An $HCl$ molecule has rotational,translational,and vibrational motions. If the $rms$ velocity of $HCl$ molecules in its gaseous phase is $\bar{v}$,$m$ is its mass,and $k_B$ is the Boltzmann constant,then its temperature will be:

Given below are two statements:
Statement $I$: The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement $II$: The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms,the rms speed will become $2v$.
In the light of the above statements,choose the correct answer from the options given below.

The temperature of a gas is $-68^{\circ} C$. To what temperature should it be heated,so that the r.m.s. velocity of the molecules be doubled (in $^{\circ} C$)?

The $rms$ speed of air molecules in a vessel is $90 \times 10^2 \ m/s$. If half of the gas leaks out at constant temperature,the $rms$ speed of the remaining air molecules will be

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 ratio of $r.m.s.$ velocities of oxygen and hydrogen at a given temperature is: