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

= $α \times L_{0} \times Δ t$

where $α$ = linear expansivity of the material

$L_{0}$ = Initial length of the material

$Δ t$ = Change in temperature

$∴$ The safety gap = $2 \times 10^{- 5} \times 20 \times (75 - 25)$

$2 \times 10^{- 5} \times 20 \times (75 - 25)$

= $2 \times 10^{- 5} \times 10^{3}$

$2 \times 10^{- 5} \times 10^{3}$

= $2 \times 10^{- 2} m$

= 0.02 m