Let a body of volume #v# and density #d# be placed in a liquid of density #rho#.The body is insoluble in the liquid.
If #v_i# volume be immersed,then the weight of the displaced liquid or the buoyant force #F_buarr# experienced by the body will be
#F_buarr=v_irhog.......[1]#
By the principle of floatation this upward buoyant force experinced by the body should balance the weight of the body #Wdarr=vdg# to make the body float.
As per equation [1] the magnitude of buoyant force #F_b# depends on #v_i and rho#. With increase of the immersed volume #v_i# (subject to the maximum v,the volume of the body) and also with increase in the value of #rho# the buoyant force #F_buarr# increases.
So overall state of floatation is determined by the value of #F_buarr#
When #wdarr>(F_buarr)_max=vrhog->"the body sinks"#
When #wdarr<=(F_buarr)_max=vrhog->"the body floats"#
During floatation
#wdarr=F_buarr=v_irhog#
In the above figure it has been shown how state of floatation of an egg in water can be controlled by changing the density of water with dissolution of common salt in it in requisite amount.
