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Question

# A bridge is made from 20m long iron rods. At temperature 18∘C, the distance between two rods is 0.4cm. Up to what temperature will the bridge be in good shape? (Take coefficient of Linear expansion of iron is 11.5×10−6∘C)

A
35.4C
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B
55.2C
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C
25.4C
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D
15.7C
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Solution

## The correct option is A 35.4∘CGiven,length of the rods l=20m=2000cm,temperature, T1=18∘C, andthe distance between the two rods is 0.4cm Let the maximum temperature at which the bridge is still in a good shape be T2. The bridge will be in a good shape until the two rods expand by 0.2cm each as the temperature increases. Since the rod has to expand on both sides the total expansion of each rod can be upto 0.4cm The formula of linear expansion is: Δll=αΔT,where ΔT=T2−T1, Δl is the expansion in the length =0.4 cm and α is the linear expansion coefficient of iron =11.5×10−6 ∘C ∴0.42000=11.5×10−6×(T2−18) or, T2−18=0.42000×11.5×10−6 ⇒T2=18+0.42000×11.5×10−6=(18+17.4)∘C ⇒T2=35.4∘C

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