The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction $\left(\varepsilon_{z z}\right)$ is _________ (rounded off to 2 decimal places).

Use the Young's Modulus $E=200 \mathrm{GPa}$ and Poisson's ratio $v=0.27$.

A simply supported beam of length 1 m is subjected to a uniformly distributed bending moment of 1 N m per m throughout the length as shown in the figure given below. The bending moment at the mid-point of the beam is __________ N m (rounded off to the nearest integer).

An isotropic brittle material is tested in the universal testing machine. The stress-strain diagram for the material shows a bi-linear elastic behavior as shown in the figure given below. The strain energy density is _________ MJ m³- (rounded off to 2 decimal places).

A rigid circular disc of radius $r$ (in m ) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega$ (in rad s-1). The velocities (in $\mathrm{m} \mathrm{s}^{-1}$ ) at points O and A , respectively, are