-1}\right]$

Length of steel tap at

$\begin{array}{l}T={27}^{0}c\\ l=1m=100cm\end{array}$

At temperature $T_1={45}^0$ The length of the steel rod

$\begin{array}{l}{l}_1=63cm\\ \alpha =1.2\times {10}^{-5}{k}^{-1}\end{array}$

Actual length of steel rod at

$\begin{array}{l}{T}_1={45}^{0}l\\ l^1=l[1+\alpha (T_1-T)]\end{array}$

$l^1=100[1+1.2\times {10}^{-5}(45-27)]$

$l^1=100.0216cm$

Actual length of steel rod at $T_1={45}^{0}C$

$l_2=\left(\frac{100.0216}{100}\right)\times 63=63.0136cm$