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JEE Main202622 January 2026Morning ShiftPhysicsKinetic Theory of GasesActual

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 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)

Options

  1. AP_ B =P_ A
  2. BP_ B =P_ A (M ² l² / 3 R T )
  3. CP_ B =P_ A (M ² l² / R T )
  4. DP_ B =P_ A (M ² l² / 2 R T )

Correct answer

D. P_ B =P_ A (M ² l² / 2 R T )

Step-by-step solution

A[(P + dP) - P] = (dm)( ^2 x) dP = (dm) A ^2 x dP = ( )(A)(dx) ^2 x A also [PM = RT] = PM RT dP = ( PM RT ) ^2 x , dx _ P_A ^ P_B dP P = ^2 M RT ₀^ x , dx ( P_B P_A ) = ^2 ^2 M 2RT P_B = P_A e^ M ^2 ^2 2RT

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