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A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be (a) proportional to l (b) inversely proportional to l (c) independent of l (d) independent of A |
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Answer» Correct Answer is: (c) independent of l Let α = coefficient of thermal expansion, Y = Young modulus of the wire. If the wire were free to contract, its decrease in length would be lαt, where t = decrease in temperature. To maintain constant length, lαt becomes the effective elongation. ∴ strain = lαt/l = αt. Let T = tension ∴ stress = T/A Using Y = stress/strain,T = YAαt. |
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