At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at $47^{\circ}C$ (in $; K$)?

If $V_{rms}$ of $O_2$ molecule is equal to $V_{rms}$ of $H_2$ molecule at $20 K$,the temperature of $O_2$ is:

$A$ gas $A$ has $N$ molecules at temperature $T$ with mass $m$. Another gas $B$ has $2N$ molecules at the same temperature $T$ with mass $2m$. Both are contained in a vessel. If the $rms$ velocity of molecules of gas $B$ is $v$,and the $x$-component of the mean square velocity of molecules of gas $A$ is $w^2$,find the ratio $w^2/v^2$.

The r.m.s. speed of oxygen molecules at $47^{\circ} C$ is equal to that of the hydrogen molecules kept at . . . . . . ${ }^{\circ} C$. (Mass of oxygen molecule/mass of hydrogen molecule $= 32 / 2$)

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: