The $N_2$ molecule is $14$ times heavier than the $H_2$ molecule. At what temperature will the $rms$ speed of $H_2$ molecules be equal to the $rms$ speed of $N_2$ molecules at $27^{\circ}C$?

Five molecules of a gas have speeds $1, 2, 4, 8$ and $16 \, m/s$ at some instant. The root mean square velocity of the gas molecules is ..... $m/s$.

The temperature at which the rms speed of molecules in hydrogen gas will be double of its initial value at $27^{\circ} C$ is (in $^{\circ} C$)

The given diagram shows isotherms for a fixed mass of an ideal gas at temperatures $T_1$ and $T_2$. What is the value of the ratio $\frac{\text{r.m.s. speed of the molecules at temperature } T_2}{\text{r.m.s. speed of the molecules at temperature } T_1}$?

When the rms velocity of a gas is denoted by $V$,which of the following relations is true? ($T=$ absolute temperature of the gas)

The $v_{rms}$ value for a hydrogen molecule at $300 \ K$ is $1930 \ m/s$. Then the $v_{rms}$ for an oxygen molecule at $900 \ K$ is . . . . . . $m/s$.