ANS:D - (radius)⁴

The statement "(radius)^4" likely refers to the concept of hydrostatic pressure in a cylindrical vessel under specific conditions. However, it's important to clarify that the hydrostatic pressure in a cylindrical vessel does not directly follow a 4r4 relationship with the radius. The hydrostatic pressure at a certain depth in a liquid column is given by the formula: P=ρ⋅g⋅h Where:

• P is the pressure at the given depth,
• ρ is the density of the liquid,
• g is the acceleration due to gravity, and
• h is the depth of the liquid.

This formula indicates that the pressure at a certain depth in a liquid column is directly proportional to the density of the liquid, the acceleration due to gravity, and the depth of the liquid. In a cylindrical vessel, if we consider pressure at different depths, the depth itself plays a crucial role in determining the hydrostatic pressure, not the radius. The pressure does not follow a direct 4r4 relationship with the radius of the vessel. The term "(radius)^4" is not typically associated with hydrostatic pressure in cylindrical vessels. It's possible that there might be confusion or a specific context in which this relationship is being discussed. However, in the context of hydrostatic pressure in a cylindrical vessel, the primary factors influencing pressure are depth, density of the liquid, and acceleration due to gravity, as described by the hydrostatic pressure formula mentioned earlier.