If the rms speed of the molecules of a gas at a temperature of $77^{\circ} C$ is $50 \,ms^{-1}$, then the rms speed of the same gas molecules at a temperature of $150.5^{\circ} C$ is (in $\,ms^{-1}$)

Let $\overline{V}$, $V_{\text{rms}}$, and $V_{p}$ denote the mean speed, root mean square speed, and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement$(s)$ is/are correct?

At a given temperature,which gas has a higher speed: light or heavy?

At a given temperature,the ratio of $r.m.s.$ velocities of a hydrogen molecule and a helium atom will be:

Let the r.m.s. velocity of a molecule of a given mass of gas be $C_{1}$ at temperature $27^{\circ} C$. When the temperature is increased to $327^{\circ} C$,the r.m.s. velocity is $C_{2}$. Then the ratio $\frac{C_{2}}{C_{1}}$ is

What is the ${v_{rms}}$ of gas molecules in equilibrium?