The root mean-square $(rms)$ speed of oxygen molecules $(O_2)$ at a certain absolute temperature is $\upsilon$. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen,the $rms$ speed would be

The velocities of $4$ gas molecules are given by $1 \ km/s, 3 \ km/s, 5 \ km/s$ and $7 \ km/s$. Calculate the difference between the average velocity and the root mean square $(RMS)$ velocity. (in $km/s$)

The temperature at which the rms speed of oxygen molecules is $75 \%$ of the rms speed of nitrogen molecules at a temperature of $287^{\circ} C$ is: (in $^{\circ} C$)

At what temperature $(^oC)$ is the average speed of hydrogen molecules equal to the average speed of oxygen molecules at $31^oC$?

$A$ flask contains argon and chlorine in the ratio of $2:1$ by mass. The temperature of the mixture is $27^{\circ}\text{C}$. The ratio of root mean square speed of the molecules of the two gases $\left(\frac{v_{\text{rms}}^{\text{Ar}}}{v_{\text{rms}}^{\text{Cl}}}\right)$ is : (Atomic mass of argon $= 40.0 \text{u}$ and molecular mass of chlorine $= 70.0 \text{u}$)

$V_{rms}$ denotes the root mean square speed,$\bar{V}$ the average speed,and $V_m$ the most probable speed of gas molecules. Which of the following is the correct relationship?