Adding salt to plain water increases its density, which in turn affects its buoyancy. Buoyancy is the upward force exerted by a fluid (in this case, salt water) on an object submerged in it or floating on its surface. The denser the fluid, the greater the buoyant force it exerts.

When salt is dissolved in water, the water molecules become more tightly packed due to the presence of the dissolved salt ions. This results in an increase in the water's density. As the density of the water increases, the buoyant force it exerts on an object also increases.

Mathematically, the buoyant force (Fb) is determined by the density of the fluid (ρ), the acceleration due to gravity (g), and the volume of the object displaced by the fluid (V):

Fb = ρ * g * V

Since the density of the salt water increases due to the dissolved salt, the buoyant force acting on an object in the salt water also increases compared to plain water. As a result, objects that float in plain water may float higher or with greater stability in salt water due to the increased buoyant force. Conversely, objects that sink in plain water may sink slower or even float in salt water because of the higher buoyant force.

Therefore, adding salt to plain water does indeed change the buoyancy of the water, making it more buoyant and capable of supporting a greater weight of objects before they sink.