Correct Answer - Option 4 : 1 : 1

__CONCEPT:__

Root mean square velocity of the gas

- Root mean square velocity (RMS value)is the square root of the mean of squares of the velocity of individual gas molecules.
- It is given as,

\(⇒ v_{rms}=\sqrt{\frac{3RT}{M}}\)

Where vrms= Root-mean-square velocity, M = Molar mass of the gas (Kg/mole), R= Molar gas constant and T = Temperature in Kelvin

__CALCULATION:__

- Since the same gas is filled in two containers of the same volume, same temperature, and with the pressure of ratio 1 : 2.

Given M_{1} = M_{2} = M, V_{1} = V_{2} = V, T_{1} = T_{2} = T and \(\frac{P_{1}}{P_{2}}=\frac{1}{2}\)

- The rms speed of the gas is given as,

\(⇒ v_{rms}=\sqrt{\frac{3RT}{M}}\) -----(1)

- The rms speed for container 1 is given as,

\(⇒ v_{rms1}=\sqrt{\frac{3RT}{M}}\) -----(2)

- The rms speed for container 2 is given as,

\(\Rightarrow v_{rms2}=\sqrt{\frac{3RT}{M}}\) -----(3)

By equation 2 and equation 3,

\(\Rightarrow\frac{v_{rms1}}{v_{rms2}}=\frac{1}{1}\)

Hence, option 4 is correct.