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Two gases A and B present separately in two vessels X and Y at the same temperature and pressure
with molecular weights M and 2M respectively are effused out. The orifice in vessel X is circular
while that in Y is a square. If the radius of the circular orifice is equal to that the length of the square
orifice, the ratio of rates of effusion of gas A to that of gas B is

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$π \sqrt{2}$

$\sqrt{\frac{π}{2}}$

$2 π$

$\sqrt{\frac{2}{π}}$

answer is A.

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Detailed Solution

$γ α \frac{A}{\sqrt{M}}; \frac{γ_{x}}{γ_{y}} = \frac{{πr}^{2}}{r^{2}} \times \sqrt{\frac{2 M}{M}} = \sqrt{2} π$

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