List of top Strength of Materials Questions on Stress and Strain asked in GATE CE

A 2D thin plate (plane stress) has $E=1.0~\text{N/m}^2$ and Poisson's ratio $\mu=0.5$. The displacement field is $u=Cx^2y$, $v=0$ (in m). Distances $x,y$ are in m. The stresses are $\sigma_{xx}=40xy~\text{N/m}^2$ and $\tau_{xy}=\alpha x^2~\text{N/m}^2$. Find $\alpha$ (in $\text{N/m}^4$, integer). 

A 2D thin plate (plane stress) has $E=1.0~\text{N/m}^2$ and Poisson’s ratio $\mu=0.5$. The displacement field is $u=Cx^2y$, $v=0$ (in m). Distances $x,y$ are in m. The stresses are $\sigma_{xx}=40xy~\text{N/m}^2$ and $\tau_{xy}=\alpha x^2~\text{N/m}^2$. Find $\alpha$ (in $\text{N/m}^4$, integer).