The speeds of $5$ gas molecules are $2, 3, 4, 5,$ and $6$ units respectively. What is the $rms$ speed of these molecules?

At a given temperature,the $rms$ velocity of a gas molecule of mass $m$ is proportional to:

$A$ gas is at a temperature of $0^{\circ}C$. To what temperature in $^{\circ}C$ must the gas be heated so that the $rms$ speed of its molecules becomes double?

Find the $v_{rms}$ of nitrogen gas at $300 \ K$.

For a gas at a temperature $T$,the root-mean-square velocity ${v_{rms}}$,the most probable speed ${v_{mp}}$,and the average speed ${v_{av}}$ obey the relationship:

$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in a vessel which is maintained at temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by $V_2^2$ and the mean square of the $X$-component velocity of the molecules of gas $A$ is denoted by $V_1^2$, then $\frac{V_1}{V_2}$ is