N molecules each of mass m of gas A and 2 N molecules each of mass 2m of gas B are contained in the same vessel which is maintined at a temperature T. The mean square of the velocity of the molecules of B type is denoted by `v^(2)` and the mean square of the x-component of the velocity of a tye is denoted by `omega^(2)`. What is the ratio of `omega^(2)//v^(2) = ?`

Options

A. 2
B. 1
C. `(1//3)`
D. `(2//3)`

Answer

4

Explanation

`V_(rms)=sqrt((3RT)/(M_(w)))`
`V_(rms)=sqrt((3RT)/(mN_(a)))`
`V^(2)_(rms) propto (1)/(m)`
`(V^(2)_(rmsA))/(V^(2)_(rms B)) = (m_(B))/(m_(A))`
`(3W^(2))/(V^(2))=(2m)/(m)`
`(W^(2))/(V^(2))=(2)/(3)`