If two nodes are observed at a frequency of $$1800$$ rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is

A single degree of freedom system having mass $$1$$ $$kg$$ and stiffness $$10$$ $$kN/m$$ initially at rest is subjected to an impulse force of magnitude $$5$$ $$kN$$ for $${10^{ - 4}}$$ seconds. The amplitude in $$mm$$ of the resulting free vibration is

Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:

The rate of heat loss from the turbine per $$kg$$ of steam flow rate is $$5$$ $$kW.$$ Neglecting changes in potential energy of steam, the power developed in $$kW$$ by the steam turbine per $$kg$$ of steam flow rate, is

A cylinder contains $$5\,\,{m^3}$$ of an ideal gas at a pressure of $$1$$ bar. This gas is compressed in a reversible isothermal process till its pressure increases to $$5$$ bar. The work in $$kJ$$ required for this process is