A cylindrical tube $A B$ 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 perpendicular to $A B$ 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)
Select the correct option:
A
$P_B=P_A \exp \left(M \omega^2 l^2 / 2 R T\right)$
B
$P_B=P_A$
C
$P_B=P_A \exp \left(M \omega^2 l^2 / 3 R T\right)$
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