Molecular velocities of two gases at the same temperature are $v_1$ and $v_2$. Their masses are $m_1$ and $m_2$ respectively. Which of the following expressions is correct?

The $rms$ velocity of a gas depends upon

At what temperature,the rate of effusion of $N_2$ would be $1.625$ times that of $SO_2$ at $50\,^{\circ}C$ ............ $K$

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 $T$ $(K)$,the $P$,$V$ and $u_{rms}$ of $1$ mole of an ideal gas were measured. The following graph is obtained. What is its slope $(m)$? ($x$-axis $= PV$; $y$-axis $= u_{rms}^2$,$M =$ Molar mass)

$A$ $50 \, L$ container holds $0.5 \, mol$ of $O_2$ gas at $27 \, ^oC$ and $2 \, atm$ pressure. If half of the $O_2$ molecules are removed from the container,what happens to the $rms$ speed of the $O_2$ molecules?