# The r ms speed of the molecules of a ideal gas which is at a pressure $10^5 \;m^{-2}$ & density $45\;kgm^{-3}$ is _________

$(A)\; 100 m/s \\ (B) \; 150\;m/s \\ (C)\;200\;m/s \\ (D)\;250\;m/s$

Since $PM= dRT => \large\frac{T}{M} =\frac{P}{dR} =\frac{10^5}{45 \times 8.3}$
now, $V_{rms} =\sqrt { \large\frac{3RT}{M} =\sqrt {\frac 3P}{d}} =\sqrt {\large\frac{3 \times 10^5 \times 3}{25}}$
$\qquad = 3 \times 2 \times \sqrt {10^3}$
Hence C is the correct answer.