Question

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 mean square of $x$ component of velocity of molecules of gas $A$ is $w^2$. The ratio of $w^2/v^2$ is :

• A. $1$
• B. $3$
• C. $1/3$
• D. $1/2$

Answer 1

The correct option is D $1/2$

At a given temperature, the mean square velocity is inversely proportional to molar mass.
$u^2=\frac{3RT}{M}$
The molar mass of $A$ is equal to one half the molar mass of $B$.
Hence, the mean square velocity of $A$ is equal to twice the mean square velocity of $B$.
The ratio of the mean square velocities of $A$ and $B$ is $1:2$.