Answer Happy

An object with height h, mass M, and a uniform
cross-sectional area A floats upright in a liquid with
density ρ.
a) Calculate the vertical distance from the surface of the
liquid to the bottom of the floating object at equilibrium.
Express your answer in terms of some or all the
variables h, M, ρ, A.
b) A downward force with magnitude F is applied
to the top of the object. At the new equilibrium position, how much
farther below the surface of the liquid is the bottom of the object
than it was in part A? (Assume that some of the object remains
above the surface of the liquid.)
Express your answer in terms of some or all the
variables h, M, ρ, A, F and
acceleration due to gravity g.
c) Your result in part B shows that if the force is
suddenly removed, the object will oscillate up and down in SHM.
Calculate the period of this motion in terms of the
density ρ of the liquid, the mass M, and
cross-sectional area A of the object. Neglect the damping
due to fluid friction.
Express your answer in terms of some or all the
variables h, M, ρ, A and acceleration due
to gravity g.