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

If the ratio of vapour density for hydrogen and oxygen is $\frac{1}{16}$,then under constant pressure,the ratio of their rms velocities will be

Two vessels having equal volume contain molecular hydrogen at $1 \text{ atm}$ and helium at $2 \text{ atm}$ respectively. If both samples are at the same temperature,the mean velocity of hydrogen molecules is

At what temperature will the $rms$ speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere $?$ (Given: Mass of oxygen molecule $(m) = 2.76 \times 10^{-26} \, kg$,Boltzmann's constant $k_B = 1.38 \times 10^{-23} \, JK^{-1}$)

If the rms velocity of a perfect gas at $27^{\circ} C$ is $500 \,m \cdot s^{-1}$,the same at $927^{\circ} C$ will be

Equal volumes of two gases are kept in different containers having densities in the ratio $1:16$. They exert equal pressures on the walls of their respective containers. Then the ratio of their r.m.s. velocities is