At what temperature in $K$ will the $r.m.s.$ speed of a hydrogen molecule be equal to the escape velocity from the Earth?

If the rms speed of the molecules of a gas at a temperature of $77^{\circ} C$ is $50 \,ms^{-1}$, then the rms speed of the same gas molecules at a temperature of $150.5^{\circ} C$ is (in $\,ms^{-1}$)

At what temperature does the $r.m.s.$ speed of air molecules become double that at $N.T.P.$?

To what temperature should the hydrogen at $327^{\circ} C$ be cooled at constant pressure,so that the root mean square velocity of its molecules becomes half of its previous value (in $^{\circ} C$)?

Out of hydrogen and air,which will have a higher root mean square speed $(v_{\text{rms}})$?

At a given temperature,if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ is the velocity of sound in it,then these are related as $\left( \gamma = \frac{C_P}{C_v} \right)$: