The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (g_moon = g_earth/6) is

A mass $$m$$ attached to a spring is subjected to a harmonic force as shown in the figure. The amplitude of the forced motion is observed to be $$50$$ mm. The value of m (in kg) is

A mono-atomatic ideal gas $$\left( {\gamma = 1.67,} \right.$$ molecular weight$$=40$$ $$\left. \, \right)$$ is compressed adiabatically from $$0.1$$ $$MPa,$$ $$300K$$ to $$0.2$$ $$MPa.$$ The universal gas constant is $$8.314$$ $$kJ$$ $$kmo{l^{ - 1}}{K^{ - 1}}.$$ The work of compression of the gas (in $$kJ$$ $$k{g^{ - 1}}$$) is

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is