A cylindrical piece of cork of base area ‘A’ and height ‘h’ floats in a liquid of density ρe. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a ** of T = 2π√(hρ/ρeg) where ρ is the density of cork. (Ignore damping due to viscosity of the liquid).
Let x be the depression created.
Excess upthrust caused is, Ue= gρeAx
Restoring force = U = gAρe x
mass = m = Ahρ
Now F = mα; α = acceleration
Ahρα = -gAρex
