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Metal rods of length 20m each are laid end to end to form...

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

A.

0.20m

B.

0.22m

C.

0.25m

D.

0.02m

Correct answer is D

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