Question

Question #d1ad2

Answer 1

Let the wooden cylinder be immersed up to height `h` in the oil.
In the equilibrium position for floating

Force of buoyancy `=` Weight of cylinder
Weight of oil displaced `=` Weight of cylinder
`pir^2hg_"oil"=pir^2xx"height of Cylinder"xxg_("wood")`
`=>h="height of Cylinder"xxg_("wood")/g_"oil"`
`=>h=1.2xx0.6/0.85=847mm`

Center of gravity lies at a height of `1200/2=600mm` from the bottom of cylinder

As center of buoyancy is the center of gravity of the oil displaced.
`=>` Center of buoyancy lies at a height of `847/2=423.5mm` from the bottom of cylinder

We know that location of the center of gravity of the body below the center of buoyancy leads to stable equilibrium.

In the given problem, center of gravity of cylinder lies above the center of buoyancy. Therefore, this leads to unstable equilibrium.