question_answer 41)

                  A steel rod \[(Y=2.0\times {{10}^{11}}\,N{{m}^{-2}}\,and\,\,\alpha ={{10}^{-50}}\,{{C}^{-1}})\]of length, 1 in and area of cross-section \[1\,\,c{{m}^{2}}\] is heated from \[0{}^\circ \text{C}\]  to \[\text{2}00{}^\circ \text{C}\], without being allowed to extend of bend. What is the tension produced in the rod?                

Answer:

                  Thermal strees \[=Y\,\alpha \,\Delta T\,=2\times \,{{10}^{11}}\times \,{{10}^{-5}}\,\times \,200\]                 \[=4\times {{10}^{8}}\,N{{m}^{-2}}\]             \ Tension, T = Thermal strees × Area of cross-section                 \[=4\times {{10}^{8}}N{{m}^{2}}\times {{10}^{4}}{{m}^{2}}\]                 \[=4\times {{10}^{4}}N\]