A uniform heavy rod of weight W, cross-sectional area A and length L is hanging from a fixed support. Young's modulus of the material of the rod is Y. Neglect the lateral contraction. Find the elongation of the rod.
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To find elongation of the rod, you must determine total extension of the rod. Here Y is the Young’s Modulus i.e Stress/strain. From top of the rod, distance x is considered at an element length dx. The tension acting below dx is caused by the weight of the rod. Therefore, from calculation, the clear elongation length of the rod is W1/2AY.
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