Today's Problem: on buoyancy   


    

A cylindrical piece of wood of cross-sectional area A₀ is floating with its axis vertical in a

liquid of density r₁ in a cylindrical container of base of area A₁. This container is itself   

floating in a liquid of density r₂ in a cylindrical container of base area A₂. This container

again is floating in a liquid of density r₃ in a cylindrical container of base area A₃ and so

forth and so on up to a total of n containers. A vertically downward force is applied to the

piece of wood and its magnitude is increased slowly from 0 to F such that the equilibrium

of the system is not disturbed at any moment. Also, F is such that each of the floating

bodies is still floating in its respective liquid.

(i)         What is the rise in the liquid level in the first container relative to the container?

(ii)        What extra length of the piece of wood goes into the liquid in the process?

(iii)       What is the rise in the liquid level in the i^th container relative to the container?

Click Here for Solution.