A cylinder of length L floats with its entire length immersed in two liquids as shown in the fig.

The upper liquid is water and the lower liquid has density twice that of water. The two liquid are immiscible. The cylinder is in equilibrium with its `(3)/(4)` lenght in the denser liquid and `(1)/(4)` of its length in water. The thickness of water layer is `(L)/(4)` only. Find.
(a) the specific gravity of the material of the cylinder.
(b) the time period of oscillations if the cylinder is depressed by some small distance `(lt(L)/(4))` and released. Neglect viscosity and change in level of liquids when the cylinder moves.

Answer

(a) `(7)/(4)`
(b) `pisqrt((7L)/(4g))[1+(1)/sqrt(2)]`