Steel bars each of length 3m at 28°C are to be used for constructing a rail line. If the linear expansitivity of the steel is 1 x \(10^{-5}K^{-1}\),what is ...
Question 1 Report
Steel bars each of length 3m at 28°C are to be used for constructing a rail line. If the linear expansitivity of the steel is 1 x \(10^{-5}K^{-1}\),what is the safety gap that must be left between the successive bars if the highest temperature expected is 40°C?
Answer Details
The steel bars will undergo thermal expansion as the temperature increases from 28°C to 40°C. To prevent the bars from buckling or bending, a safety gap must be left between successive bars.
The change in length of a steel bar can be calculated using the formula:
ΔL = αLΔT
Where:
α = linear expansitivity of steel = 1 x 10^-5 K^-1
L = original length of steel bar = 3m
ΔT = change in temperature = (40°C - 28°C) = 12°C
Substituting the given values:
ΔL = (1 x 10^-5 K^-1)(3m)(12°C) = 3.6 x 10^-4 m
The safety gap to be left between the successive bars would be equal to the change in length of a single bar, which is 3.6 x 10^-4 m or 0.36 mm (since 1 m = 100 cm).
Converting this to cm, we get:
0.36 mm = 0.036 cm
Therefore, the safety gap that must be left between successive bars is 0.036 cm.
Hence, the correct option is:
- 3.6x10^-1 cm
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