If liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid?
I don't think so, because if you can find a derivation for the buoyant force you will see that it depends on the fact that the pressure of a liquid increases with depth.
No, if the liquid pressure were the same at all depths, there would not be a buoyant force on an object submerged in that liquid.
To understand why, let's first clarify the concept of buoyant force. When an object is immersed in a fluid (liquid or gas), it experiences an upward force called the buoyant force. This force is exerted by the fluid and depends on two factors: the density of the fluid and the volume of the submerged part of the object.
In a fluid at rest, the pressure increases with depth. This increase in pressure is due to the weight of the fluid above exerting a force downwards. The pressure at any given depth can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.
Now, if the liquid pressure were the same at all depths, it would mean that the pressure does not increase with depth. This scenario is not realistic for a fluid at rest, as the weight of the fluid above would inevitably cause an increase in pressure with depth.
However, if we imagine a hypothetical situation where the pressure is indeed the same at all depths, it means that the fluid is not influenced by gravity or external forces. In this case, there would be no pressure difference between the top and bottom of the object submerged in the fluid. Consequently, there would be no buoyant force acting on the object.
In reality, when a fluid is subject to gravity, there is a pressure difference with depth, resulting in a buoyant force that pushes an object upwards. This buoyant force counteracts the weight of the object and gives the sensation of reduced weight when submerged in a fluid.