The Poisson's ratio for a perfectly incompressible linear elastic material is

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 ________ .

If the Poisson's ratio of an elastic material is $$0.4$$, the ratio of modulus of rigidity to Young's modulus is _____ .

The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic solid is ________