A steel tape of $300 \mathrm{~cm}$ length is graduated at $27^{\circ} \mathrm{C}$. The length of a steel rod…
A steel tape of $300 \mathrm{~cm}$ length is graduated at $27^{\circ} \mathrm{C}$. The length of a steel rod measured using the tape is found to be $110 \mathrm{~cm}$ at $50^{\circ} \mathrm{C}$. The actual length of steel rod at 50 ${ }^{\circ} \mathrm{C}$ is
$\left(\alpha_{\text {steel }}=1.2 \times 10^{-5} \mathrm{~K}^{-1}\right)$
$110.03 \mathrm{~cm}$
$110.10 \mathrm{~cm}$
$110.07 \mathrm{~cm}$
$110.62 \mathrm{~cm}$
Solution
Let $L^{\prime}$ be the length of steel rod.
$\begin{aligned} & \mathrm{L}^{\prime}=\mathrm{L}+\mathrm{L} \alpha \Delta \mathrm{T} \\ & =300+300 \times 1.2 \times 10^{-5} \times(50-27) \\ & =300+0.0828=300.0828 \mathrm{~m}\end{aligned}$
The actual length of steel rod at $50^{\circ} \mathrm{C}$ is
$\mathrm{L}_2=\frac{300.0828}{300} \times 110=110.03 \mathrm{~cm}$