Explanation

(a)
$v_{rms} = \sqrt{\frac{3RT}{M}}$
$\therefore v_{rms} \propto \sqrt{T}$
$\Rightarrow \ \frac{v_{rms}}{{v'}_{rms}} = \sqrt{\frac{T}{{T^{'}}^{'}}}$
$\frac{1}{2} = \sqrt{\frac{T}{T^{'}}}\ \ \ \left\lbrack \because{{V^{'}}^{'}}_{rms} = 2v_{rms} \right\rbrack$
$\frac{1}{4} = \frac{T}{{T^{'}}^{'}}$
${T^{'}}^{'} = 4T$
Hence, the rms velocity doubles when the temperature is increased four times