A horizontal cylinder, closed at one end, is rotated with a constant angular velocity $\omega$ about a vertical axis passing through the open end of the cylinder as shown in the figure. The outside air pressure is $P_0$, temperature is $T$ and the molar mass of the air is $\mu$. Assume air to be an ideal gas and the temperature $T$ remaining constant everywhere. The air pressure inside the cylinder is best described by

• A

  $P=P_0\left[1+\log \left(1+\frac{\mu \omega^2 x^2}{2 R T}\right)\right]$
• B

  $P=P_0\left(1+\frac{\mu \omega^2 x^2}{2 R T}\right)$
• C

  $P=P_0\left[1+\exp \left(-\frac{2 R T}{\mu \omega^2 x^2}\right)\right]$
• Correct answer
  D

  $P=P_0 \exp \left(\frac{\mu \omega^2 x^2}{2 R T}\right)$

Hence, the correct answer is option: 'D'.