The molecules of a given mass of a gas have RMS velocity of 200 ms⁻¹ at 27^oC and 1.0 × 10⁵ Nm⁻² pressure. When the temperature and pressure of the gas are respectively, 127^oC and 0.05 × 10⁵ Nm⁻², the r.m.s. velocity of its molecules in ms⁻¹ is : 

\(\frac{400}{\sqrt{3}}\)

\(v_{RMS} ∝ \sqrt{T}\)

\(\frac{V_{RMS_{300K}}}{V_{RMS_{400K}}} = \frac{\sqrt{300 K}}{\sqrt{400 K}}\)

\(V_{\text{RMS at 400K}}\)=\(\sqrt{\frac{400}{300}}\) × \(V_{\text{RMS at 300K}}\)

\(V_{RMS_{300 K}} = 200 m/s \) [from question]

⇒ \(V_{RMS_{400 K}} = \frac{400}{\sqrt{3}}\)