The relationship between the density of a liquid and the buoyant force it exerts on a mass is directly proportional. This means that as the density of the liquid increases, the buoyant force it exerts on a submerged object also increases.

Here's why:

* Buoyant Force: The buoyant force is the upward force exerted by a fluid that opposes the weight of an immersed object. It's equal to the weight of the fluid displaced by the object.

* Density: Density is the mass per unit volume of a substance. A denser liquid has more mass packed into the same volume.

How Density Affects Buoyant Force

1. More Mass Displaced: When a denser liquid is used, the same volume of the liquid will have a greater mass. This means that when an object is submerged, it displaces a greater mass of liquid.

2. Greater Weight of Displaced Liquid: Since the displaced mass is greater, the weight of the displaced liquid will also be greater.

3. Stronger Buoyant Force: The buoyant force is equal to the weight of the displaced liquid, so a greater weight of displaced liquid results in a stronger buoyant force.

Mathematical Representation

The buoyant force (F_b) can be calculated using Archimedes' Principle:

F_b = ρVg

where:

* ρ = density of the fluid

* V = volume of the displaced fluid (equal to the volume of the submerged object)

* g = acceleration due to gravity

In conclusion: A denser liquid will exert a stronger buoyant force on an immersed object due to the greater weight of the displaced liquid.