In an experiment, water flows out from four holes drilled at the same height around a container and falls at equal distances from the base. This…

Correct Option

The correct option is

Liquid pressure is equal at the same depth.

Explanation

The Hydrostatics, specifically the behavior of liquid pressure at a specific depth within a container. It tests the relationship between the depth of a fluid and the pressure exerted by it in different directions.

Detailed Analysis

The experiment involves water flowing out from four holes drilled at the same vertical height (depth) around a container. The observation that the water falls at equal distances from the base leads to the following conclusions:

• Velocity of Efflux: The horizontal range (distance) covered by the water jet is directly proportional to the horizontal velocity with which the water exits the hole. Since the ranges are equal, the velocity of efflux is identical for all holes.
• Pressure and Velocity: According to Torricelli’s Law, the velocity of efflux is determined by the pressure head at that point ($v = \sqrt{2gh}$). Equal velocities imply that the pressure exerting force on the water is equal at all the holes.
• Validation: Since all holes are located at the same depth, this observation validates that liquid pressure is uniform and equal at all points lying on the same horizontal plane.

Analysis of Other Options:

• Liquid pressure increases linearly with depth.: While it is scientifically correct that liquid pressure increases linearly with depth ($P = \rho gh$), this specific experiment does not validate that law because the depth is kept constant. To validate Liquid pressure increases linearly with depth., holes would need to be drilled at different heights.
• Liquid pressure is dependent on the material of the container.: Liquid pressure depends on the density of the fluid and the depth, not on the material of the container.
• Atmospheric pressure is uniform at all points.: Atmospheric pressure acts on the surface, but the equal flow from the holes is a result of the internal liquid pressure distribution, not atmospheric uniformity alone.

Key Takeaway

Pascal’s Principle (Hydrostatics): In a static liquid, pressure is isotropic and remains constant at all points located at the same horizontal depth, provided the fluid is continuous and at rest.