A narrow horizontal cylindrical tube is filled with a gas. The tube rotates in a horizontal plane with an angular velocity \(w\) about a perpendicular axis through one of its ends A. The length of the tube is \(l\) and cross sectional area is \(S\). Total mass of contained gas is \(M\). When the tube was at rest initially, it had a pressure \({ p }_{ o }\) and a temperature \(T\).

Assuming that the temperature remained constant, find the Pressure in the tube as a function of distance x from the end A.

If \(\large p=\dfrac { { { p }_{ o }l{ e }^{ k{ w }^{ 2 }{ x }^{ 2 } } } }{ \int _{ 0 }^{ l }{ { e }^{ k{ w }^{ 2 }{ x }^{ 2 } } \, dx } } \) for some constant \(k\), find \(\dfrac { { p }_{ o }klS }{ M } \)

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