Maximum fluctuation of kinetic energy in an engine has been calculated to be $$2600$$ J. Assuming that the engine runs at an average speed of $$200$$ rpm, the polar mass moment of inertia ( in kg.m² ) of a flywheel to keep the speed fluctuation within $$\, \pm 0.5\% $$ of the average speed is _______ .

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by $$m$$ and the spring constants are denoted by $${k_1}$$ and $${k_2}$$ as shown below.

A pure substance at $$8$$ $$MPa$$ and $${400^ \circ }C$$ is having a specific internal energy of $$2864$$ $$kJ/kg$$ and a specific volume of $$0.03432\,{m^3}/kg.$$ Its specific enthalpy (in $$kJ/kg$$) is ____________

Steam at a velocity of $$10$$ $$m/s$$ enters the impulse turbine stage with symmetrical blading having blade angle $${30^ \circ }.$$ The enthalpy drop in the stage is $$100kJ.$$ The nozzle angle is $${20^ \circ }.$$ The maximum blade efficiency (in percent) is ____________.