On any planet,the presence of an atmosphere implies ($C_{rms}$ = root mean square velocity of molecules and $V_e$ = escape velocity):

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 $\,ms^{-1}$)

The root mean square (rms) velocity of an ideal gas at temperature $T$ is $v$. If the temperature is increased to $4 T$, the rms velocity of the gas is

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $O_2$,vessel $B$ contains only $N_2$,and vessel $C$ contains a mixture of equal quantities of $O_2$ and $N_2$. If the rms speed of $O_2$ molecules in vessel $A$ is $v_1$ and that of $N_2$ molecules in vessel $B$ is $v_2$,then the rms speed of $O_2$ molecules in vessel $C$ is:

If $V_{rms}$ of $O_2$ molecule is equal to $V_{rms}$ of $H_2$ molecule at $20 K$,the temperature of $O_2$ is:

At temperature $T,$ the $r.m.s.$ speed of helium molecules is the same as the $r.m.s.$ speed of hydrogen molecules at normal temperature and pressure $(NTP)$. The value of $T$ is ....... $^\circ C$.