A metallic rod of $$500$$mm length and $$50$$mm diameter, when subjected to a tensile force of $$100$$kN at the ends, experiences an increase in its length by $$0.5$$mm and a reduction in its diameter by $$0.015$$mm. The Poisson's ratio of the rod material is _______ .

A rigid uniform rod $$AB$$ of length $$L$$ and mass $$m$$ is hinged at $$C$$ such that $$AC = L/3, CB = 2L/3.$$ Ends $$A$$ and $$B$$ are supported by springs of spring constant $$k.$$ The natural frequency of the system is given by

Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency of vibration of the beam, with a $$0.5$$ kg mass attached at the free tip, is $$100Hz$$. The flexural rigidity (in $$N.{m^2}$$) of the beam is _________.

The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called