The average speed of a gas molecule is $400 \, m/s$. Calculate its $rms$ speed at the same temperature in $m/s$.

For one mole of a monoatomic gas (molar mass $= M$),the root mean square velocity is $U_{rms}$. What is the relationship between the average kinetic energy $(E)$ and $U_{rms}$?

The most probable speed of $O_2$ molecules at $T \ K$ is

The ratio between the $RMS$ velocity of $N_2$ at $200 \ K$ and that of $CO$ at $800 \ K$ is (molecular mass of $N_2 = 28 \ g \ mol^{-1}$, molecular mass of $CO = 28 \ g \ mol^{-1}$)

At $600 \ K$,the root mean square (rms) speed of gas $X$ (molar mass $= 40 \ g \ mol^{-1}$) is equal to the most probable speed of gas $Y$ at $90 \ K$. The molar mass of the gas $Y$ is $....... \ g \ mol^{-1}$. (Nearest integer)

If a gas contains only three molecules that move with velocities of $100, 200, 500 \ ms^{-1}$. What is the rms velocity of that gas in $ms^{-1}$?