Metal rods of length 20m each are laid end to end to form a bridge at 25oC. What gap will be provided between consecutive rails for the bridge to withstand ...

Metal rods of length 20m each are laid end to end to form a bridge at 25oC. What gap will be provided between consecutive rails for the bridge to withstand 75oC?

[Linear expansivity of the material = 2.0 x 10-5K-1]

Answer Details

The problem involves finding the gap to be provided between the consecutive metal rods, which are laid end to end to form a bridge at 25°C, so that the bridge can withstand a temperature of 75°C. The linear expansivity of the material is given as 2.0 x 10^-5 K^-1. When the temperature of a material increases, it expands in length. The amount of expansion is given by the coefficient of linear expansion, which is the increase in length per unit length per unit increase in temperature. Let x be the gap to be provided between consecutive rails at 25°C. When the temperature increases to 75°C, each metal rod will expand by a length of (20m x 2.0 x 10^-5 K^-1 x 50K) = 0.02m. Therefore, the total increase in length for two consecutive rods and the gap between them will be 0.04m. To ensure that the bridge can withstand the increased temperature, the gap between the consecutive rails should be equal to the total increase in length, which is 0.04m. Since there are two gaps between three rods, the gap to be provided between consecutive rails is half of 0.04m, which is equal to 0.02m. Therefore, the answer is option D, 0.02m.