At what temperature is the $rms$ speed of hydrogen molecules equal to the $rms$ speed of oxygen molecules at $47^{\circ}C$ (in $K$)?

At what temperature in $K$ will the $r.m.s.$ speed of a hydrogen molecule be equal to the escape velocity from the Earth?

For a particular ideal gas,which of the following graphs represents the variation of the mean squared velocity of the gas molecules with temperature?

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$. What is the ratio of their $r.m.s.$ velocities?

At temperature $T$,$N$ molecules of gas $A$ each having mass $m$ and at the same temperature $2N$ molecules of gas $B$ each having mass $2m$ are filled in a container. The mean square velocity of molecules of gas $B$ is $v^2$ and the mean square of the $x$-component of velocity of molecules of gas $A$ is $w^2$. The ratio of $w^2/v^2$ is:

The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)