Four molecules of a gas have speeds $1, 2, 3$ and $4 \ km/s$. The value of root mean square speed of the gas molecules is

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic),the second contains chlorine (diatomic) and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $(v_{rms})$ and choose the correct answer from the options given below:

At what temperature is the $rms$ speed of air molecules doubled compared to its value at $NTP$?

Two containers $A$ and $B$ contain an ideal gas at the same temperature. If the masses of the molecules are $m_A$ and $m_B$ respectively,what is the relationship between their momenta $p_A$ and $p_B$?

$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in a vessel which is maintained at temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by $V_2^2$ and the mean square of the $X$-component velocity of the molecules of gas $A$ is denoted by $V_1^2$, then $\frac{V_1}{V_2}$ is

The root mean square speed of the molecules of a gas is