If $C_1, C_2, C_3, ......$ represent the speeds of $n_1, n_2, n_3, ......$ molecules,then the root mean square speed is

The ratio of root mean square velocity of hydrogen at $50 \, K$ to that of nitrogen at $500 \, K$ is closest to

Which of the following statement$(s)$ is (are) correct regarding the root mean square speed $(U_{rms})$ and average translational kinetic energy $(\varepsilon_{av})$ of a molecule in a gas at equilibrium?
$(1)$ $U_{rms}$ is doubled when its temperature is increased four times
$(2)$ $\varepsilon_{av}$ at a given temperature does not depend on its molecular mass
$(3)$ $U_{rms}$ is inversely proportional to the square root of its molecular mass
$(4)$ $\varepsilon_{av}$ is doubled when its temperature is increased four times

At $27 \ ^oC$,the ratio of $rms$ velocities of ozone to oxygen is

Consider a mixture of $SO_2$ and $O_2$ kept at room temperature. Compared to the oxygen molecule,the $SO_2$ molecule will hit the wall with

The density ratio of $O_2$ and $H_2$ is $16 : 1$. The ratio of their $V_{rms}$ is