A) \[{{v}_{rms}}=\sqrt{\frac{3MT}{R}}\]
B) \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\]
C) \[{{v}_{rms}}=\sqrt{\frac{3RM}{T}}\]
D) \[{{v}_{rms}}=\sqrt{3RMT}\]
Correct Answer: B
Solution :
According to kinetic theory of gases \[P=\frac{MNv_{rms}^{2}}{3V}\] or \[3pV=MNv_{rms}^{2}\] or \[3RT=MNv_{rms}^{2}\] (By gas Eq. \[pV=RT\]) or \[3RT=Mv_{rms}^{2}\] \[\Rightarrow \] \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\]
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