question_answer

The molecules of a given mass of a gas have r.m.s. velocity of \[200\,\,m{{s}^{-1}}\] at \[27{{\,}^{o}}C\] and \[1.0\times {{10}^{5}}\,N{{m}^{-2}}\] pressure. When the temperature and pressure of the gas are respectively, \[127{{\,}^{o}}C\] and \[0.05\times {{10}^{5}}\,N{{m}^{-2}},\] the r.m.s. velocity of its molecules in \[m{{s}^{1}}\] is :                                                                                                                                [NEET - 2016]

A)  \[100\sqrt{2}\]  

B)       \[\frac{400}{\sqrt{3}}\]

C)  \[\frac{100\sqrt{2}}{3}\]           

D)       \[\frac{100}{3}\]

Correct Answer: B

Solution :

[b]

\[\Rightarrow \]   \[v=\frac{400}{\sqrt{3}}\,m/s\]