Pressure increases with the depth of the liquid column.
Explanation
In fluid statics, the pressure at a point within a liquid at rest is determined by the weight of the liquid column above it. This is known as hydrostatic pressure. The governing relationship is given by the formula \( P = P_{atm} + \rho g h \), where \( \rho \) is the fluid density, \( g \) is the acceleration due to gravity, and \( h \) is the depth below the surface.
Statement-wise Analysis:
- Pressure is maximum at the surface of the liquid. is Incorrect. Pressure is minimum at the free surface of the liquid (equal to atmospheric pressure) and increases as one moves deeper into the liquid.
- Pressure is inversely proportional to the area of the container's base. is Incorrect. Hydrostatic pressure depends only on the depth of the liquid column, the density of the liquid, and gravity. It is independent of the shape or the base area of the container (a phenomenon known as the Hydrostatic Paradox).
- Pressure increases with the depth of the liquid column. is Correct. As indicated by the hydrostatic formula (\( P \propto h \)), pressure increases linearly with the depth of the liquid column because the weight of the overlying fluid increases.
- Pressure acts only in the vertical downward direction. is Incorrect. Pressure is a scalar quantity. At any given point in a static fluid, pressure acts equally in all directions, not just vertically downwards. The force resulting from this pressure acts perpendicular to any surface in contact with the fluid.
Key Takeaway:
Liquid pressure in a static fluid is directly proportional to depth and density (\( P = h\rho g \)) and acts equally in all directions at a specific point, independent of the container's shape or area.