By what factor will the $r.m.s.$ velocity change if the temperature is raised from $27^\circ C$ to $327^\circ C$?

At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

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

$A$ container is divided into two equal parts $L$ and $R$. If the root mean square (rms) speed of the molecules in part $L$ is equal to the average speed of the molecules in part $R$,find the ratio of the mass of a molecule in part $L$ to the mass of a molecule in part $R$.

When the temperature of a gas is raised from $27^{\circ} C$ to $90^{\circ} C$,the increase in the rms velocity of the gas molecules is: (in $\%$)

The temperature at which the root mean square velocity of a molecule will be doubled than its value at $100^{\circ}C$ is: