Explanation

(a) The rms velocity of an ideal gas is
$v_{rms} = \sqrt{\frac{3RT}{M}}$
Where $T$ is the absolute temperature and $M$ is the molar mass of an ideal gas
Since $M$ remains the same
$\therefore v_{rms} \propto \sqrt{T}$
$\frac{v_{rms}^{'}}{v_{rms}} = \sqrt{\frac{T^{'}}{T}} = \sqrt{\frac{3T}{T}}$
$\Rightarrow v^{'}rms = \sqrt{3}v_{rms}$