The gas having average speed four times as that of $SO_{2}$ (molecular mass $64$) is

The molecules of a given mass of a gas have $r.m.s.$ velocity of $200 \,m s^{-1}$ at $27^o C$ and $1.0 \times 10^5 \,N m^{-2}$ pressure. When the temperature and pressure of the gas are respectively $127^o C$ and $0.05 \times 10^5 \,N m^{-2},$ the $r.m.s.$ velocity of its molecules in $m s^{-1}$ is

The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the $R$.$M$.$S$. velocity of its molecules at $100 \ K$,what does it become at $400 \ K$?

If the pressure of a gas is doubled while keeping the temperature constant,what will happen to the root mean square $(RMS)$ speed of the gas molecules?

$N$ molecules of gas $A$,each having mass $m$,and $2N$ molecules of gas $B$,each of mass $2m$,are contained in the same vessel at a constant temperature $T$. The mean square velocity of $B$ is $V^2$ and the mean square of the $x$-component of $A$ is $\omega^2$. The value of $\frac{\omega^2}{V^2}$ is

The average speed $\bar{v}$ and $r.m.s.$ speed $v_{rms}$ of the molecules are related as