A beam is loaded as shown in the figure

The bending moment, in $$Nm$$, at point $$R$$ is _______.

A metallic bar of uniform cross-section with specific weight of $$100$$ kN/m³ is hung vertically down. The length and Young's modulus of the bar are $$100$$ m and $$200$$ GPa, respectively. The elongation of the bar, in mm, due to its own weight is __________ .

If the principal stress values are $$120$$ MPa, $$-50$$ MPa and $$10$$ MPa in a given state of stress, then maximum shear stress in the material, in MPa, is _______.

In an off-set slider crank mechanism, shown in figure, the crank is rotated at a constant speed of $$150$$ rpm. The value of the angle $$\theta $$ shown in the figure is $${20^ \circ }$$ . What is the ratio of forward to return stroke time? Can this mechanism be used in an application involving quick return?