A cylindrical tube $$AB$$ of length $$l$$, closed at both ends contains an ideal gas of 1 mol having molecular weight $$M$$. The tube is rotated in a horizontal plane with constant angular velocity $$\omega$$ about an axis pe1pendicular to $$AB$$ and passing through the edge at end $$A$$ , as shown in the figure. If $$P_{A}$$ and $$P_{B}$$ are the pressures at $$A$$ and $$B$$ respectively, then
(Consider the temperature is same at all points in the tube)