The velocity of the molecules of a gas at temperature $120\,K$ is $v$. At what temperature in $K$ will the velocity be $2v$?

If the $r.m.s.$ velocity values for hydrogen,nitrogen,and oxygen are $V_H, V_N$,and $V_O$ respectively at a given temperature,then:

The root mean square speed of molecules of nitrogen gas at $27^{\circ} C$ is approximately $.......m/s$. (Given: mass of a nitrogen molecule $= 4.6 \times 10^{-26} \, kg$ and Boltzmann constant $k_{B} = 1.4 \times 10^{-23} \, J K^{-1}$)

At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

The effect of temperature on Maxwell's speed distribution is correctly shown by

The $v_{rms}$ value for a hydrogen molecule at $300 \ K$ is $1930 \ m/s$. Then the $v_{rms}$ for an oxygen molecule at $900 \ K$ is . . . . . . $m/s$.