• # question_answer A 10 cm long and 5 cm diameter steel rod fits snugly between two rigid walls 10 cm apart at room temperature. Young's modulus of elasticity and coefficient of linear expansion of steel are $2\times {{10}^{6}}\,\text{kg/c}{{\text{m}}^{\text{2}}}$ and $12\times {{10}^{-\,6}}$ per ${}^\circ C$ respectively. The stress developed in rod due to a $100{}^\circ C$ rise in temperature will be: A) $6\times {{10}^{-\,10}}\,\text{kg/c}{{\text{m}}^{\text{2}}}$ B) $6\times {{10}^{-\,10}}\,\text{kg/c}{{\text{m}}^{\text{2}}}$C) $2.4\times {{10}^{3}}\,\text{kg/c}{{\text{m}}^{\text{2}}}$   D) $2.4\times {{10}^{4}}\,\text{kg/c}{{\text{m}}^{\text{2}}}$

Correct Answer: C

Solution :

${{\sigma }_{t}}=E\,\alpha .\Delta \theta$ $=2\times {{10}^{6}}\times 12\times {{10}^{-6}}\times 100$ $=2.4\times {{10}^{3}}\,\text{kg/c}{{\text{m}}^{\text{2}}}$

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