Two gases `A` and `B` present separately in two vessels `X` and `Y` at the same temperature 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 of the length of the square orifice the ratio of rates of effusion of gas `A` to that of gas `B`

Options

A. `sqrt(2)pi`
B. `sqrt((pi)/(2))`
C. `2 pi`
D. `sqrt((2)/(pi))`

Answer

A

Explanation

`(r_(x))/(r_(y))=sqrt((2M)/(M))xx(A_(x))/(A_(y))` where `A_(x)` and `A_(y)` are the area of cross section of orifice.
`:. (r_(x))/(r_(y))=sqrt(2)xx(pi r^(2))/(l^(2))r`=radius of a radius orifice
`l=` length of square orifice.