The root mean square velocity of a gas molecule is proportional to:

Explain the speed of molecules of a gas and the average speed $(u_{av})$.

At the same temperature,the root mean square velocities of two gases are $v_1$ and $v_2$,and their molar masses are $m_1$ and $m_2$ respectively. Which of the following relations is correct?

At temperature $T \ K$,the $rms$ speed of $CO_2$ is $x \ cm/s$. At what temperature (in $K$) will the $rms$ speed of nitrous oxide $(N_2O)$ be $4x \ cm/s$ (in $T$)?

At what temperature (in $K$) is the $rms$ velocity of $SO_2$ molecules equal to the $rms$ velocity of $O_2$ molecules at $27^{\circ} C$?

At what temperature $K$ will the $rms$ speed of $SO_2$ gas be equal to the $rms$ speed of $O_2$ gas at $303 \ K$?