A mixture of two gasses $A$ and $B$ is kept in a vessel which is maintained at a temperature $T$. In the vessel there are $N$ molecules each of mass $m$, of the gas $A$ and $2N$ molecules each of mass $2m$ of the gas $B$. The mean square velocity of the molecules of the gas $B$ is $v^2$ and the mean square velocity of the molecules of the gas $A$ along the $x$ direction is $w^2$. The value of $\frac{w^2}{v^2}$ is