Correct Answer - Option 3 : (0.5, −0.15)
Concept:
\({\epsilon_x} = \frac{{{\sigma _x}}}{E} - \mu \left( {\frac{{{\sigma _y}}}{E} + \frac{{{\sigma _z}}}{E}} \right)\)
Calculation:
σ1 = 100 MPa, μ = 0.3 and ϵ = 200 MPa
∵ It is uniaxial tensile stress so, σ2 = σ3 = 0
\({\epsilon_1} = \frac{{{\sigma _1}}}{E} - \mu \left( {\frac{{{\sigma _2}}}{E} + \frac{{{\sigma _3}}}{E}} \right)\)
\( \Rightarrow {\epsilon_1} = \frac{{{\sigma _1}}}{E} = \frac{{100}}{{200}} = 0.5\)
\( \Rightarrow {\epsilon_2} = \frac{{{\sigma _2}}}{E} - \mu \left( {\frac{{{\sigma _1}}}{E} + \frac{{{\sigma _3}}}{E}} \right) = - \mu \frac{{{\sigma _1}}}{E}\)
\( \Rightarrow {\epsilon_2} = - 0.3\left( {\frac{{100}}{{200}}} \right) = - 0.15\therefore \left( {{\epsilon_1},\epsilon{_2}} \right) = \left( {0.5, - 0.15} \right)\)