A bar of rectangular cross-sectional area of $$50$$ mm² is pulled from both the sides by equal forces of $$100$$ N as shown in the figure below. The shear stress (in MPa) along the plane making an angle $$45$$⁰ with the axis, shown as a dashed line in the figure, is _______.

A 1 m × 10 mm $$ \times $$ 10 mm cantilever beam is subjected to a uniformly distributed load per unit length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point P is ____________.

A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in mm) is _______.

An engine, connected with a flywheel, is designed to operate at an average angular speed of $$800$$ rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to be $$6240$$ J. In order to keep the fluctuation of the angular speed within $$ \pm 1\% $$ of its average value, the moment of inertia (in kg-m²) of the flywheel should be ____________.