Question

The length of the railway line between cities A and B is 30 km. 3001 rails of equal length are laid with 300 equal gaps between them. The minimum and maximum temperatures are ${25}^{\circ }C$ and ${40}^{\circ }C$ during winter and summer respectively. If $\alpha$ of iron is $12\times {10}^{-6}{}^{\circ }{C}^{-1}$, find how much gap is to be left between adjacent rails?

Answer 1

$\Delta L=\alpha L_1\Delta L$
On putting the values,
$\Delta L=15\times 12\times {10}^{-5}\times 30\times {10}^{3}m$
$=18\times {10}^{-2}\times 30m$
Now, this change of length needs will be compensated equally by the 3000 gaps.
Therefore, the gap $\Delta L$ for a single junction will be:
$=18\times {10}^{-2}\times \frac{30}{3000}$
$=18\times {10}^{-4}m=18mm$