When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure intensity varies A. linearly with radial distance B. as the square of the radial distance C. inversely as the square of the radial distance D. inversely as the radial distance

linearly with radial distance
as the square of the radial distance
inversely as the square of the radial distance
inversely as the radial distance

The correct answer is: C. inversely as the square of the radial distance.

The pressure intensity at a point in a rotating fluid is given by the following equation:

$$P = P_0 + \rho \omega^2 r^2$$

where $P_0$ is the pressure at the center of the fluid, $\rho$ is the density of the fluid, $\omega$ is the angular velocity of the fluid, and $r$ is the radial distance from the center of the fluid.

As you can see from the equation, the pressure intensity increases with the square of the radial distance. This is because the centrifugal force acting on a particle in a rotating fluid increases with the square of the radial distance. The centrifugal force pushes the particle away from the center of the fluid, which increases the pressure at that point.

The other options are incorrect because they do not take into account the centrifugal force. Option A states that the pressure intensity varies linearly with radial distance. This is not correct because the pressure intensity increases more rapidly with radial distance than linearly. Option B states that the pressure intensity varies as the square of the radial distance. This is correct, but it is not the only factor that affects the pressure intensity. Option D states that the pressure intensity varies inversely as the radial distance. This is not correct because the pressure intensity increases with radial distance.