Q142 / 150 · MHT CET 2024 (11 May Shift 1) · Physics

Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. The gap to be kept between the two segments of railway track is $\left(\alpha_{\text {stect }}=1.3 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$

  • A
    1.68 mm
  • Correct answer
    B
    3.64 mm
  • C
    2.06 mm
  • D
    4.32 mm

Solution

$\begin{array}{ll} & \mathrm{L}_2-\mathrm{L}_1=\mathrm{L}_1 \alpha\left(\mathrm{t}_2-\mathrm{t}_1\right) \\ \therefore & \mathrm{L}_2-\mathrm{L}_1=10 \times\left(1.3 \times 10^{-5}\right) \times(45-17) \\ \therefore & \mathrm{L}_2-\mathrm{L}_1=3.64 \mathrm{~mm}\end{array}$

Hence, the correct answer is option: 'B'.

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