If the r.m.s. velocity of hydrogen molecules is $4$ times that of an oxygen molecule at $47^{\circ} C$,the temperature of the hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are $2$ and $32$ respectively). (in $^{\circ} C$)

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?

If the mass of a $He$ atom is $4$ times that of a hydrogen atom,then the mean velocity of $He$ is:

The speeds of gas molecules are $2, 3, 4, 5, 6 \ km/s$. The $rms$ speed is ............. $km/s$.

$A$ mixture of $2\, moles$ of helium gas (atomic mass $= 4\, u$) and $1\, mole$ of argon gas (atomic mass $= 40\, u$) is kept at $300\, K$ in a container. The ratio of their rms speeds $\left[ \frac{V_{rms}(\text{helium})}{V_{rms}(\text{argon})} \right]$ is close to:

When the temperature of an ideal gas is increased from $27^\circ C$ to $227^\circ C$,its $r.m.s.$ speed changes from $400 \ m/s$ to $V_s$. The value of $V_s$ is ........ $m/s$.