Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment…

Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. Increase in length of the segment of railway track is ' $x$ ' $\times 10^{-5} \mathrm{~m}$. The value of ' $x$ ' is $\left(\alpha_{\text{steel }}=\right.$ $\left.1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$
  1. 168
  2. 204
  3. 336
  4. 530

Solution

$\begin{array}{ll} & \mathrm{L}_2-\mathrm{L}_1=\mathrm{L}_1 \alpha\left(\mathrm{t}_2-\mathrm{t}_1\right) \\ \therefore \quad & \mathrm{x} \times 10^{-5}=10 \times 1.2 \times 10^{-5} \times(45-17) \\ \therefore \quad & \mathrm{x} \times 10^{-5}=10 \times 1.2 \times 10^{-5} \times 28 \\ \therefore \quad & x=336\end{array}$

Asked in: MHT CET 2024 (02 May Shift 1)

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