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: __

σ_{1} = 100 MPa, μ = 0.3 and ϵ = 200 MPa

∵ It is uniaxial tensile stress so, σ_{2} = σ3 = 0

\({\epsilon_1} = \frac{{{\sigma _1}}}{E} - \mu \left( {\frac{{{\sigma _2}}}{E} + \frac{{{\sigma _3}}}{E}} \right)\)

\( \Rightarrow {\epsilon_1} = \frac{{{\sigma _1}}}{E} = \frac{{100}}{{200}} = 0.5\)

\( \Rightarrow {\epsilon_2} = \frac{{{\sigma _2}}}{E} - \mu \left( {\frac{{{\sigma _1}}}{E} + \frac{{{\sigma _3}}}{E}} \right) = - \mu \frac{{{\sigma _1}}}{E}\)

\( \Rightarrow {\epsilon_2} = - 0.3\left( {\frac{{100}}{{200}}} \right) = - 0.15\therefore \left( {{\epsilon_1},\epsilon{_2}} \right) = \left( {0.5, - 0.15} \right)\)