Four molecules of a gas have speeds $1, 2, 3$ and $4 \ km/s$. The value of root mean square speed of the gas molecules 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 $400 \ K$?

The $rms$ speed of hydrogen molecules at room temperature $(300 \ K)$ will be:

If the absolute temperature of a gas is increased $5$ times,the r.m.s. velocity of the gas molecules will be

The temperature of a gas is doubled $(i)$ on the absolute scale and $(ii)$ on the centigrade scale. The increase in the root mean square velocity of the gas will be:

$N$ 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