Correct answer is (a) 10y
The explanation is: The plane strain problems are characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0, where (ux, uy, uz) denote the components of the displacement vector u in the (x, y, z) coordinatesystem. The displacement field results in the following strain field:
\(\epsilon_{xz}=\epsilon_{yz}=\epsilon_{zz}=0, \epsilon_{xx}=\frac{\partial u_x}{\partial x}, 2\epsilon_{xy}=\frac{\partial u_x}{\partial y}+\frac{\partial u_y}{\partial x}\) and \(\epsilon_{yy}=\frac{\partial u_y}{\partial y}\)
Thus, \(\epsilon_{yy}=\frac{\partial 5y^2}{\partial y}\)
=5*\(\frac{\partial y^2}{\partial y}\)
=5*2y
=10y.