• # question_answer A rod of length 1000 mm and co-efficient of linear expansion $a={{10}^{-4}}$ per degree is placed symmetrically between fixed walls separated by 1001 mm. The Young's modulus of the rod is ${{10}^{11}}\text{ }N/{{m}^{2}}$. If the temperature is increased by $20{}^\circ C\,$, then the stress developed in the rod is (in$N/{{m}^{2}}$): A) 10               B) ${{10}^{8}}$ C) $2\times {{10}^{8}}$ D) cannot be calculated

 The change in length of rod due to increase in temperature in absence of walls is $\Delta \ell =\ell \alpha \Delta T$$=1000\times {{10}^{-4}}\times 20\,mm$$=2\,mm$ But the rod can expend upto 1001 mm only. At that temperature its natural length is = 1002 mm. $\therefore$ compression = 1 mm $\therefore$ mechanical stress = $Y\frac{\Delta \ell }{\ell }={{10}^{11}}\times \frac{1}{1000}$ $={{10}^{8}}N/{{m}^{2}}$