The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

The r.m.s. speed of a group of $7$ gas molecules having speeds $(6, 4, 2, 0, -2, -4, -6) \, m/s$ is ...... $m/s$.

The root mean square speed of molecules of a given mass of a gas at $27^{\circ} C$ and $1$ atmosphere pressure is $200\, ms^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} C$ and $2$ atmosphere pressure is $\frac{x}{\sqrt{3}}\, ms^{-1}$. The value of $x$ will be ......$ms^{-1}$.

At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at $47^{\circ}C$ (in $; K$)?

At what temperature in $K$ will the $r.m.s.$ speed of a hydrogen molecule be equal to the escape velocity from the Earth?

The $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.