Question

$2N$ molecules of an ideal gas '$X$' each of mass '$m$' and $4N$ molecules of another ideal gas $Y,$ each of mass $3m$ are maintained at the same absolute temperature in the same vessel. The rms velocity are $V1$ and $V2$ respectively then (along x-coordinate axis)$\frac{v_x}{v_y}$

• A. $\sqrt{3}:1$
• B. $1:\sqrt{3}$
• C. $3:1$
• D. $1:3$

Answer 1

Answer: (A)

$\sqrt{3}:1$

$\begin{array}{c}\text{R.M.S velocity, Vrms}\alpha \sqrt{\frac{T}{m}}\\ \begin{array}{c}{T}_1=T_2\\ m_1=m\\ m_2=3m\end{array}\\ \therefore \frac{V_1}{V_2}=\sqrt{3}\\ \text{Required ratio is}\sqrt{3}:1\end{array}$