ANS:C - when there is no motion of one fluid layer relative to an adjacent layer.

The statement "The pressure intensity is the same in all directions at a point in a fluid" refers to a condition known as hydrostatic equilibrium, which occurs when the fluid is at rest and there are no shearing forces or accelerations present. Out of the options provided, the correct condition under which the pressure intensity is the same in all directions at a point in a fluid is: when the fluid is at rest having zero velocity. Here's why this is the correct condition:

• Hydrostatic Pressure: When a fluid is at rest and not in motion (zero velocity), the pressure exerted by the fluid at any point is isotropic, meaning it is the same in all directions. This is because in a static fluid, the pressure is solely determined by the weight of the fluid above the point of interest (hydrostatic pressure).
• Frictionless Fluid (Option 1): A fluid being frictionless does not necessarily imply uniform pressure in all directions. Frictionlessness refers to the absence of viscous forces, not to the distribution of pressure.
• No Motion Relative to Adjacent Layers (Option 3): This condition typically refers to laminar flow rather than static fluid conditions. In laminar flow, adjacent layers move at different velocities, affecting pressure distributions differently than in a static fluid.
• Regardless of Motion Relative to Adjacent Layers (Option 4): This statement is ambiguous and doesn't specify a condition related to pressure uniformity at a point in a fluid.