A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to center of gravity $$(CG)$$ of the mobile and the rest of the dimensions of the mobile phone are shown. The mobile is kept on a flat horizontal surface.

Given in addition that the eccentric mass = $$2$$ grams, eccentricity = $$2.19$$ mm, mass of the mobile = $$90$$ grams, g = $$9.81$$ $$m/{s^2}.$$ Uniform speed of the motor in $$RPM$$ for which the mobile will get just lifted off the ground at the end $$Q$$ is approximately

Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,

Temperature of nitrogen in a vessel of volume $$2{m^3}$$ is $$288$$ $$K.$$ $$A$$ $$U$$-tube manometer connected to the vessel shows a reading of $$70$$ $$cm$$ of mercury (level higher in the end open to atmosphere). The universal gas constant is $$8314$$ $$J/kmol$$-$$K,$$ atmospheric pressure is $$1.01325$$ bar, acceleration due to gravity is $$9.81$$ $$m/{s^2}$$ and density of mercury is $$13600$$ $$kg/{m^3}.$$ The mass of nitrogen (in $$kg$$) in the vessel is _________