The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

Three particles have speeds of $2u$,$10u$,and $11u$. Which of the following statements is correct?

Temperature of an ideal gas, initially at $27^{\circ} C$, is raised by $6^{\circ} C$. The rms velocity of the gas molecules will

At which temperature will the velocity of $O_2$ molecules be equal to the velocity of $N_2$ molecules at $0 ^\circ C$?

The temperature at which the root mean square velocity of hydrogen molecules equals their escape velocity from the Earth is closest to: [Boltzmann constant $k_B = 1.38 \times 10^{-23} \, J/K$,Avogadro number $N_A = 6.02 \times 10^{23} \, mol^{-1}$,Molar mass of $H_2 = 2 \times 10^{-3} \, kg/mol$,Radius of Earth $R_e = 6.4 \times 10^6 \, m$,Gravitational acceleration $g = 10 \, m/s^2$]

The temperature of an ideal gas is reduced from $927^\circ C$ to $27^\circ C$. The $r.m.s.$ velocity of the molecules becomes