Metal rods of length 20m each are laid end to end to form a bridge at 25°C. What gap will be provided between consecutive rails for the bridge to withstand 75°C? [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:

Option D = 0.02m

Explanation

Safety gap = expansion of the rod

= α×L0×Δtα×L0×Δt

where αα = linear expansivity of the material

L0L0 = Initial length of the material

ΔtΔt = Change in temperature

∴∴ The safety gap = 2×10^-5×20×(75−25)

= 2×10^-5×20×(75−25)

= 2×10^-5×10³

2×10^-5×10³

= 2×1010^-2

= 0.02 m