State the law of floatation and describe its cases.

(N/A) The law of floatation states that a body floats on the surface of a liquid if the weight of the body is equal to the weight of the liquid displaced by the submerged part of the body.
When a body is partially or completely immersed in a liquid,it experiences two forces:
$(1)$ Weight of the body $(W)$: $W = V_s \rho_s g$ (acting downwards),where $V_s$ is the volume of the body and $\rho_s$ is the density of the body.
$(2)$ Buoyant force $(F_b)$: $F_b = V_f \rho_f g$ (acting upwards),where $V_f$ is the volume of the displaced liquid and $\rho_f$ is the density of the liquid.
Cases:
$(a)$ If $W > F_b$: The body sinks in the liquid (e.g.,an iron nail).
$(b)$ If $W = F_b$: The body remains in equilibrium at any depth (e.g.,a submarine).
$(c)$ If $W < F_b$: The body floats on the surface of the liquid (e.g.,a wooden block).