First of all, let's explain how has the buoyant force is made:
As the pressure in deep parts is bigger than the higher parts, we can say that the forces in deep parts of fluid are bigger than the higher parts of it. so we have the force difference in higher parts and the deep parts of the fluid. so there will be a net force upwards.
$F_2 -F_2$=$\;$ $P_2A-P_1A$=$\;$ $\rho_2gh_2A$-$\rho_1gh_1A$= $\;$ $F_b=Ag(\rho_ {fliud}h_2-\rho_{fliud}h_1)$= $\;$ $F_b=\rho_{fliud}V_{object}g $
we have three kinds of buoyancy:
1-Positive Buoyancy:
Positive buoyancy occurs when an object is lighter than the fluid it displaces. The object will float because the buoyant force is greater than the object’s weight.
$F_b=mg$ $\;$ so $\;$ $\rho_{fliud}V_{object}g $=$\rho_{object}V_{object}g$ $\;$ and $\;$
$\rho_{fliud}V_{objectin}$=$\rho_{object}V_{object}$ $\;$ means that $\;$ $\rho_{fluid}$>$\rho_{object}$
2-Negative Buoyancy:
Negative buoyancy occurs when an object is denser than the fluid it displaces. The object will sink because its weight is greater than the buoyant force.
$F_b<mg$ $\;$ so $\;$ $\rho_{fliud}V_{object}g $=$\rho_{object}V_{object}g$ $\;$ and $\;$
$\rho_{fliud}$<$\rho_{object}$
3-Neutral Buoyancy:
Neutral buoyancy occurs when an object’s weight is equal to the fluid it displaces.
$F_b=mg$ $\;$ so $\;$ $\rho_{fliud}V_{object}g $=$\rho_{object}V_{object}g$ $\;$ and $\;$
$\rho_{fliud}$=$\rho_{object}$
hope this help!
