# If two gases of molecular weights M1 and M2 are at same pressure and temperature, ratio of their r.m.s. speed will be Option 1) $M_2:M_1$ Option 2) $M_1:M_2$ Option 3) $\sqrt M_1:\sqrt M_2$ Option 4) $\sqrt M_2:\sqrt M_1$

P Plabita

As we learnt in

Root mean square velocity -

$V_{rms}= \sqrt{\frac{3RT}{M}}$

$= \sqrt{\frac{3P}{\rho }}$

- wherein

R = Universal gas constant

M = molar mass

P = pressure due to gas

$\rho$ = density

$V_{rms}\propto \frac{1}{\sqrt{M}}$

$\therefore \frac{V_{1}}{V_{2}}= \frac{\sqrt{M_{2}}}{\sqrt{M_{1}}}$

Option 1)

$M_2:M_1$

Incorrect

Option 2)

$M_1:M_2$

Incorrect

Option 3)

$\sqrt M_1:\sqrt M_2$

Incorrect

Option 4)

$\sqrt M_2:\sqrt M_1$

correct

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