The temperature of a gas is $-50^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed is increased by $3$ times?

$N$ 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 speed of an oxygen molecule in a gas is $u$. If the temperature is doubled and the molecule dissociates into two atoms,the speed will be:

If the rms speed of the molecules of a gas at a temperature of $77^{\circ} C$ is $50 \,ms^{-1}$, then the rms speed of the same gas molecules at a temperature of $150.5^{\circ} C$ is (in $\,ms^{-1}$)

At a given temperature,the $r.m.s.$ velocity of molecules of a gas is

If the root mean square velocity of a hydrogen molecule at a given temperature and pressure is $2 \,km/s$, the root mean square velocity of oxygen at the same condition in $km/s$ is: