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…

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