A cylindrical tube AB of length l, closed at both ends contains an… | JEE Main 2026 (22 Jan, Shift 1)

Q12JEE Main 2026 · 22 JAN · SHIFT 1Difficult

Rotational Kinematics & Dynamics

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 perpendicular 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)

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Answer: (c)

Pressure gradient gives centripetal force: $\dfrac{dP}{dx} = \rho\omega^2 x$ , with $\rho = \dfrac{PM}{RT}$ .
$\int_{P_A}^{P_B}\dfrac{dP}{P} = \dfrac{M\omega^2}{RT}\int_0^l x\,dx \Rightarrow \ln\dfrac{P_B}{P_A} = \dfrac{M\omega^2 l^2}{2RT}$
$P_B = P_A e^{M\omega^2 l^2/2RT}$ , so the answer is (c).

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