Two rods of different materials having coefficients of thermal expansion ${\mathrm{\alpha }}_1$ and ${\mathrm{\alpha }}_2$ and Young's moduli Y₁ and Y₂ are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

• A

  $\frac{{\mathrm{Y}}_1}{{\mathrm{Y}}_2}=\frac{{\mathrm{\alpha }}_1}{{\mathrm{\alpha }}_2}$

• B

  $\frac{{\mathrm{Y}}_1}{{\mathrm{Y}}_2}=\frac{{\mathrm{\alpha }}_2}{{\mathrm{\alpha }}_1}$

• C

  $\frac{{\mathrm{Y}}_1}{{\mathrm{Y}}_2}=\sqrt{\left(\frac{{\mathrm{\alpha }}_1}{{\mathrm{\alpha }}_2}\right)}$

• D

  $\frac{{\mathrm{Y}}_1}{{\mathrm{Y}}_2}=\sqrt{\left(\frac{{\mathrm{\alpha }}_2}{{\mathrm{\alpha }}_1}\right)}$