Explanation:
For hydrogen \({v_H} = \sqrt {\frac{{3RT}}{{{M_H}}}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
For oxygen \({v_0} = \sqrt {\frac{{3RT}}{{{M_0}}}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
Given \(v_{H}=v_{1}\) and \(v_{0}=v_{2}\) at same temperature
\(\begin{gathered}\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{M_{0}}{M_{H}}} \\M_{0}=32, M_{H}=2 \\\therefore \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{32}{2}}=\sqrt{16}=4 .\end{gathered}\)