What is the ${v_{rms}}$ of gas molecules in equilibrium?

At what temperature is the $R$.$M$.$S$. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $K$)? (Molecular weight of hydrogen $= 2$,molecular weight of oxygen $= 32$)

At what temperature will the root mean square $(rms)$ speed of oxygen molecules be sufficient to escape from the Earth's atmosphere? (Mass of an oxygen molecule $m = 2.76 \times 10^{-26} \, kg$,Boltzmann constant $k_B = 1.38 \times 10^{-23} \, JK^{-1}$,Escape velocity of Earth $v_e = 11.2 \, km/s$)

At a temperature of $27 \, ^\circ C$,the $rms$ speed of a gas is $1930 \, m/s$. The gas is:

The $rms$ speed of air molecules in a vessel is $90 \times 10^2 \ m/s$. If half of the gas leaks out at constant temperature,the $rms$ speed of the remaining air molecules will be

The temperature of an ideal gas is reduced from $927^\circ C$ to $27^\circ C$. The $r.m.s.$ velocity of the molecules becomes