Question

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▪︎Solve Numerical

A bridge is made from 20 m long iron rods. at temperature 18⁰ C, the distance between two rods is 0.4 cm. up to what temperature will the bridge be in good shape? ​

Answer 1

Answer:

The bridge will be in good shape till both the rods expand by 0.2 cm as the temperature is increased. Let at temperature T, both the rods expand by 0.2 cm i.e. the total expansion is 0.4 cm.

Answer 2

Explanation:

Length of the iron rod =20m=2000cm at 18∘C

Distance between the length of two rods, =0.4cm Temperature coefficient of linear expansion of iron =11.5×10−6C−1

The bridge will be in good shape until both the rods expand by 0.2 cm as the temperature is increased. Let at temperature T, both the rods expand by 0.2 cm i.e. the total expansion is 0.4 cm.

Using the formula for the linear expansion of solids, we have 

lΔl=alΔT

∴20000.4=11.5×10−6×(T−18)

T=18+2000×11.5×10−60.4=35.4∘C