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

An ideal reheat Rankine cycle operates between the pressure limits of $$10$$ $$kPa$$ and $$8$$ $$MPa,$$ with reheat being done at $$4$$ $$MPa.$$ The temperature of steam at the inlets of both turbines is $${500^ \circ }C$$ and the enthalpy of steam is $$3185$$ $$kJ/kg$$ at the exit of the high pressure turbine and $$2247$$ $$kJ/kg$$ at the exit of low pressure turbine. The enthalpy of water at the exit from the pump is $$191$$ $$kJ/kg$$. Use the following table for relevant data.

Disregarding the pump work, the cycle efficiency (in percentage ) is ________________