The $r.m.s.$ speed of gas molecules at $800 \ K$ will be

The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200 \, m/s$ at $27^{\circ}C$ and $1.0 \times 10^5 \, N/m^2$ pressure. When the temperature is $127^{\circ}C$ and pressure is $0.5 \times 10^5 \, N/m^2$,the $r.m.s.$ velocity in $m/s$ will be

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

$N$ $(N < 100)$ molecules of a gas have velocities $1, 2, 3, ..., N \text{ km/s}$ respectively. Then:

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 gas having an average speed four times that of $SO_2$ (molecular mass $64$) is