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 ...

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