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

If the speeds of $5$ molecules of a gas are $2, 3, 4, 5,$ and $6$ units,what is the value of their $rms$ speed?

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \ m \ s^{-1}$, then the rms speed of Helium molecules at the same temperature is

The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)

If the $rms$ speed of oxygen molecules at $0^{\circ} {C}$ is $160 \; {m/s}$,find the $rms$ speed of hydrogen molecules at $0^{\circ} {C}$ (in ${m/s}$).

What is $v_{rms}$? Write the equation of $v_{rms}$ in terms of: $(1)$ density,$(2)$ mass of a molecule,$(3)$ molar mass.