At which temperature the r.m.s. velocity of a hydrogen molecule...

The r.m.s velocity of the molecule of a gas of molecular weight $M$ at Kelvin temperature $T$is given by, ${V}_{rms} = \sqrt{\dfrac{3RT}{M}}$.

Let ${M}_{O}$ and ${M}_{H}$ are molecular weight of oxygen and hydrogen and ${T}_{O}$ and ${T}_{H}$ the corresponding Kelvin temperature at which ${V}_{r . m . s}$ is same for both,

${V}_{r . m . s} = \sqrt{\dfrac{3R{T}_{O}}{{M}_{O}}} = \sqrt{\dfrac{3R{T}_{H}}{{M}_{H}}}$. Hence $\dfrac{{T}_{O}}{{M}_{O}} = \dfrac{{T}_{H}}{{M}_{H}}$

${T}_{O} = 273 ° C + 47 ° C = 320K$, 

${M}_{O} = 32$, 

${M}_{H} = 2 ⇒ {T}_{H} = \dfrac{2}{32} \times 320 = 20K$