At what temperature will the root mean square speed $(\nu_{rms})$ of oxygen gas molecules be equal to the $\nu_{rms}$ of hydrogen gas molecules at $27 \, ^\circ C$? $(M_{O_2} = 32 \, g \, mol^{-1}, M_{H_2} = 2 \, g \, mol^{-1})$

$A$ vessel is partitioned into two equal halves by a fixed diathermic separator. Two different ideal gases are filled in the left $(L)$ and right $(R)$ halves. The rms speed of the molecules in the $L$ part is equal to the mean speed of the molecules in the $R$ part. Then the ratio of the mass of a molecule in the $L$ part to that of a molecule in the $R$ part is

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $\,K$)?

For a given gas,the velocities of $5$ molecules are $2, 3, 4, 5,$ and $6$. What is the $rms$ velocity?

If at $STP$,the velocity of sound in a gas $(\gamma = 1.5)$ is $600 \, m/s$,the $r.m.s.$ velocity of the gas molecules at $STP$ will be ........... $m/s$.

$A$ 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: