Metal rods of length 20m each are laid end to end to form a bridge at 25oC. What gap will be provided between consecutive rails for the bridge to withstand 75oC?
[Linear expansivity of the material = 2.0 x 10-5K-1
[Linear expansivity of the material = 2.0 x 10-5K-1
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Correct Answer: Option D
Explanation:
Safety gap = expansion of the rod
= \(\alpha \times L_0 \times \Delta t\)
where \(\alpha\) = linear expansivity of the material
\(L_0\) = Initial length of the material
\(\Delta t\) = Change in temperature
\(\therefore\) The safety gap = \(2 \times 10^{-5} \times 20 \times (75 - 25)\)
= \(2 \times 10^{-5} \times 10^3\)
= \(2 \times 10^{-2} m\)
= 0.02 m
Safety gap = expansion of the rod
= \(\alpha \times L_0 \times \Delta t\)
where \(\alpha\) = linear expansivity of the material
\(L_0\) = Initial length of the material
\(\Delta t\) = Change in temperature
\(\therefore\) The safety gap = \(2 \times 10^{-5} \times 20 \times (75 - 25)\)
= \(2 \times 10^{-5} \times 10^3\)
= \(2 \times 10^{-2} m\)
= 0.02 m