A rod is subjected to an uniaxial load within linear elastic limit. When the change in the stress is $$200$$ MPa, the change in the strain is $$0.001.$$ If the Poisson's ratio of the rod is $$0.3$$ the modulus of rigidity (in GPa) is ________ .

In a plane stress condition, the components of stress at a point are $${\sigma _x} = 20$$ MPa, $${\sigma _y} = 80$$ MPa and $${\tau _{xy}} = 40$$ MPa, The maximum shear stress (in MPa) at the point is

A cantilever beam OP is connected to another beam PQ with a pin joint as shown in figure. A load of $$10$$ kN is applied at the mid-point of PQ. The magnitude of bending moment (in kN-m) at fixed end $$O$$ is

The deflection of a spring with 20 active turns under a load of 1000 N is 10 mm. The spring is made into two pieces each of 10 active coils and placed in parallel under the same load. The deflection of the system is