The $RMS$ velocity of oxygen molecules at $NTP$ is $0.5 \,km/s$. The $RMS$ velocity for the hydrogen molecule at $NTP$ is (in $\,km/s$)

The atmosphere on a planet is possible only if [where $v_{rms}$ is the root mean square speed of gas molecules on the planet and $v_e$ is the escape speed on its surface]

The r.m.s. speed of the molecules of a gas at $100^{\circ} C$ is $v$. The temperature at which the r.m.s. speed will be $\sqrt{3} v$ is: (in $^{\circ} C$)

If the pressure of a gas is doubled while keeping the temperature constant,what will happen to the root mean square $(RMS)$ speed of the gas molecules?

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at $-20\,^{\circ} C$? (Atomic mass of $Ar = 39.9 \; u$,of $He = 4.0 \; u$)

The temperature at which the $r.m.s.$ velocity of hydrogen molecules is $4.5$ times that of an oxygen molecule at $47^{\circ} C$ is (Molecular weight of hydrogen and oxygen molecules are $2$ and $32$ respectively). (in $^{\circ} C$)