Two steel rails

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

Two steel rails, each of length 10.0 m10.0\,\text{m} at 0∘C0^{\circ}\text{C}, are laid with a clearance of 3.0 mm3.0\,\text{mm} between their ends. The temperature of the track may rise to 40∘C40^{\circ}\text{C} in summer. The coefficient of linear expansion of steel is 1.2×10−5  K−11.2\times10^{-5}\;\text{K}^{-1}. (i) State the relation connecting change in length of a solid rod with rise in temperature. (ii) Calculate whether the chosen clearance is adequate. If inadequate, determine the extra gap that should have been provided so that the rails do not exert compressive force on each other at 40∘C40^{\circ}\text{C}.

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