Correct Answer  Option 2 :
\(\sqrt{\dfrac{M_2}{M_1}}\)
Concept:

Root Mean Square Speed: It is defined as the square root of the mean of squares of the speed of different molecules.
 The rootmeansquare speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
From the expansion of pressure,
\(P = \frac{1}{3}{\rm{\rho v}}_{rms}^2\)
\({v_{rms}} = \sqrt {\frac{{3P}}{\rho }} \)
\(V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}} \)
\([\because \rho = \frac{M}{V}]\)
⇒ vrms ∝ T
Where, R = universal gas constant, M = molar mass, P = pressure due to density,ρ = density.
Explanation:
As, the two gases molecular weights M_{1 }and M_{2}, given,
we have the formula,
\(V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}} \)
\( {V_{rms}} = \sqrt {\frac{{3RT}}{M}}\)
\( \therefore {V_{rms}}\alpha \frac{1}{M} \)
\( \therefore \frac{{{V_1}}}{{{V_2}}} = \sqrt {\frac{{{M_2}}}{{{M_1}}}}\)