If RMS velocity of ${\mathrm{CH}}_4$ at 27°C is $0.2{\mathrm{ms}}^{–1}$, the RMS velocity at 927°C.

Detailed solution:

The relationship between RMS velocity is its directly proportionality to square root of its temperature.

$\frac{{\mathrm{V}}_1}{{\mathrm{V}}_2}=\sqrt{\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}}$

$\frac{0.2}{\mathrm{V}}=\sqrt{\frac{300}{1200}}$

V= 0.4 m/s

The required answer is C.